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<!DOCTYPE html> <html lang="en" class="no-js"> <head> <meta charset="UTF-8"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <meta name="applicable-device" content="pc,mobile"> <meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="robots" content="max-image-preview:large"> <meta name="access" content="Yes"> <meta name="360-site-verification" content="1268d79b5e96aecf3ff2a7dac04ad990" /> <title>Thermal WIMPs and the scale of new physics: global fits of Dirac dark matter effective field theories | The European Physical Journal C</title> <meta name="twitter:site" content="@SpringerLink"/> <meta name="twitter:card" content="summary_large_image"/> <meta name="twitter:image:alt" content="Content cover image"/> <meta name="twitter:title" content="Thermal WIMPs and the scale of new physics: global fits of Dirac dark matter effective field theories"/> <meta name="twitter:description" content="The European Physical Journal C - We assess the status of a wide class of WIMP dark matter (DM) models in light of the latest experimental results using the global fitting framework GAMBIT. We..."/> <meta name="twitter:image" content="https://static-content.springer.com/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig1_HTML.png"/> <meta name="journal_id" content="10052"/> <meta name="dc.title" content="Thermal WIMPs and the scale of new physics: global fits of Dirac dark matter effective field theories"/> <meta name="dc.source" content="The European Physical Journal C 2021 81:11"/> <meta name="dc.format" content="text/html"/> <meta name="dc.publisher" content="Springer"/> <meta name="dc.date" content="2021-11-11"/> <meta name="dc.type" content="OriginalPaper"/> <meta name="dc.language" content="En"/> <meta name="dc.copyright" content="2021 The Author(s)"/> <meta name="dc.rights" content="2021 The Author(s)"/> <meta name="dc.rightsAgent" content="journalpermissions@springernature.com"/> <meta name="dc.description" content="We assess the status of a wide class of WIMP dark matter (DM) models in light of the latest experimental results using the global fitting framework GAMBIT. We perform a global analysis of effective field theory (EFT) operators describing the interactions between a gauge-singlet Dirac fermion and the Standard Model quarks, the gluons and the photon. In this bottom-up approach, we simultaneously vary the coefficients of 14 such operators up to dimension 7, along with the DM mass, the scale of new physics and several nuisance parameters. Our likelihood functions include the latest data from Planck, direct and indirect detection experiments, and the LHC. For DM masses below 100&nbsp;GeV, we find that it is impossible to satisfy all constraints simultaneously while maintaining EFT validity at LHC energies. For new physics scales around 1&nbsp;TeV, our results are influenced by several small excesses in the LHC data and depend on the prescription that we adopt to ensure EFT validity. Furthermore, we find large regions of viable parameter space where the EFT is valid and the relic density can be reproduced, implying that WIMPs can still account for the DM of the universe while being consistent with the latest data."/> <meta name="prism.issn" content="1434-6052"/> <meta name="prism.publicationName" content="The European Physical Journal C"/> <meta name="prism.publicationDate" content="2021-11-11"/> <meta name="prism.volume" content="81"/> <meta name="prism.number" content="11"/> <meta name="prism.section" content="OriginalPaper"/> <meta name="prism.startingPage" content="1"/> <meta name="prism.endingPage" content="33"/> <meta name="prism.copyright" content="2021 The Author(s)"/> <meta name="prism.rightsAgent" content="journalpermissions@springernature.com"/> <meta name="prism.url" content="https://link.springer.com/article/10.1140/epjc/s10052-021-09712-6"/> <meta name="prism.doi" content="doi:10.1140/epjc/s10052-021-09712-6"/> <meta name="citation_pdf_url" content="https://link.springer.com/content/pdf/10.1140/epjc/s10052-021-09712-6.pdf"/> <meta name="citation_fulltext_html_url" content="https://link.springer.com/article/10.1140/epjc/s10052-021-09712-6"/> <meta name="citation_journal_title" content="The European Physical Journal C"/> <meta name="citation_journal_abbrev" content="Eur. Phys. J. C"/> <meta name="citation_publisher" content="Springer Berlin Heidelberg"/> <meta name="citation_issn" content="1434-6052"/> <meta name="citation_title" content="Thermal WIMPs and the scale of new physics: global fits of Dirac dark matter effective field theories"/> <meta name="citation_volume" content="81"/> <meta name="citation_issue" content="11"/> <meta name="citation_publication_date" content="2021/11"/> <meta name="citation_online_date" content="2021/11/11"/> <meta name="citation_firstpage" content="1"/> <meta name="citation_lastpage" content="33"/> <meta name="citation_article_type" content="Regular Article - Theoretical Physics "/> <meta name="citation_fulltext_world_readable" content=""/> <meta name="citation_language" content="en"/> <meta name="dc.identifier" content="doi:10.1140/epjc/s10052-021-09712-6"/> <meta name="DOI" content="10.1140/epjc/s10052-021-09712-6"/> <meta name="size" content="1121158"/> <meta name="citation_doi" content="10.1140/epjc/s10052-021-09712-6"/> <meta name="citation_springer_api_url" content="http://api.springer.com/xmldata/jats?q=doi:10.1140/epjc/s10052-021-09712-6&api_key="/> <meta name="description" content="We assess the status of a wide class of WIMP dark matter (DM) models in light of the latest experimental results using the global fitting framework GAMBIT."/> <meta name="dc.creator" content="Athron, Peter"/> <meta name="dc.creator" content="Kozar, Neal Avis"/> <meta name="dc.creator" content="Balázs, Csaba"/> <meta name="dc.creator" content="Beniwal, Ankit"/> <meta name="dc.creator" content="Bloor, Sanjay"/> <meta name="dc.creator" content="Bringmann, Torsten"/> <meta name="dc.creator" content="Brod, Joachim"/> <meta name="dc.creator" content="Chang, Christopher"/> <meta name="dc.creator" content="Cornell, Jonathan M."/> <meta name="dc.creator" content="Farmer, Ben"/> <meta name="dc.creator" content="Fowlie, Andrew"/> <meta name="dc.creator" content="Gonzalo, Tomás E."/> <meta name="dc.creator" content="Handley, Will"/> <meta name="dc.creator" content="Kahlhoefer, Felix"/> <meta name="dc.creator" content="Kvellestad, Anders"/> <meta name="dc.creator" content="Mahmoudi, Farvah"/> <meta name="dc.creator" content="Prim, Markus T."/> <meta name="dc.creator" content="Raklev, Are"/> <meta name="dc.creator" content="Renk, Janina J."/> <meta name="dc.creator" content="Scaffidi, Andre"/> <meta name="dc.creator" content="Scott, Pat"/> <meta name="dc.creator" content="Stöcker, Patrick"/> <meta name="dc.creator" content="Vincent, Aaron C."/> <meta name="dc.creator" content="White, Martin"/> <meta name="dc.creator" content="Wild, Sebastian"/> <meta name="dc.creator" content="Zupan, Jure"/> <meta name="dc.subject" content="Elementary Particles, Quantum Field Theory"/> <meta name="dc.subject" content="Nuclear Physics, Heavy Ions, Hadrons"/> <meta name="dc.subject" content="Quantum Field Theories, String Theory"/> <meta name="dc.subject" content="Measurement Science and Instrumentation"/> <meta name="dc.subject" content="Astronomy, Astrophysics and Cosmology"/> <meta name="dc.subject" content="Nuclear Energy"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=Cosmological lower bound on heavy neutrino masses; citation_author=BW Lee, S Weinberg; citation_volume=39; citation_publication_date=1977; citation_pages=165-168; citation_doi=10.1103/PhysRevLett.39.165; citation_id=CR1"/> <meta name="citation_reference" content="citation_journal_title=Eur. Phys. J. C; citation_title=The waning of the WIMP? A review of models, searches, and constraints; citation_author=G Arcadi, M Dutra; citation_volume=78; citation_publication_date=2018; citation_pages=203; citation_doi=10.1140/epjc/s10052-018-5662-y; citation_id=CR2"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=GeV-scale thermal WIMPs: not even slightly ruled out; citation_author=RK Leane, TR Slatyer, JF Beacom, KCY Ng; citation_volume=98; citation_publication_date=2018; citation_pages=023016; citation_doi=10.1103/PhysRevD.98.023016; citation_id=CR3"/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=Non-relativistic effective theory of dark matter direct detection; citation_author=J Fan, M Reece, L-T Wang; citation_volume=1011; citation_publication_date=2010; citation_pages=042; citation_doi=10.1088/1475-7516/2010/11/042; citation_id=CR4"/> <meta name="citation_reference" content="P. Agrawal, Z. Chacko, C. Kilic, R.K. Mishra, A classification of dark matter candidates with primarily spin-dependent interactions with matter. arXiv:1003.1912 "/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Dark moments and the DAMA-CoGeNT puzzle; citation_author=A Fitzpatrick, KM Zurek; citation_volume=82; citation_publication_date=2010; citation_pages=075004; citation_doi=10.1103/PhysRevD.82.075004; citation_id=CR6"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Dark matter direct detection constraints from gauge bosons loops; citation_author=A Crivellin, U Haisch; citation_volume=90; citation_publication_date=2014; citation_pages=115011; citation_doi=10.1103/PhysRevD.90.115011; citation_id=CR7"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=You can hide but you have to run: direct detection with vector mediators; citation_author=F D’Eramo, BJ Kavanagh, P Panci; citation_volume=08; citation_publication_date=2016; citation_pages=111; citation_doi=10.1007/JHEP08(2016)111; citation_id=CR8"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Analysis strategies for general spin-independent WIMP-nucleus scattering; citation_author=M Hoferichter, P Klos, J Menéndez, A Schwenk; citation_volume=94; citation_publication_date=2016; citation_pages=063505; citation_doi=10.1103/PhysRevD.94.063505; citation_id=CR9"/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=Studying generalised dark matter interactions with extended halo-independent methods; citation_author=F Kahlhoefer, S Wild; citation_volume=10; citation_publication_date=2016; citation_pages=032; citation_doi=10.1088/1475-7516/2016/10/032; citation_id=CR10"/> <meta name="citation_reference" content="citation_journal_title=Nucl. Phys. B; citation_title=Gamma ray line constraints on effective theories of dark matter; citation_author=J Goodman, M Ibe; citation_volume=844; citation_publication_date=2011; citation_pages=55-68; citation_doi=10.1016/j.nuclphysb.2010.10.022; citation_id=CR11"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Deducing the nature of dark matter from direct and indirect detection experiments in the absence of collider signatures of new physics; citation_author=M Beltran, D Hooper, EW Kolb, ZC Krusberg; citation_volume=80; citation_publication_date=2009; citation_pages=043509 043509; citation_doi=10.1103/PhysRevD.80.043509; citation_id=CR12"/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=Gamma-ray constraints on effective interactions of the dark matter; citation_author=K Cheung, P-Y Tseng, T-C Yuan; citation_volume=06; citation_publication_date=2011; citation_pages=023; citation_doi=10.1088/1475-7516/2011/06/023; citation_id=CR13"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=An effective theory of Dirac dark matter; citation_author=R Harnik, GD Kribs; citation_volume=79; citation_publication_date=2009; citation_pages=095007; citation_doi=10.1103/PhysRevD.79.095007; citation_id=CR14"/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=On the effective operators for Dark Matter annihilations; citation_author=A Simone, A Monin, A Thamm, A Urbano; citation_volume=02; citation_publication_date=2013; citation_pages=039; citation_doi=10.1088/1475-7516/2013/02/039; citation_id=CR15"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Dark matter interpretation of the Fermi-LAT observation toward the Galactic Center; citation_author=C Karwin, S Murgia, TMP Tait, TA Porter, P Tanedo; citation_volume=95; citation_publication_date=2017; citation_pages=103005; citation_doi=10.1103/PhysRevD.95.103005; citation_id=CR16"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Indirect detection constraints on s and t channel simplified models of dark matter; citation_author=LM Carpenter, R Colburn, J Goodman, T Linden; citation_volume=94; citation_publication_date=2016; citation_pages=055027; citation_doi=10.1103/PhysRevD.94.055027; citation_id=CR17"/> <meta name="citation_reference" content="citation_journal_title=Phys. Dark Universe; citation_title=Simplified models for dark matter searches at the LHC; citation_author=J Abdallah; citation_volume=9–10; citation_publication_date=2015; citation_pages=8-23; citation_doi=10.1016/j.dark.2015.08.001; citation_id=CR18"/> <meta name="citation_reference" content="citation_journal_title=Int. J. Mod. Phys. A; citation_title=Review of LHC dark matter searches; citation_author=F Kahlhoefer; citation_volume=32; citation_publication_date=2017; citation_pages=1730006; citation_doi=10.1142/S0217751X1730006X; citation_id=CR19"/> <meta name="citation_reference" content="citation_journal_title=Eur. Phys. J. C; citation_title=Extended dark matter EFT; citation_author=T Alanne, F Goertz; citation_volume=80; citation_publication_date=2020; citation_pages=446; citation_doi=10.1140/epjc/s10052-020-7999-2; citation_id=CR20"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Model-independent constraints with extended dark matter EFT; citation_author=T Alanne, G Arcadi, F Goertz, V Tenorth, S Vogl; citation_volume=10; citation_publication_date=2020; citation_pages=172; citation_doi=10.1007/JHEP10(2020)172; citation_id=CR21"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=The Tevatron at the frontier of dark matter direct detection; citation_author=Y Bai, PJ Fox, R Harnik; citation_volume=12; citation_publication_date=2010; citation_pages=048; citation_doi=10.1007/JHEP12(2010)048; citation_id=CR22"/> <meta name="citation_reference" content="citation_journal_title=EPL; citation_title=Contact interactions probe effective dark matter models at the LHC; citation_author=H Dreiner, D Schmeier, J Tattersall; citation_volume=102; citation_publication_date=2013; citation_pages=51001; citation_doi=10.1209/0295-5075/102/51001; citation_id=CR23"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Mono-everything: combined limits on dark matter production at colliders from multiple final states; citation_author=N Zhou, D Berge, D Whiteson; citation_volume=87; citation_publication_date=2013; citation_pages=095013; citation_doi=10.1103/PhysRevD.87.095013; citation_id=CR24"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Taking a razor to dark matter parameter space at the LHC; citation_author=PJ Fox, R Harnik, R Primulando, C-T Yu; citation_volume=86; citation_publication_date=2012; citation_pages=015010; citation_doi=10.1103/PhysRevD.86.015010; citation_id=CR25"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=LHC bounds on interactions of dark matter; citation_author=A Rajaraman, W Shepherd, TM Tait, AM Wijangco; citation_volume=84; citation_publication_date=2011; citation_pages=095013; citation_doi=10.1103/PhysRevD.84.095013; citation_id=CR26"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Constraints on dark matter from colliders; citation_author=J Goodman, M Ibe; citation_volume=82; citation_publication_date=2010; citation_pages=116010; citation_doi=10.1103/PhysRevD.82.116010; citation_id=CR27"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Missing energy signatures of dark matter at the LHC; citation_author=PJ Fox, R Harnik, J Kopp, Y Tsai; citation_volume=85; citation_publication_date=2012; citation_pages=056011; citation_doi=10.1103/PhysRevD.85.056011; citation_id=CR28"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Maverick dark matter at colliders; citation_author=M Beltran, D Hooper, EW Kolb, ZA Krusberg, TM Tait; citation_volume=09; citation_publication_date=2010; citation_pages=037; citation_doi=10.1007/JHEP09(2010)037; citation_id=CR29"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Beyond effective field theory for dark matter searches at the LHC; citation_author=O Buchmueller, MJ Dolan, C McCabe; citation_volume=01; citation_publication_date=2014; citation_pages=025; citation_doi=10.1007/JHEP01(2014)025; citation_id=CR30"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Dark matter characterization at the LHC in the effective field theory approach; citation_author=A Belyaev, L Panizzi, A Pukhov, M Thomas; citation_volume=04; citation_publication_date=2017; citation_pages=110; citation_doi=10.1007/JHEP04(2017)110; citation_id=CR31"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Setting limits on effective field theories: the case of dark matter; citation_author=F Pobbe, A Wulzer, M Zanetti; citation_volume=08; citation_publication_date=2017; citation_pages=074; citation_doi=10.1007/JHEP08(2017)074; citation_id=CR32"/> <meta name="citation_reference" content="ATLAS: G. Aad et al., Search for dark matter candidates and large extra dimensions in events with a jet and missing transverse momentum with the ATLAS detector. JHEP 04, 075 (2013). arXiv:1210.4491 "/> <meta name="citation_reference" content="CMS: S. Chatrchyan et al., Search for dark matter and large extra dimensions in monojet events in $$pp$$ collisions at $$\sqrt{s}=7$$  TeV. JHEP 09, 094 (2012). arXiv:1206.5663 "/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Asymmetric dark matter and effective operators; citation_author=MR Buckley; citation_volume=84; citation_publication_date=2011; citation_pages=043510; citation_doi=10.1103/PhysRevD.84.043510; citation_id=CR35"/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=Global constraints on effective dark matter interactions: relic density, direct detection, indirect detection, and collider; citation_author=K Cheung, P-Y Tseng, Y-LS Tsai, T-C Yuan; citation_volume=1205; citation_publication_date=2012; citation_pages=001; citation_id=CR36"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Closing in on asymmetric dark matter I: model independent limits for interactions with quarks; citation_author=J March-Russell, J Unwin, SM West; citation_volume=08; citation_publication_date=2012; citation_pages=029; citation_doi=10.1007/JHEP08(2012)029; citation_id=CR37"/> <meta name="citation_reference" content="citation_journal_title=Nucl. Phys. B; citation_title=Constraining the interaction strength between dark matter and visible matter: I.Fermionic dark matter; citation_author=J-M Zheng, Z-H Yu; citation_volume=854; citation_publication_date=2012; citation_pages=350-374; citation_doi=10.1016/j.nuclphysb.2011.09.009; citation_id=CR38"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Interplay of the LHC and non-LHC dark matter searches in the effective field theory approach; citation_author=A Belyaev, E Bertuzzo; citation_volume=99; citation_publication_date=2019; citation_pages=015006; citation_doi=10.1103/PhysRevD.99.015006; citation_id=CR39"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=MeV dark matter: model independent bounds; citation_author=E Bertuzzo, CJ Caniu Barros, G Grilli di Cortona; citation_volume=09; citation_publication_date=2017; citation_pages=116; citation_doi=10.1007/JHEP09(2017)116; citation_id=CR40"/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=Tools for model-independent bounds in direct dark matter searches; citation_author=M Cirelli, E Nobile, P Panci; citation_volume=10; citation_publication_date=2013; citation_pages=019; citation_doi=10.1088/1475-7516/2013/10/019; citation_id=CR41"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Matrix element analyses of dark matter scattering and annihilation; citation_author=J Kumar, D Marfatia; citation_volume=88; citation_publication_date=2013; citation_pages=014035; citation_doi=10.1103/PhysRevD.88.014035; citation_id=CR42"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Thermal dark matter implies new physics not far above the weak scale; citation_author=C Balázs, T Li, JL Newstead; citation_volume=08; citation_publication_date=2014; citation_pages=061; citation_doi=10.1007/JHEP08(2014)061; citation_id=CR43"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Effective field theory of dark matter: a global analysis; citation_author=S Liem, G Bertone; citation_volume=9; citation_publication_date=2016; citation_pages=77; citation_doi=10.1007/JHEP09(2016)077; citation_id=CR44"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Singlet Majorana fermion dark matter: a comprehensive analysis in effective field theory; citation_author=S Matsumoto, S Mukhopadhyay, Y-LS Tsai; citation_volume=10; citation_publication_date=2014; citation_pages=155; citation_doi=10.1007/JHEP10(2014)155; citation_id=CR45"/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=Global constraints on vector-like WIMP effective interactions; citation_author=M Blennow, P Coloma, E Fernandez-Martinez, PAN Machado, B Zaldivar; citation_volume=04; citation_publication_date=2016; citation_pages=015; citation_doi=10.1088/1475-7516/2016/04/015; citation_id=CR46"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Effective theory of WIMP dark matter supplemented by simplified models: singlet-like Majorana fermion case; citation_author=S Matsumoto, S Mukhopadhyay, Y-LS Tsai; citation_volume=94; citation_publication_date=2016; citation_pages=065034; citation_doi=10.1103/PhysRevD.94.065034; citation_id=CR47"/> <meta name="citation_reference" content="GAMBIT Collaboration: P. Athron, C. Balázs et al., GAMBIT: the global and modular beyond-the-standard-model inference tool. Eur. Phys. J. C 77, 784 (2017). arXiv:1705.07908 . Addendum in [190]"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Theory for baryon number and dark matter at the LHC; citation_author=M Duerr, P Fileviez Perez; citation_volume=91; citation_publication_date=2015; citation_pages=095001; citation_doi=10.1103/PhysRevD.91.095001; citation_id=CR49"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Extra U(1), effective operators, anomalies and dark matter; citation_author=E Dudas, L Heurtier, Y Mambrini, B Zaldivar; citation_volume=11; citation_publication_date=2013; citation_pages=083; citation_doi=10.1007/JHEP11(2013)083; citation_id=CR50"/> <meta name="citation_reference" content="citation_journal_title=SciPost Phys.; citation_title=Dark matter in anomaly-free gauge extensions; citation_author=M Bauer, S Diefenbacher, T Plehn, M Russell, DA Camargo; citation_volume=5; citation_publication_date=2018; citation_pages=036; citation_doi=10.21468/SciPostPhys.5.4.036; citation_id=CR51"/> <meta name="citation_reference" content="GAMBIT Dark Matter Workgroup: T. Bringmann, J. Conrad et al., DarkBit: a GAMBIT module for computing dark matter observables and likelihoods. Eur. Phys. J. C 77, 831 (2017). arXiv:1705.07920 "/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=The effective field theory of dark matter direct detection; citation_author=AL Fitzpatrick, W Haxton, E Katz, N Lubbers, Y Xu; citation_volume=1302; citation_publication_date=2013; citation_pages=004; citation_doi=10.1088/1475-7516/2013/02/004; citation_id=CR53"/> <meta name="citation_reference" content="GAMBIT Cosmology Workgroup: J.J. Renk, P. Stöcker et al., CosmoBit: a GAMBIT module for computing cosmological observables and likelihoods. JCAP 02, 022 (2021). arXiv:2009.03286 "/> <meta name="citation_reference" content="T.E. Gonzalo, GAMBIT: the global and modular BSM inference tool, in Tools for High Energy Physics and Cosmology (2021). arXiv:2105.03165 "/> <meta name="citation_reference" content="S. Bloor, T.E. Gonzalo et al., The GAMBIT universal model machine: from Lagrangians to likelihoods. arXiv:2107.00030 "/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Unitarity and monojet bounds on models for DAMA, CoGeNT, and CRESST-II; citation_author=IM Shoemaker, L Vecchi; citation_volume=86; citation_publication_date=2012; citation_pages=015023; citation_doi=10.1103/PhysRevD.86.015023; citation_id=CR57"/> <meta name="citation_reference" content="citation_journal_title=Phys. Lett. B; citation_title=On the validity of the effective field theory for dark matter searches at the LHC; citation_author=G Busoni, A Simone, E Morgante, A Riotto; citation_volume=728; citation_publication_date=2014; citation_pages=412-421; citation_doi=10.1016/j.physletb.2013.11.069; citation_id=CR58"/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=On the validity of the effective field theory for dark matter searches at the LHC, part II: complete analysis for the -channel; citation_author=G Busoni, A Simone, J Gramling, E Morgante, A Riotto; citation_volume=06; citation_publication_date=2014; citation_pages=060; citation_doi=10.1088/1475-7516/2014/06/060; citation_id=CR59"/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=On the validity of the effective field theory for dark matter searches at the LHC part III: analysis for the -channel; citation_author=G Busoni, A Simone, T Jacques, E Morgante, A Riotto; citation_volume=09; citation_publication_date=2014; citation_pages=022; citation_doi=10.1088/1475-7516/2014/09/022; citation_id=CR60"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Unitarity bounds on dark matter effective interactions at LHC; citation_author=M Endo, Y Yamamoto; citation_volume=06; citation_publication_date=2014; citation_pages=126; citation_doi=10.1007/JHEP06(2014)126; citation_id=CR61"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Unitarisation of EFT amplitudes for dark matter searches at the LHC; citation_author=N Bell, G Busoni, A Kobakhidze, DM Long, MA Schmidt; citation_volume=08; citation_publication_date=2016; citation_pages=125; citation_doi=10.1007/JHEP08(2016)125; citation_id=CR62"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Robust collider limits on heavy-mediator Dark Matter; citation_author=D Racco, A Wulzer, F Zwirner; citation_volume=05; citation_publication_date=2015; citation_pages=009; citation_doi=10.1007/JHEP05(2015)009; citation_id=CR63"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=The last gasp of dark matter effective theory; citation_author=S Bruggisser, F Riva, A Urbano; citation_volume=11; citation_publication_date=2016; citation_pages=069; citation_doi=10.1007/JHEP11(2016)069; citation_id=CR64"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=Unitarity limits on the mass and radius of dark matter particles; citation_author=K Griest, M Kamionkowski; citation_volume=64; citation_publication_date=1990; citation_pages=615; citation_doi=10.1103/PhysRevLett.64.615; citation_id=CR65"/> <meta name="citation_reference" content="GAMBIT Collaboration, Supplementary data: thermal WIMPs and the scale of new physics: global fits of dirac dark matter effective field theories (2021). https://zenodo.org/record/4836397 "/> <meta name="citation_reference" content="F. Bishara, J. Brod, B. Grinstein, J. Zupan, DirectDM: a tool for dark matter direct detection. arXiv:1708.02678 "/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Effective field theory for dark matter direct detection up to dimension seven; citation_author=J Brod, A Gootjes-Dreesbach, M Tammaro, J Zupan; citation_volume=10; citation_publication_date=2018; citation_pages=065; citation_doi=10.1007/JHEP10(2018)065; citation_id=CR68"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=DAMA/LIBRA and leptonically interacting Dark Matter; citation_author=J Kopp, V Niro, T Schwetz, J Zupan; citation_volume=80; citation_publication_date=2009; citation_pages=083502; citation_doi=10.1103/PhysRevD.80.083502; citation_id=CR69"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=LEP shines light on dark matter; citation_author=PJ Fox, R Harnik, J Kopp, Y Tsai; citation_volume=84; citation_publication_date=2011; citation_pages=014028; citation_doi=10.1103/PhysRevD.84.014028; citation_id=CR70"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=UV completions of magnetic inelastic and Rayleigh dark matter for the Fermi line(s); citation_author=N Weiner, I Yavin; citation_volume=87; citation_publication_date=2013; citation_pages=023523; citation_doi=10.1103/PhysRevD.87.023523; citation_id=CR71"/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=Loop-induced dark matter direct detection signals from gamma-ray lines; citation_author=MT Frandsen, U Haisch, F Kahlhoefer, P Mertsch, K Schmidt-Hoberg; citation_volume=10; citation_publication_date=2012; citation_pages=033; citation_doi=10.1088/1475-7516/2012/10/033; citation_id=CR72"/> <meta name="citation_reference" content="G. Paz, A.A. Petrov, M. Tammaro, J. Zupan, Shining dark matter in Xenon1T. Phys. Rev. D 103, L051703 (2021). https://doi.org/10.1103/PhysRevD.103.L051703 . arXiv:2006.12462 "/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Faint light from dark matter: classifying and constraining dark matter-photon effective operators; citation_author=BJ Kavanagh, P Panci, R Ziegler; citation_volume=04; citation_publication_date=2019; citation_pages=089; citation_doi=10.1007/JHEP04(2019)089; citation_id=CR74"/> <meta name="citation_reference" content="citation_journal_title=Eur. Phys. J. C; citation_title=Light and darkness: consistently coupling dark matter to photons via effective operators; citation_author=C Arina, A Cheek, K Mimasu, L Pagani; citation_volume=81; citation_publication_date=2021; citation_pages=223; citation_doi=10.1140/epjc/s10052-021-09010-1; citation_id=CR75"/> <meta name="citation_reference" content="citation_journal_title=Phys. Lett. B; citation_title=On mono-W signatures in spin-1 simplified models; citation_author=U Haisch, F Kahlhoefer, TMP Tait; citation_volume=760; citation_publication_date=2016; citation_pages=207-213; citation_doi=10.1016/j.physletb.2016.06.063; citation_id=CR76"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Standard model anatomy of WIMP dark matter direct detection II: QCD analysis and hadronic matrix elements; citation_author=RJ Hill, MP Solon; citation_volume=91; citation_publication_date=2015; citation_pages=043505; citation_doi=10.1103/PhysRevD.91.043505; citation_id=CR77"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Renormalization group effects in dark matter interactions; citation_author=F Bishara, J Brod, B Grinstein, J Zupan; citation_volume=03; citation_publication_date=2020; citation_pages=089; citation_doi=10.1007/JHEP03(2020)089; citation_id=CR78"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Weak mixing below the weak scale in dark-matter direct detection; citation_author=J Brod, B Grinstein, E Stamou, J Zupan; citation_volume=02; citation_publication_date=2018; citation_pages=174; citation_doi=10.1007/JHEP02(2018)174; citation_id=CR79"/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=On the importance of loop-induced spin-independent interactions for dark matter direct detection; citation_author=U Haisch, F Kahlhoefer; citation_volume=1304; citation_publication_date=2013; citation_pages=050; citation_doi=10.1088/1475-7516/2013/04/050; citation_id=CR80"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=New constraints on dark matter effective theories from standard model loops; citation_author=A Crivellin, F D’Eramo, M Procura; citation_volume=112; citation_publication_date=2014; citation_pages=191304; citation_doi=10.1103/PhysRevLett.112.191304; citation_id=CR81"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=The impact of heavy-quark loops on LHC dark matter searches; citation_author=U Haisch, F Kahlhoefer, J Unwin; citation_volume=07; citation_publication_date=2013; citation_pages=125; citation_doi=10.1007/JHEP07(2013)125; citation_id=CR82"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Mono-Higgs detection of dark matter at the LHC; citation_author=A Berlin, T Lin, L-T Wang; citation_volume=06; citation_publication_date=2014; citation_pages=078; citation_doi=10.1007/JHEP06(2014)078; citation_id=CR83"/> <meta name="citation_reference" content="SuperCDMS: R. Agnese et al., New results from the search for low-mass weakly interacting massive particles with the CDMS low ionization threshold experiment. Phys. Rev. Lett. 116, 071301 (2016). arXiv:1509.02448 "/> <meta name="citation_reference" content="CRESST: G. Angloher et al., Results on light dark matter particles with a low-threshold CRESST-II detector. Eur. Phys. J. C 76, 25 (2016). arXiv:1509.01515 "/> <meta name="citation_reference" content="CRESST: A.H. Abdelhameed et al., First results from the CRESST-III low-mass dark matter program. Phys. Rev. D 100, 102002 (2019). arXiv:1904.00498 "/> <meta name="citation_reference" content="P. Agnes et al., DarkSide-50 532-day dark matter search with low-radioactivity argon. Phys. Rev. D 98, 102006 (2018). https://doi.org/10.1103/PhysRevD.98.102006 . arXiv:1802.07198 "/> <meta name="citation_reference" content="LUX: D.S. Akerib et al., Results from a search for dark matter in the complete LUX exposure. Phys. Rev. Lett. 118, 021303 (2017). arXiv:1608.07648 "/> <meta name="citation_reference" content="PICO: C. Amole et al., Dark matter search results from the PICO-60 C $$_3$$ F $$_8$$ bubble chamber. Phys. Rev. Lett. 118, 251301 (2017). arXiv:1702.07666 "/> <meta name="citation_reference" content="PICO: C. Amole et al., Dark matter search results from the complete exposure of the PICO-60 C $$_3$$ F $$_8$$ bubble chamber. Phys. Rev. D 100, 022001 (2019). arXiv:1902.04031 "/> <meta name="citation_reference" content="PandaX-II: A. Tan et al., Dark matter results from first 98.7 days of data from the PandaX-II experiment. Phys. Rev. Lett. 117, 121303 (2016). arXiv:1607.07400 "/> <meta name="citation_reference" content="PandaX-II: X. Cui et al., Dark matter results from 54-ton-day exposure of PandaX-II experiment. Phys. Rev. Lett. 119, 181302 (2017). arXiv:1708.06917 "/> <meta name="citation_reference" content="XENON: E. Aprile et al., Dark matter search results from a one ton-year exposure of XENON1T. Phys. Rev. Lett. 121, 111302 (2018). arXiv:1805.12562 "/> <meta name="citation_reference" content="ATLAS: G. Aad et al., Search for new phenomena in events with an energetic jet and missing transverse momentum in $$pp$$ collisions at $$\sqrt{s} = 13$$  TeV with the ATLAS detector. arXiv:2102.10874 "/> <meta name="citation_reference" content="CMS: A.M. Sirunyan et al., Search for new physics in final states with an energetic jet or a hadronically decaying $$W$$ or $$Z$$ boson and transverse momentum imbalance at $$\sqrt{s}=13\,\text{TeV}$$ . Phys. Rev. D 97, 092005 (2018). arXiv:1712.02345 "/> <meta name="citation_reference" content="Fermi-LAT: M. Ackermann et al., Searching for dark matter annihilation from Milky Way dwarf spheroidal galaxies with six years of Fermi large area telescope data. Phys. Rev. Lett. 115, 231301 (2015). arXiv:1503.02641 "/> <meta name="citation_reference" content="IceCube Collaboration: M.G. Aartsen et al., Improved limits on dark matter annihilation in the Sun with the 79-string IceCube detector and implications for supersymmetry. JCAP 04, 022 (2016). arXiv:1601.00653 "/> <meta name="citation_reference" content="Planck: N. Aghanim et al., Planck 2018 results. VI. Cosmological parameters. Astron. Astrophys. 641, A6 (2020). arXiv:1807.06209 "/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. C; citation_title=Weakly interacting massive particle-nucleus elastic scattering response; citation_author=N Anand, AL Fitzpatrick, WC Haxton; citation_volume=89; citation_publication_date=2014; citation_pages=065501; citation_doi=10.1103/PhysRevC.89.065501; citation_id=CR99"/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=Chiral effective theory of dark matter direct detection; citation_author=F Bishara, J Brod, B Grinstein, J Zupan; citation_volume=1702; citation_publication_date=2017; citation_pages=009; citation_doi=10.1088/1475-7516/2017/02/009; citation_id=CR100"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=From quarks to nucleons in dark matter direct detection; citation_author=F Bishara, J Brod, B Grinstein, J Zupan; citation_volume=11; citation_publication_date=2017; citation_pages=059; citation_doi=10.1007/JHEP11(2017)059; citation_id=CR101"/> <meta name="citation_reference" content="Particle Data Group: P.A. Zyla et al., Review of particle physics. Prog. Theor. Exp. Phys. 083, C01 (2020)"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Accurate evaluation of hadronic uncertainties in spin-independent WIMP-nucleon scattering: disentangling two- and three-flavor effects; citation_author=A Crivellin, M Hoferichter, M Procura; citation_volume=89; citation_publication_date=2014; citation_pages=054021; citation_doi=10.1103/PhysRevD.89.054021; citation_id=CR103"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=Strange electromagnetic form factors of the nucleon with -improved Wilson fermions; citation_author=D Djukanovic, K Ottnad, J Wilhelm, H Wittig; citation_volume=123; citation_publication_date=2019; citation_pages=212001; citation_doi=10.1103/PhysRevLett.123.212001; citation_id=CR104"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=Strange quark magnetic moment of the nucleon at the physical point; citation_author=RS Sufian, Y-B Yang; citation_volume=118; citation_publication_date=2017; citation_pages=042001; citation_doi=10.1103/PhysRevLett.118.042001; citation_id=CR105"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Flavor diagonal tensor charges of the nucleon from (2 + 1 + 1)-flavor lattice QCD; citation_author=R Gupta, B Yoon; citation_volume=98; citation_publication_date=2018; citation_pages=091501; citation_doi=10.1103/PhysRevD.98.091501; citation_id=CR106"/> <meta name="citation_reference" content="Flavour Lattice Averaging Group: S. Aoki et al., FLAG review 2019: Flavour Lattice Averaging Group (FLAG). Eur. Phys. J. C 80, 113 (2020). arXiv:1902.08191 "/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Quark spins and anomalous ward identity; citation_author=J Liang, Y-B Yang, T Draper, M Gong, K-F Liu; citation_volume=98; citation_publication_date=2018; citation_pages=074505; citation_doi=10.1103/PhysRevD.98.074505; citation_id=CR108"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Chiral-odd generalized parton distributions in constituent quark models; citation_author=B Pasquini, M Pincetti, S Boffi; citation_volume=72; citation_publication_date=2005; citation_pages=094029; citation_doi=10.1103/PhysRevD.72.094029; citation_id=CR109"/> <meta name="citation_reference" content="GAMBIT Collaboration: P. Athron et al., Global analyses of Higgs portal singlet dark matter models using GAMBIT. Eur. Phys. J. C 79, 38 (2019). arXiv:1808.10465 "/> <meta name="citation_reference" content="QCDSF-UKQCD: R. Horsley, Y. Nakamura et al., Hyperon sigma terms for 2 + 1 quark flavours. Phys. Rev. D 85, 034506 (2012). arXiv:1110.4971 "/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=Lattice computation of the nucleon scalar quark contents at the physical point; citation_author=S Durr; citation_volume=116; citation_publication_date=2016; citation_pages=172001; citation_doi=10.1103/PhysRevLett.116.172001; citation_id=CR112"/> <meta name="citation_reference" content="xQCD: Y.-B. Yang, A. Alexandru, T. Draper, J. Liang, K.-F. Liu, $$\pi $$ N and strangeness sigma terms at the physical point with chiral fermions. Phys. Rev. D 94, 054503 (2016). arXiv:1511.09089 "/> <meta name="citation_reference" content="ETM: A. Abdel-Rehim, C. Alexandrou et al., Direct evaluation of the quark content of nucleons from lattice QCD at the physical point. Phys. Rev. Lett. 116, 252001 (2016). arXiv:1601.01624 "/> <meta name="citation_reference" content="RQCD: G.S. Bali, S. Collins et al., Direct determinations of the nucleon and pion terms at nearly physical quark masses. Phys. Rev. D 93, 094504 (2016). arXiv:1603.00827 "/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Nucleon axial, tensor, and scalar charges and -terms in lattice QCD; citation_author=C Alexandrou, S Bacchio; citation_volume=102; citation_publication_date=2020; citation_pages=054517; citation_doi=10.1103/PhysRevD.102.054517; citation_id=CR116"/> <meta name="citation_reference" content="JLQCD: N. Yamanaka, S. Hashimoto, T. Kaneko, H. Ohki, Nucleon charges with dynamical overlap fermions. Phys. Rev. D 98, 054516 (2018). arXiv:1805.10507 "/> <meta name="citation_reference" content="S. Borsanyi, Z. Fodor et al., Ab-initio calculation of the proton and the neutron’s scalar couplings for new physics searches. arXiv:2007.03319 "/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=The chiral representation of the scattering amplitude and the pion-nucleon sigma term; citation_author=JM Alarcon, J Martin Camalich, JA Oller; citation_volume=85; citation_publication_date=2012; citation_pages=051503; citation_id=CR119"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=High-precision determination of the pion-nucleon term from Roy–Steiner equations; citation_author=M Hoferichter, J Ruiz de Elvira, B Kubis, U-G Meissner; citation_volume=115; citation_publication_date=2015; citation_pages=092301; citation_doi=10.1103/PhysRevLett.115.092301; citation_id=CR120"/> <meta name="citation_reference" content="V. Dmitrašinović, H.-X. Chen, A. Hosaka, Baryon fields with $$U_L(3)$$ Ö $$U_R(3)$$ chiral symmetry. V. Pion-nucleon and kaon-nucleon $${{\varSigma }}$$ terms. Phys. Rev. C 93, 065208 (2016). arXiv:1812.03414 "/> <meta name="citation_reference" content="citation_journal_title=J. Phys. G; citation_title=Extracting the -term from low-energy pion-nucleon scattering; citation_author=J Ruiz de Elvira, M Hoferichter, B Kubis, U-G Meissner; citation_volume=45; citation_publication_date=2018; citation_pages=024001; citation_doi=10.1088/1361-6471/aa9422; citation_id=CR122"/> <meta name="citation_reference" content="E. Friedman, A. Gal, The pion-nucleon $${\sigma }$$ term from pionic atoms. Phys. Lett. B 792, 340–344 (2019). arXiv:1901.03130 "/> <meta name="citation_reference" content="citation_journal_title=Nucl. Phys. A; citation_title=Cosmic abundances of stable particles: improved analysis; citation_author=P Gondolo, G Gelmini; citation_volume=360; citation_publication_date=1991; citation_pages=145-179; citation_doi=10.1016/0550-3213(91)90438-4; citation_id=CR124"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Early kinetic decoupling of dark matter: when the standard way of calculating the thermal relic density fails; citation_author=T Binder, T Bringmann, M Gustafsson, A Hryczuk; citation_volume=96; citation_publication_date=2017; citation_pages=115010; citation_doi=10.1103/PhysRevD.96.115010; citation_id=CR125"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Asymmetric dark matter; citation_author=DE Kaplan, MA Luty, KM Zurek; citation_volume=79; citation_publication_date=2009; citation_pages=115016; citation_doi=10.1103/PhysRevD.79.115016; citation_id=CR126"/> <meta name="citation_reference" content="A. Pukhov, CalcHEP 2.3: MSSM, structure functions, event generation, batchs, and generation of matrix elements for other packages. arXiv:hep-ph/0412191 "/> <meta name="citation_reference" content="citation_journal_title=Comput. Phys. Commun.; citation_title=CalcHEP 3.4 for collider physics within and beyond the Standard Model; citation_author=A Belyaev, ND Christensen, A Pukhov; citation_volume=184; citation_publication_date=2013; citation_pages=1729-1769; citation_doi=10.1016/j.cpc.2013.01.014; citation_id=CR128"/> <meta name="citation_reference" content="citation_journal_title=Prog. Part. Nucl. Phys.; citation_title=Dark matter and the early Universe: a review; citation_author=A Arbey, F Mahmoudi; citation_volume=119; citation_publication_date=2021; citation_pages=103865; citation_doi=10.1016/j.ppnp.2021.103865; citation_id=CR129"/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=DarkSUSY 6: an advanced tool to compute dark matter properties numerically; citation_author=T Bringmann, J Edsjö, P Gondolo, P Ullio, L Bergström; citation_volume=1807; citation_publication_date=2018; citation_pages=033; citation_doi=10.1088/1475-7516/2018/07/033; citation_id=CR130"/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=DarkSUSY: computing supersymmetric dark matter properties numerically; citation_author=P Gondolo, J Edsjo; citation_volume=0407; citation_publication_date=2004; citation_pages=008; citation_doi=10.1088/1475-7516/2004/07/008; citation_id=CR131"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Co-annihilating dark matter: effective operator analysis and collider phenomenology; citation_author=NF Bell, Y Cai, AD Medina; citation_volume=89; citation_publication_date=2014; citation_pages=115001; citation_doi=10.1103/PhysRevD.89.115001; citation_id=CR132"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=The coannihilation codex; citation_author=MJ Baker; citation_volume=12; citation_publication_date=2015; citation_pages=120; citation_id=CR133"/> <meta name="citation_reference" content="citation_journal_title=Phys. Dark Universe; citation_title=Gamma ray signals from dark matter: concepts, status and prospects; citation_author=T Bringmann, C Weniger; citation_volume=1; citation_publication_date=2012; citation_pages=194-217; citation_doi=10.1016/j.dark.2012.10.005; citation_id=CR134"/> <meta name="citation_reference" content="Fermi-LAT: M. Ackermann et al., The Fermi Galactic Center GeV excess and implications for dark matter. Astrophys. J. 840, 43 (2017). arXiv:1704.03910 "/> <meta name="citation_reference" content="CTA: A. Acharyya et al., Sensitivity of the Cherenkov Telescope Array to a dark matter signal from the Galactic Centre. JCAP 01, 057 (2021). arXiv:2007.16129 "/> <meta name="citation_reference" content="Super-Kamiokande: K. Choi et al., Search for neutrinos from annihilation of captured low-mass dark matter particles in the Sun by Super-Kamiokande. Phys. Rev. Lett. 114, 141301 (2015). arXiv:1503.04858 "/> <meta name="citation_reference" content="IceCube: M.G. Aartsen et al., Search for annihilating dark matter in the Sun with 3 years of IceCube data. Eur. Phys. J. C 77, 146 (2017). arXiv:1612.05949 [Erratum: Eur. Phys. J. C 79, 214 (2019)]"/> <meta name="citation_reference" content="N. Avis Kozar, A. Caddell, L. Fraser-Leach, P. Scott, A.C. Vincent, Capt’n General: a generalized stellar dark matter capture and heat transport code (2021). arXiv:2105.06810 "/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=Form factors for dark matter capture by the Sun in effective theories; citation_author=R Catena, B Schwabe; citation_volume=04; citation_publication_date=2015; citation_pages=042; citation_doi=10.1088/1475-7516/2015/04/042; citation_id=CR140"/> <meta name="citation_reference" content="citation_journal_title=Astrophys. J.; citation_title=A new generation of standard solar models; citation_author=N Vinyoles, AM Serenelli; citation_volume=835; citation_publication_date=2017; citation_pages=202; citation_doi=10.3847/1538-4357/835/2/202; citation_id=CR141"/> <meta name="citation_reference" content="citation_journal_title=ARA&A; citation_title=The chemical composition of the Sun; citation_author=M Asplund, N Grevesse, AJ Sauval, P Scott; citation_volume=47; citation_publication_date=2009; citation_pages=481-522; citation_doi=10.1146/annurev.astro.46.060407.145222; citation_id=CR142"/> <meta name="citation_reference" content="IceCube Collaboration: M.G. Aartsen, R. Abbasi et al., Search for dark matter annihilations in the Sun with the 79-String IceCube detector. Phys. Rev. Lett. 110, 131302 (2013). arXiv:1212.4097 "/> <meta name="citation_reference" content="P. Scott, C. Savage, J. Edsjö, The IceCube Collaboration: R. Abbasi et al., Use of event-level neutrino telescope data in global fits for theories of new physics. JCAP 11, 57 (2012). arXiv:1207.0810 "/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Indirect dark matter signatures in the cosmic dark ages. I. Generalizing the bound on s-wave dark matter annihilation from Planck results; citation_author=TR Slatyer; citation_volume=93; citation_publication_date=2016; citation_pages=023527; citation_doi=10.1103/PhysRevD.93.023527; citation_id=CR145"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Indirect dark matter signatures in the cosmic dark ages II. Ionization, heating and photon production from arbitrary energy injections; citation_author=TR Slatyer; citation_volume=93; citation_publication_date=2016; citation_pages=023521; citation_doi=10.1103/PhysRevD.93.023521; citation_id=CR146"/> <meta name="citation_reference" content="citation_journal_title=JCAP; citation_title=Exotic energy injection with ExoCLASS: application to the Higgs portal model and evaporating black holes; citation_author=P Stöcker, M Krämer, J Lesgourgues, V Poulin; citation_volume=1803; citation_publication_date=2018; citation_pages=018; citation_doi=10.1088/1475-7516/2018/03/018; citation_id=CR147"/> <meta name="citation_reference" content="Planck: N. Aghanim et al., Planck 2018 results. V. CMB power spectra and likelihoods. Astron. Astrophys. 641, A5 (2020). arXiv:1907.12875 "/> <meta name="citation_reference" content="citation_journal_title=MNRAS; citation_title=The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant; citation_author=F Beutler, C Blake; citation_volume=416; citation_publication_date=2011; citation_pages=3017-3032; citation_doi=10.1111/j.1365-2966.2011.19250.x; citation_id=CR149"/> <meta name="citation_reference" content="A.J. Ross, L. Samushia et al., The clustering of the SDSS DR7 main Galaxy sample—I. A 4 per cent distance measure at z = 0.15. MNRAS 449, 835–847 (2015). arXiv:1409.3242 "/> <meta name="citation_reference" content="BOSS: S. Alam et al., The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample. MNRAS 470, 2617–2652 (2017). arXiv:1607.03155 "/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Constraints on dark matter annihilation from AMS-02 results; citation_author=J Kopp; citation_volume=88; citation_publication_date=2013; citation_pages=076013; citation_doi=10.1103/PhysRevD.88.076013; citation_id=CR152"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=New limits on dark matter annihilation from AMS cosmic ray positron data; citation_author=L Bergström, T Bringmann, I Cholis, D Hooper, C Weniger; citation_volume=111; citation_publication_date=2013; citation_pages=171101; citation_doi=10.1103/PhysRevLett.111.171101; citation_id=CR153"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=Dark matter annihilations and decays after the AMS-02 positron measurements; citation_author=A Ibarra, AS Lamperstorfer, J Silk; citation_volume=89; citation_publication_date=2014; citation_pages=063539; citation_doi=10.1103/PhysRevD.89.063539; citation_id=CR154"/> <meta name="citation_reference" content="citation_journal_title=Astrophys. J.; citation_title=Cosmic anti-protons as a probe for supersymmetric dark matter?; citation_author=L Bergstrom, J Edsjo, P Ullio; citation_volume=526; citation_publication_date=1999; citation_pages=215-235; citation_doi=10.1086/307975; citation_id=CR155"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. D; citation_title=The galactic antiproton spectrum at high energies: background expectation vs. exotic contributions; citation_author=T Bringmann, P Salati; citation_volume=75; citation_publication_date=2007; citation_pages=083006; citation_doi=10.1103/PhysRevD.75.083006; citation_id=CR156"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Lett.; citation_title=Novel dark matter constraints from antiprotons in light of AMS-02; citation_author=A Cuoco, M Krämer, M Korsmeier; citation_volume=118; citation_publication_date=2017; citation_pages=191102 191102; citation_doi=10.1103/PhysRevLett.118.191102; citation_id=CR157"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Res.; citation_title=Dark matter or correlated errors: systematics of the AMS-02 antiproton excess; citation_author=J Heisig, M Korsmeier, MW Winkler; citation_volume=2; citation_publication_date=2020; citation_pages=043017; citation_doi=10.1103/PhysRevResearch.2.043017; citation_id=CR158"/> <meta name="citation_reference" content="citation_journal_title=Phys. Rev. Res.; citation_title=AMS-02 antiprotons’ consistency with a secondary astrophysical origin; citation_author=M Boudaud, Y Génolini; citation_volume=2; citation_publication_date=2020; citation_pages=023022; citation_doi=10.1103/PhysRevResearch.2.023022; citation_id=CR159"/> <meta name="citation_reference" content="citation_journal_title=Astrophys. J.; citation_title=Bayesian analysis of cosmic-ray propagation: evidence against homogeneous diffusion; citation_author=G Jóhannesson; citation_volume=824; citation_publication_date=2016; citation_pages=16; citation_doi=10.3847/0004-637X/824/1/16; citation_id=CR160"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Universal properties of pseudoscalar mediators in dark matter extensions of 2HDMs; citation_author=M Bauer, M Klassen, V Tenorth; citation_volume=07; citation_publication_date=2018; citation_pages=107; citation_doi=10.1007/JHEP07(2018)107; citation_id=CR161"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Collide and conquer: constraints on simplified dark matter models using mono-X collider searches; citation_author=AJ Brennan, MF McDonald, J Gramling, TD Jacques; citation_volume=05; citation_publication_date=2016; citation_pages=112; citation_doi=10.1007/JHEP05(2016)112; citation_id=CR162"/> <meta name="citation_reference" content="A. Alloul, N.D. Christensen, C. Degrande, C. Duhr, B. Fuks, FeynRules 2.0—a complete toolbox for tree-level phenomenology. Comput. Phys. Commun. 185, 2250–2300 (2014). arXiv:1310.1921 "/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=MadGraph 5: going beyond; citation_author=J Alwall, M Herquet, F Maltoni, O Mattelaer, T Stelzer; citation_volume=06; citation_publication_date=2011; citation_pages=128; citation_doi=10.1007/JHEP06(2011)128; citation_id=CR164"/> <meta name="citation_reference" content="citation_journal_title=Comput. Phys. Commun.; citation_title=A brief introduction to PYTHIA 8.1; citation_author=T Sjostrand, S Mrenna, PZ Skands; citation_volume=178; citation_publication_date=2008; citation_pages=852-867; citation_doi=10.1016/j.cpc.2008.01.036; citation_id=CR165"/> <meta name="citation_reference" content="DELPHES 3: J. de Favereau, C. Delaere et al., DELPHES 3, a modular framework for fast simulation of a generic collider experiment. JHEP 02, 057 (2014). arXiv:1307.6346 "/> <meta name="citation_reference" content="CMS Collaboration, Simplified likelihood for the re-interpretation of public CMS results. CMS-NOTE-2017-001 (2017)"/> <meta name="citation_reference" content="GAMBIT Collider Workgroup: C. Balázs, A. Buckley et al., ColliderBit: a GAMBIT module for the calculation of high-energy collider observables and likelihoods. Eur. Phys. J. C 77, 795 (2017). arXiv:1705.07919 "/> <meta name="citation_reference" content="GAMBIT Collaboration: P. Athron et al., Combined collider constraints on neutralinos and charginos. Eur. Phys. J. C 79, 395 (2019). arXiv:1809.02097 "/> <meta name="citation_reference" content="citation_journal_title=Astrophys. J.; citation_title=Trigonometric parallaxes of high mass star forming regions: the structure and kinematics of the Milky Way; citation_author=MJ Reid; citation_volume=783; citation_publication_date=2014; citation_pages=130; citation_doi=10.1088/0004-637X/783/2/130; citation_id=CR170"/> <meta name="citation_reference" content="citation_journal_title=MNRAS; citation_title=The local high-velocity tail and the galactic escape speed; citation_author=AJ Deason, A Fattahi; citation_volume=485; citation_publication_date=2019; citation_pages=3514-3526; citation_doi=10.1093/mnras/stz623; citation_id=CR171"/> <meta name="citation_reference" content="ATLAS: G. Aad et al., Measurement of the top-quark mass in $$t{\bar{t}}+1$$ -jet events collected with the ATLAS detector in $$pp$$ collisions at $$\sqrt{s}=8$$  TeV. JHEP 11, 150 (2019). arXiv:1905.02302 "/> <meta name="citation_reference" content="GAMBIT Scanner Workgroup: G.D. Martinez, J. McKay et al., Comparison of statistical sampling methods with ScannerBit, the GAMBIT scanning module. Eur. Phys. J. C 77, 761 (2017). arXiv:1705.07959 "/> <meta name="citation_reference" content="LUX-ZEPLIN: D.S. Akerib et al., Projected WIMP sensitivity of the LUX-ZEPLIN dark matter experiment. Phys. Rev. D 101, 052002 (2020). arXiv:1802.06039 "/> <meta name="citation_reference" content="DARWIN: J. Aalbers et al., DARWIN: towards the ultimate dark matter detector. JCAP 11, 017 (2016). arXiv:1606.07001 "/> <meta name="citation_reference" content="citation_journal_title=Eur. Phys. J. Plus; citation_title=DarkSide-20k: a 20 tonne two-phase LAr TPC for direct dark matter detection at LNGS; citation_author=CE Aalseth; citation_volume=133; citation_publication_date=2018; citation_pages=131; citation_doi=10.1140/epjp/i2018-11973-4; citation_id=CR176"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Constraining dark sectors with monojets and dijets; citation_author=M Chala, F Kahlhoefer, M McCullough, G Nardini, K Schmidt-Hoberg; citation_volume=07; citation_publication_date=2015; citation_pages=089; citation_doi=10.1007/JHEP07(2015)089; citation_id=CR177"/> <meta name="citation_reference" content="citation_journal_title=JHEP; citation_title=Constraints on Z’ models from LHC dijet searches and implications for dark matter; citation_author=M Fairbairn, J Heal, F Kahlhoefer, P Tunney; citation_volume=09; citation_publication_date=2016; citation_pages=018; citation_doi=10.1007/JHEP09(2016)018; citation_id=CR178"/> <meta name="citation_reference" content="citation_journal_title=SciPost Phys.; citation_title=Dark matter EFT, the third-neutrino WIMPs; citation_author=I Bischer, T Plehn, W Rodejohann; citation_volume=10; citation_publication_date=2021; citation_pages=039; citation_doi=10.21468/SciPostPhys.10.2.039; citation_id=CR179"/> <meta name="citation_reference" content="R. Barbieri, A view of flavour physics in 2021. Acta Phys. Polon. B 52, 789 (2021). https://doi.org/10.5506/APhysPolB.52.789 . arXiv:2103.15635 "/> <meta name="citation_reference" content="ATLAS, CMS, LHCb: E. Graverini, Flavour anomalies: a review. J. Phys. Conf. Ser. 1137, 012025 (2019). arXiv:1807.11373 "/> <meta name="citation_reference" content="LHCb: R. Aaij et al., Test of lepton universality in beauty-quark decays. arXiv:2103.11769 "/> <meta name="citation_reference" content="PandaX: H. Zhang et al., Dark matter direct search sensitivity of the PandaX-4T experiment. Sci. China Phys. Mech. Astron. 62, 31011 (2019). arXiv:1806.02229 "/> <meta name="citation_reference" content="XENON: E. Aprile et al., Projected WIMP sensitivity of the XENONnT dark matter experiment. JCAP 11, 031 (2020). arXiv:2007.08796 "/> <meta name="citation_reference" content="MAGIC, Fermi-LAT: M.L. Ahnen et al., Limits to dark matter annihilation cross-section from a combined analysis of MAGIC and Fermi-LAT observations of dwarf satellite galaxies. JCAP 02, 039 (2016). arXiv:1601.06590 "/> <meta name="citation_reference" content="H.E.S.S.: H. Abdallah et al., Search for dark matter annihilations towards the inner Galactic halo from 10 years of observations with H.E.S.S. Phys. Rev. Lett. 117, 111301 (2016). arXiv:1607.08142 "/> <meta name="citation_reference" content="AMS: M. Aguilar et al., The Alpha Magnetic Spectrometer (AMS) on the international space station: part II—results from the first seven years. Phys. Rep. 894, 1–116 (2021)"/> <meta name="citation_reference" content="citation_journal_title=Eur. Phys. J. Plus; citation_title=Pippi—painless parsing, post-processing and plotting of posterior and likelihood samples; citation_author=P Scott; citation_volume=127; citation_publication_date=2012; citation_pages=138; citation_doi=10.1140/epjp/i2012-12138-3; citation_id=CR188"/> <meta name="citation_reference" content="A. Semenov, LanHEP: a package for the automatic generation of Feynman rules in field theory. Version 3.0. Comput. Phys. Commun. 180, 431–454 (2009). arXiv:0805.0555 "/> <meta name="citation_reference" content="GAMBIT Collaboration: P. Athron, C. Balázs et al., GAMBIT: the global and modular beyond-the-standard-model inference tool. Addendum for GAMBIT 1.1: Mathematica backends, SUSYHD interface and updated likelihoods. Eur. Phys. J. C 78, 98 (2018). arXiv:1705.07908 . Addendum to [48]"/> <meta name="citation_author" content="Athron, Peter"/> <meta name="citation_author_institution" content="School of Physics and Astronomy, Monash University, Melbourne, Australia"/> <meta name="citation_author_institution" content="Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, China"/> <meta name="citation_author" content="Kozar, Neal Avis"/> <meta name="citation_author_institution" content="Arthur B. McDonald Canadian Astroparticle Physics Research Institute, Kingston, Canada"/> <meta name="citation_author_institution" content="Department of Physics, Engineering Physics and Astronomy, Queen’s University, Kingston, Canada"/> <meta name="citation_author" content="Balázs, Csaba"/> <meta name="citation_author_institution" content="School of Physics and Astronomy, Monash University, Melbourne, Australia"/> <meta name="citation_author" content="Beniwal, Ankit"/> <meta name="citation_author_email" content="ankit.beniwal@uclouvain.be"/> <meta name="citation_author_institution" content="Center for Cosmology, Particle Physics and Phenomenology, Université catholique de Louvain, Louvain-la-Neuve, Belgium"/> <meta name="citation_author" content="Bloor, Sanjay"/> <meta name="citation_author_email" content="sanjay.bloor12@imperial.ac.uk"/> <meta name="citation_author_institution" content="Department of Physics, Blackett Laboratory, Imperial College London, London, UK"/> <meta 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We perform a global analysis of effective field theory (EFT) operators describing the interactions between a gauge-singlet Dirac fermion and the Standard Model quarks, the gluons and the photon. In this bottom-up approach, we simultaneously vary the coefficients of 14 such operators up to dimension 7, along with the DM mass, the scale of new physics and several nuisance parameters. Our likelihood functions include the latest data from Planck, direct and indirect detection experiments, and the LHC. For DM masses below 100 GeV, we find that it is impossible to satisfy all constraints simultaneously while maintaining EFT validity at LHC energies. For new physics scales around 1 TeV, our results are influenced by several small excesses in the LHC data and depend on the prescription that we adopt to ensure EFT validity. Furthermore, we find large regions of viable parameter space where the EFT is valid and the relic density can be reproduced, implying that WIMPs can still account for the DM of the universe while being consistent with the latest data."/> <meta property="og:image" content="https://static-content.springer.com/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig1_HTML.png"/> <meta name="format-detection" content="telephone=no"> <link rel="apple-touch-icon" sizes="180x180" href=/oscar-static/img/favicons/darwin/apple-touch-icon-92e819bf8a.png> <link rel="icon" type="image/png" sizes="192x192" href=/oscar-static/img/favicons/darwin/android-chrome-192x192-6f081ca7e5.png> <link rel="icon" type="image/png" sizes="32x32" href=/oscar-static/img/favicons/darwin/favicon-32x32-1435da3e82.png> <link rel="icon" type="image/png" sizes="16x16" href=/oscar-static/img/favicons/darwin/favicon-16x16-ed57f42bd2.png> <link rel="shortcut icon" data-test="shortcut-icon" 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We perform a global analysis of effective field theory (EFT) operators describing the interactions between a gauge-singlet Dirac fermion and the Standard Model quarks, the gluons and the photon. In this bottom-up approach, we simultaneously vary the coefficients of 14 such operators up to dimension 7, along with the DM mass, the scale of new physics and several nuisance parameters. Our likelihood functions include the latest data from Planck, direct and indirect detection experiments, and the LHC. For DM masses below 100 GeV, we find that it is impossible to satisfy all constraints simultaneously while maintaining EFT validity at LHC energies. For new physics scales around 1 TeV, our results are influenced by several small excesses in the LHC data and depend on the prescription that we adopt to ensure EFT validity. 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class="c-context-bar__container u-container"> <div class="c-context-bar__title"> Thermal WIMPs and the scale of new physics: global fits of Dirac dark matter effective field theories </div> <div data-test="inCoD" data-track-context="sticky banner"> <div class="c-pdf-container"> <div class="c-pdf-download u-clear-both u-mb-16"> <a href="/content/pdf/10.1140/epjc/s10052-021-09712-6.pdf" class="u-button u-button--full-width u-button--primary u-justify-content-space-between c-pdf-download__link" data-article-pdf="true" data-readcube-pdf-url="true" data-test="pdf-link" data-draft-ignore="true" data-track="content_download" data-track-type="article pdf download" data-track-action="download pdf" data-track-label="button" data-track-external download> <span class="c-pdf-download__text">Download PDF</span> <svg aria-hidden="true" focusable="false" width="16" height="16" class="u-icon"><use xlink:href="#icon-eds-i-download-medium"/></svg> </a> </div> </div> </div> </div> </div> <div class="c-article-header"> <header> <ul class="c-article-author-list c-article-author-list--long" data-test="authors-list" data-component-authors-activator="authors-list"><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Peter-Athron-Aff1-Aff2" data-author-popup="auth-Peter-Athron-Aff1-Aff2" data-author-search="Athron, Peter">Peter Athron</a><sup class="u-js-hide"><a href="#Aff1">1</a>,<a href="#Aff2">2</a></sup>, </li><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Neal_Avis-Kozar-Aff3-Aff4" data-author-popup="auth-Neal_Avis-Kozar-Aff3-Aff4" data-author-search="Kozar, Neal Avis">Neal Avis Kozar</a><sup class="u-js-hide"><a href="#Aff3">3</a>,<a href="#Aff4">4</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a 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data-track-action="open author" data-track-label="link" href="#auth-Joachim-Brod-Aff9" data-author-popup="auth-Joachim-Brod-Aff9" data-author-search="Brod, Joachim">Joachim Brod</a><sup class="u-js-hide"><a href="#Aff9">9</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Christopher-Chang-Aff7" data-author-popup="auth-Christopher-Chang-Aff7" data-author-search="Chang, Christopher">Christopher Chang</a><sup class="u-js-hide"><a href="#Aff7">7</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Jonathan_M_-Cornell-Aff10" data-author-popup="auth-Jonathan_M_-Cornell-Aff10" data-author-search="Cornell, Jonathan M.">Jonathan M. 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Vincent</a><sup class="u-js-hide"><a href="#Aff3">3</a>,<a href="#Aff4">4</a>,<a href="#Aff21">21</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Martin-White-Aff19" data-author-popup="auth-Martin-White-Aff19" data-author-search="White, Martin">Martin White</a><sup class="u-js-hide"><a href="#Aff19">19</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Sebastian-Wild-Aff22" data-author-popup="auth-Sebastian-Wild-Aff22" data-author-search="Wild, Sebastian">Sebastian Wild</a><sup class="u-js-hide"><a href="#Aff22">22</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Jure-Zupan-Aff9" data-author-popup="auth-Jure-Zupan-Aff9" data-author-search="Zupan, Jure">Jure Zupan</a><sup class="u-js-hide"><a href="#Aff9">9</a></sup> & </li><li class="c-article-author-list__item"><a data-test="author-name" data-author-popup="group-1" href="#group-1">GAMBIT Collaboration</a></li></ul><button aria-expanded="false" class="c-article-author-list__button"><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-down-medium"></use></svg><span>Show authors</span></button> <div data-test="article-metrics"> <ul class="app-article-metrics-bar u-list-reset"> <li class="app-article-metrics-bar__item"> <p class="app-article-metrics-bar__count"><svg class="u-icon app-article-metrics-bar__icon" width="24" height="24" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-accesses-medium"></use> </svg>1546 <span class="app-article-metrics-bar__label">Accesses</span></p> </li> <li class="app-article-metrics-bar__item"> <p class="app-article-metrics-bar__count"><svg class="u-icon app-article-metrics-bar__icon" width="24" height="24" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-citations-medium"></use> </svg>22 <span class="app-article-metrics-bar__label">Citations</span></p> </li> <li class="app-article-metrics-bar__item"> <p class="app-article-metrics-bar__count"><svg class="u-icon app-article-metrics-bar__icon" width="24" height="24" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-altmetric-medium"></use> </svg>12 <span class="app-article-metrics-bar__label">Altmetric</span></p> </li> <li class="app-article-metrics-bar__item"> <p class="app-article-metrics-bar__count"><svg class="u-icon app-article-metrics-bar__icon app-article-metrics-bar__icon--mentions" width="24" height="24" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-mentions-medium"></use> </svg>1 <span class="app-article-metrics-bar__label">Mention</span></p> </li> <li class="app-article-metrics-bar__item app-article-metrics-bar__item--metrics"> <p class="app-article-metrics-bar__details"><a href="/article/10.1140/epjc/s10052-021-09712-6/metrics" data-track="click" data-track-action="view metrics" data-track-label="link" rel="nofollow">Explore all metrics <svg class="u-icon app-article-metrics-bar__arrow-icon" width="24" height="24" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-arrow-right-medium"></use> </svg></a></p> </li> </ul> </div> <div class="u-mt-32"> </div> </header> </div> <div data-article-body="true" data-track-component="article body" class="c-article-body"> <section aria-labelledby="Abs1" data-title="Abstract" lang="en"><div class="c-article-section" id="Abs1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Abs1">Abstract</h2><div class="c-article-section__content" id="Abs1-content"><p>We assess the status of a wide class of WIMP dark matter (DM) models in light of the latest experimental results using the global fitting framework <span class="u-sans-serif">GAMBIT</span>. We perform a global analysis of effective field theory (EFT) operators describing the interactions between a gauge-singlet Dirac fermion and the Standard Model quarks, the gluons and the photon. In this bottom-up approach, we simultaneously vary the coefficients of 14 such operators up to dimension 7, along with the DM mass, the scale of new physics and several nuisance parameters. Our likelihood functions include the latest data from <i>Planck</i>, direct and indirect detection experiments, and the LHC. For DM masses below 100 GeV, we find that it is impossible to satisfy all constraints simultaneously while maintaining EFT validity at LHC energies. For new physics scales around 1 TeV, our results are influenced by several small excesses in the LHC data and depend on the prescription that we adopt to ensure EFT validity. Furthermore, we find large regions of viable parameter space where the EFT is valid and the relic density can be reproduced, implying that WIMPs can still account for the DM of the universe while being consistent with the latest data.</p></div></div></section> <div data-test="cobranding-download"> </div> <section aria-labelledby="inline-recommendations" data-title="Inline Recommendations" class="c-article-recommendations" data-track-component="inline-recommendations"> <h3 class="c-article-recommendations-title" id="inline-recommendations">Similar content being viewed by others</h3> <div class="c-article-recommendations-list"> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3Aplaceholder%2Fimages/placeholder-figure-springernature.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://link.springer.com/10.1007/JHEP10(2020)172?fromPaywallRec=false" data-track="select_recommendations_1" data-track-context="inline recommendations" data-track-action="click recommendations inline - 1" data-track-label="10.1007/JHEP10(2020)172">Model-independent constraints with extended dark matter EFT </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">27 October 2020</span> </div> </div> </article> </div> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3Aplaceholder%2Fimages/placeholder-figure-springernature.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://link.springer.com/10.1007/JHEP11(2016)069?fromPaywallRec=false" data-track="select_recommendations_2" data-track-context="inline recommendations" data-track-action="click recommendations inline - 2" data-track-label="10.1007/JHEP11(2016)069">The last gasp of dark matter effective theory </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">10 November 2016</span> </div> </div> </article> </div> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3Aplaceholder%2Fimages/placeholder-figure-springernature.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://link.springer.com/10.1007/JHEP10(2015)076?fromPaywallRec=false" data-track="select_recommendations_3" data-track-context="inline recommendations" data-track-action="click recommendations inline - 3" data-track-label="10.1007/JHEP10(2015)076">Dirac-fermionic dark matter in U(1)<sub>X</sub> models </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">12 October 2015</span> </div> </div> </article> </div> </div> </section> <script> window.dataLayer = window.dataLayer || []; window.dataLayer.push({ recommendations: { recommender: 'semantic', model: 'specter', policy_id: 'NA', timestamp: 1732764699, embedded_user: 'null' } }); </script> <div class="app-card-service" data-test="article-checklist-banner"> <div> <a class="app-card-service__link" data-track="click_presubmission_checklist" data-track-context="article page top of reading companion" data-track-category="pre-submission-checklist" data-track-action="clicked article page checklist banner test 2 old version" data-track-label="link" href="https://beta.springernature.com/pre-submission?journalId=10052" data-test="article-checklist-banner-link"> <span class="app-card-service__link-text">Use our pre-submission checklist</span> <svg class="app-card-service__link-icon" aria-hidden="true" focusable="false"><use xlink:href="#icon-eds-i-arrow-right-small"></use></svg> </a> <p class="app-card-service__description">Avoid common mistakes on your manuscript.</p> </div> <div class="app-card-service__icon-container"> <svg class="app-card-service__icon" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-clipboard-check-medium"></use> </svg> </div> </div> <div class="main-content"> <section data-title="Introduction"><div class="c-article-section" id="Sec1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec1"><span class="c-article-section__title-number">1 </span>Introduction</h2><div class="c-article-section__content" id="Sec1-content"><p>Despite years of searching, the identity of dark matter (DM) remains a mystery. Nevertheless, the large number of past, present and future probes of its particle interactions makes it essential to regularly revisit the constraints on the most popular theoretical candidates, in order to guide future searches.</p><p>A favoured paradigm for the particle nature of dark matter is that of Weakly Interacting Massive Particles (WIMPs), due to the fact that it allows for a simple thermal mechanism to produce DM with the cosmologically-observed abundance [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 1" title="B.W. Lee, S. Weinberg, Cosmological lower bound on heavy neutrino masses. Phys. Rev. Lett. 39, 165–168 (1977)" href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR1" id="ref-link-section-d52098281e1103">1</a>]. Such models have also attracted attention due to the large number of possible signals they predict, none of which have been definitively observed so far. Although this has led some to make claims of the demise of WIMPs [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 2" title="G. Arcadi, M. Dutra et al., The waning of the WIMP? A review of models, searches, and constraints. Eur. Phys. J. C 78, 203 (2018). [
 arXiv:1703.07364
 
 ]" href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR2" id="ref-link-section-d52098281e1106">2</a>], others have argued that such predictions are premature [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 3" title="R.K. Leane, T.R. Slatyer, J.F. Beacom, K.C.Y. Ng, GeV-scale thermal WIMPs: not even slightly ruled out. Phys. Rev. D 98, 023016 (2018). 
 arXiv:1805.10305
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR3" id="ref-link-section-d52098281e1109">3</a>].</p><p>A relatively agnostic approach to WIMP model building is to pursue a bottom-up, Effective Field Theory (EFT) approach, in which one enumerates all of the allowed higher dimensional operators which lead to interactions between DM and Standard Model (SM) particles. Any result described by an EFT can in general be explained by many high-energy theories. In this way, the EFT description is a model-independent one, as it does not depend on the Ultraviolet (UV) completion that describes an effective operator. This is, however, a double-edged sword: because an effective operator does not encode any information about the UV completion, it has no constraining power in distinguishing between the range of UV theories that can map to it – nor can all UV-complete theories be mapped to an EFT description for the energies we are interested in here.</p><p>In spite of these limitations, the bottom-up approach is well-advised given the lack of direct evidence pointing to the properties of DM. The EFT approach in particular is highly suitable for low-velocity environments such as direct detection [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="J. Fan, M. Reece, L.-T. Wang, Non-relativistic effective theory of dark matter direct detection. JCAP 1011, 042 (2010). 
 arXiv:1008.1591
 
 " href="#ref-CR4" id="ref-link-section-d52098281e1118">4</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="P. Agrawal, Z. Chacko, C. Kilic, R.K. Mishra, A classification of dark matter candidates with primarily spin-dependent interactions with matter. 
 arXiv:1003.1912
 
 " href="#ref-CR5" id="ref-link-section-d52098281e1118_1">5</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="A. Fitzpatrick, K.M. Zurek, Dark moments and the DAMA-CoGeNT puzzle. Phys. Rev. D 82, 075004 (2010). 
 arXiv:1007.5325
 
 " href="#ref-CR6" id="ref-link-section-d52098281e1118_2">6</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="A. Crivellin, U. Haisch, Dark matter direct detection constraints from gauge bosons loops. Phys. Rev. D 90, 115011 (2014). 
 arXiv:1408.5046
 
 " href="#ref-CR7" id="ref-link-section-d52098281e1118_3">7</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="F. D’Eramo, B.J. Kavanagh, P. Panci, You can hide but you have to run: direct detection with vector mediators. JHEP 08, 111 (2016). 
 arXiv:1605.04917
 
 " href="#ref-CR8" id="ref-link-section-d52098281e1118_4">8</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="M. Hoferichter, P. Klos, J. Menéndez, A. Schwenk, Analysis strategies for general spin-independent WIMP-nucleus scattering. Phys. Rev. D 94, 063505 (2016). 
 arXiv:1605.08043
 
 " href="#ref-CR9" id="ref-link-section-d52098281e1118_5">9</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 10" title="F. Kahlhoefer, S. Wild, Studying generalised dark matter interactions with extended halo-independent methods. JCAP 10, 032 (2016). 
 arXiv:1607.04418
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR10" id="ref-link-section-d52098281e1121">10</a>] and indirect detection [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="J. Goodman, M. Ibe et al., Gamma ray line constraints on effective theories of dark matter. Nucl. Phys. B 844, 55–68 (2011). 
 arXiv:1009.0008
 
 " href="#ref-CR11" id="ref-link-section-d52098281e1124">11</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="M. Beltran, D. Hooper, E.W. Kolb, Z.C. Krusberg, Deducing the nature of dark matter from direct and indirect detection experiments in the absence of collider signatures of new physics. Phys. Rev. D 80, 043509 043509 (2009). 
 arXiv:0808.3384
 
 " href="#ref-CR12" id="ref-link-section-d52098281e1124_1">12</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="K. Cheung, P.-Y. Tseng, T.-C. Yuan, Gamma-ray constraints on effective interactions of the dark matter. JCAP 06, 023 (2011). 
 arXiv:1104.5329
 
 " href="#ref-CR13" id="ref-link-section-d52098281e1124_2">13</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="R. Harnik, G.D. Kribs, An effective theory of Dirac dark matter. Phys. Rev. D 79, 095007 (2009). 
 arXiv:0810.5557
 
 " href="#ref-CR14" id="ref-link-section-d52098281e1124_3">14</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="A. De Simone, A. Monin, A. Thamm, A. Urbano, On the effective operators for Dark Matter annihilations. JCAP 02, 039 (2013). 
 arXiv:1301.1486
 
 " href="#ref-CR15" id="ref-link-section-d52098281e1124_4">15</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="C. Karwin, S. Murgia, T.M.P. Tait, T.A. Porter, P. Tanedo, Dark matter interpretation of the Fermi-LAT observation toward the Galactic Center. Phys. Rev. D 95, 103005 (2017). 
 arXiv:1612.05687
 
 " href="#ref-CR16" id="ref-link-section-d52098281e1124_5">16</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 17" title="L.M. Carpenter, R. Colburn, J. Goodman, T. Linden, Indirect detection constraints on s and t channel simplified models of dark matter. Phys. Rev. D 94, 055027 (2016). 
 arXiv:1606.04138
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR17" id="ref-link-section-d52098281e1127">17</a>]. At higher energy scales, the EFT approach starts breaking down, such that simplified models have become the theories of choice for the interpretation of LHC searches [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 18" title="J. Abdallah et al., Simplified models for dark matter searches at the LHC. Phys. Dark Universe 9–10, 8–23 (2015). 
 arXiv:1506.03116
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR18" id="ref-link-section-d52098281e1130">18</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 19" title="F. Kahlhoefer, Review of LHC dark matter searches. Int. J. Mod. Phys. A 32, 1730006 (2017). 
 arXiv:1702.02430
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR19" id="ref-link-section-d52098281e1134">19</a>] (see also Refs. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 20" title="T. Alanne, F. Goertz, Extended dark matter EFT. Eur. Phys. J. C 80, 446 (2020). 
 arXiv:1712.07626
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR20" id="ref-link-section-d52098281e1137">20</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 21" title="T. Alanne, G. Arcadi, F. Goertz, V. Tenorth, S. Vogl, Model-independent constraints with extended dark matter EFT. JHEP 10, 172 (2020). 
 arXiv:2006.07174
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR21" id="ref-link-section-d52098281e1140">21</a>] for a hybrid approach called “Extended Dark Matter EFT”). Nevertheless, there is an extensive literature on EFTs at colliders [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Y. Bai, P.J. Fox, R. Harnik, The Tevatron at the frontier of dark matter direct detection. JHEP 12, 048 (2010). 
 arXiv:1005.3797
 
 " href="#ref-CR22" id="ref-link-section-d52098281e1143">22</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="H. Dreiner, D. Schmeier, J. Tattersall, Contact interactions probe effective dark matter models at the LHC. EPL 102, 51001 (2013). 
 arXiv:1303.3348
 
 " href="#ref-CR23" id="ref-link-section-d52098281e1143_1">23</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="N. Zhou, D. Berge, D. Whiteson, Mono-everything: combined limits on dark matter production at colliders from multiple final states. Phys. Rev. D 87, 095013 (2013). 
 arXiv:1302.3619
 
 " href="#ref-CR24" id="ref-link-section-d52098281e1143_2">24</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="P.J. Fox, R. Harnik, R. Primulando, C.-T. Yu, Taking a razor to dark matter parameter space at the LHC. Phys. Rev. D 86, 015010 (2012). 
 arXiv:1203.1662
 
 " href="#ref-CR25" id="ref-link-section-d52098281e1143_3">25</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="A. Rajaraman, W. Shepherd, T.M. Tait, A.M. Wijangco, LHC bounds on interactions of dark matter. Phys. Rev. D 84, 095013 (2011). 
 arXiv:1108.1196
 
 " href="#ref-CR26" id="ref-link-section-d52098281e1143_4">26</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="J. Goodman, M. Ibe et al., Constraints on dark matter from colliders. Phys. Rev. D 82, 116010 (2010). 
 arXiv:1008.1783
 
 " href="#ref-CR27" id="ref-link-section-d52098281e1143_5">27</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="P.J. Fox, R. Harnik, J. Kopp, Y. Tsai, Missing energy signatures of dark matter at the LHC. Phys. Rev. D 85, 056011 (2012). 
 arXiv:1109.4398
 
 " href="#ref-CR28" id="ref-link-section-d52098281e1143_6">28</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="M. Beltran, D. Hooper, E.W. Kolb, Z.A. Krusberg, T.M. Tait, Maverick dark matter at colliders. JHEP 09, 037 (2010). 
 arXiv:1002.4137
 
 " href="#ref-CR29" id="ref-link-section-d52098281e1143_7">29</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="O. Buchmueller, M.J. Dolan, C. McCabe, Beyond effective field theory for dark matter searches at the LHC. JHEP 01, 025 (2014). 
 arXiv:1308.6799
 
 " href="#ref-CR30" id="ref-link-section-d52098281e1143_8">30</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="A. Belyaev, L. Panizzi, A. Pukhov, M. Thomas, Dark matter characterization at the LHC in the effective field theory approach. JHEP 04, 110 (2017). 
 arXiv:1610.07545
 
 " href="#ref-CR31" id="ref-link-section-d52098281e1143_9">31</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 32" title="F. Pobbe, A. Wulzer, M. Zanetti, Setting limits on effective field theories: the case of dark matter. JHEP 08, 074 (2017). 
 arXiv:1704.00736
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR32" id="ref-link-section-d52098281e1146">32</a>] including studies by ATLAS [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 33" title="ATLAS: G. Aad et al., Search for dark matter candidates and large extra dimensions in events with a jet and missing transverse momentum with the ATLAS detector. JHEP 04, 075 (2013). 
 arXiv:1210.4491
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR33" id="ref-link-section-d52098281e1149">33</a>] and CMS [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 34" title="CMS: S. Chatrchyan et al., Search for dark matter and large extra dimensions in monojet events in 
 
 
 
 $$pp$$
 
 
 pp
 
 
 collisions at 
 
 
 
 $$\sqrt{s}=7$$
 
 
 
 s
 
 =
 7
 
 
 TeV. JHEP 09, 094 (2012). 
 arXiv:1206.5663
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR34" id="ref-link-section-d52098281e1153">34</a>], which may help to shed light on the nature of DM when interpreted with care.</p><p>A common approach to the analysis of EFTs for DM in the literature has been to consider a single operator at a time [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="M.R. Buckley, Asymmetric dark matter and effective operators. Phys. Rev. D 84, 043510 (2011). 
 arXiv:1104.1429
 
 " href="#ref-CR35" id="ref-link-section-d52098281e1160">35</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="K. Cheung, P.-Y. Tseng, Y.-L.S. Tsai, T.-C. Yuan, Global constraints on effective dark matter interactions: relic density, direct detection, indirect detection, and collider. JCAP 1205, 001 (2012). 
 arXiv:1201.3402
 
 " href="#ref-CR36" id="ref-link-section-d52098281e1160_1">36</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="J. March-Russell, J. Unwin, S.M. West, Closing in on asymmetric dark matter I: model independent limits for interactions with quarks. JHEP 08, 029 (2012). 
 arXiv:1203.4854
 
 " href="#ref-CR37" id="ref-link-section-d52098281e1160_2">37</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="J.-M. Zheng, Z.-H. Yu et al., Constraining the interaction strength between dark matter and visible matter: I.Fermionic dark matter. Nucl. Phys. B 854, 350–374 (2012). 
 arXiv:1012.2022
 
 " href="#ref-CR38" id="ref-link-section-d52098281e1160_3">38</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="A. Belyaev, E. Bertuzzo et al., Interplay of the LHC and non-LHC dark matter searches in the effective field theory approach. Phys. Rev. D 99, 015006 (2019). 
 arXiv:1807.03817
 
 " href="#ref-CR39" id="ref-link-section-d52098281e1160_4">39</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="E. Bertuzzo, C.J. Caniu Barros, G. Grilli di Cortona, MeV dark matter: model independent bounds. JHEP 09, 116 (2017). 
 arXiv:1707.00725
 
 " href="#ref-CR40" id="ref-link-section-d52098281e1160_5">40</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 41" title="M. Cirelli, E. Del Nobile, P. Panci, Tools for model-independent bounds in direct dark matter searches. JCAP 10, 019 (2013). 
 arXiv:1307.5955
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR41" id="ref-link-section-d52098281e1163">41</a>] and compare experimental bounds on the new physics scale <span class="mathjax-tex">${\Lambda }$</span> with the values implied by the observed DM relic density. This method, however, severely limits the scope of the analysis and potentially leads to overly-aggressive exclusions, not only because it neglects (potentially destructive) interferences between different operators [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 42" title="J. Kumar, D. Marfatia, Matrix element analyses of dark matter scattering and annihilation. Phys. Rev. D 88, 014035 (2013). 
 arXiv:1305.1611
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR42" id="ref-link-section-d52098281e1184">42</a>], but also because the relic density constraint can be considerably relaxed when several operators contribute to the DM annihilation cross-section. The first global study of EFTs for scalar, fermionic and vector DM taking interference effects into account was performed in Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="C. Balázs, T. Li, J.L. Newstead, Thermal dark matter implies new physics not far above the weak scale. JHEP 08, 061 (2014). 
 arXiv:1403.5829
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR43" id="ref-link-section-d52098281e1187">43</a>], but no collider constraints were included in the analysis and no couplings to gluons were considered. More recently, Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 44" title="S. Liem, G. Bertone et al., Effective field theory of dark matter: a global analysis. JHEP 9, 77 (2016). 
 arXiv:1603.05994
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR44" id="ref-link-section-d52098281e1191">44</a>] applied Bayesian methods to perform a global analysis of scalar DM, for which only a small number of effective operators need to be considered and collider constraints can be neglected. Examples of global studies considering subspaces of a general DM EFT include Refs. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="S. Matsumoto, S. Mukhopadhyay, Y.-L.S. Tsai, Singlet Majorana fermion dark matter: a comprehensive analysis in effective field theory. JHEP 10, 155 (2014). 
 arXiv:1407.1859
 
 " href="#ref-CR45" id="ref-link-section-d52098281e1194">45</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="M. Blennow, P. Coloma, E. Fernandez-Martinez, P.A.N. Machado, B. Zaldivar, Global constraints on vector-like WIMP effective interactions. JCAP 04, 015 (2016). 
 arXiv:1509.01587
 
 " href="#ref-CR46" id="ref-link-section-d52098281e1194_1">46</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 47" title="S. Matsumoto, S. Mukhopadhyay, Y.-L.S. Tsai, Effective theory of WIMP dark matter supplemented by simplified models: singlet-like Majorana fermion case. Phys. Rev. D 94, 065034 (2016). 
 arXiv:1604.02230
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR47" id="ref-link-section-d52098281e1197">47</a>].</p><p>In the present work, we exploit the computational power of the <span class="u-sans-serif">GAMBIT</span> framework [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 48" title="GAMBIT Collaboration: P. Athron, C. Balázs et al., GAMBIT: the global and modular beyond-the-standard-model inference tool. Eur. Phys. J. C 77, 784 (2017). 
 arXiv:1705.07908
 
 . Addendum in [190]" href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR48" id="ref-link-section-d52098281e1206">48</a>] to perform the first global analysis of a very general set of effective operators up to dimension 7 that describe the interactions between a Dirac fermion DM particle (or a DM sub-component) and quarks or gluons. Such a set-up arises for example in many extensions of the SM gauge group, such as gauged baryon number [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 49" title="M. Duerr, P. Fileviez Perez, Theory for baryon number and dark matter at the LHC. Phys. Rev. D 91, 095001 (2015). 
 arXiv:1409.8165
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR49" id="ref-link-section-d52098281e1209">49</a>] or other anomaly-free gauge extensions that require additional stable fermions [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 50" title="E. Dudas, L. Heurtier, Y. Mambrini, B. Zaldivar, Extra U(1), effective operators, anomalies and dark matter. JHEP 11, 083 (2013). 
 arXiv:1307.0005
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR50" id="ref-link-section-d52098281e1212">50</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 51" title="M. Bauer, S. Diefenbacher, T. Plehn, M. Russell, D.A. Camargo, Dark matter in anomaly-free gauge extensions. SciPost Phys. 5, 036 (2018). 
 arXiv:1805.01904
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR51" id="ref-link-section-d52098281e1215">51</a>]. Our novel approach of considering many operators simultaneously enables us to study parameter regions where several types of DM interactions need to be combined in order to satisfy all constraints. Our analysis substantially improves upon the previous state-of-the-art in both the statistical rigour with which the DM EFT parameter space is interrogated, and in the new combinations of constraints that are simultaneously applied. We also increase the level of detail with which individual constraints are modelled, summarised as follows.</p><p>First, we include a much improved calculation of direct detection constraints using the <span class="u-sans-serif">GAMBIT</span> module <span class="u-sans-serif">DarkBit</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 52" title="GAMBIT Dark Matter Workgroup: T. Bringmann, J. Conrad et al., DarkBit: a GAMBIT module for computing dark matter observables and likelihoods. Eur. Phys. J. C 77, 831 (2017). 
 arXiv:1705.07920
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR52" id="ref-link-section-d52098281e1227">52</a>]. We consider the renormalization group (RG) evolution of all effective operators from the electroweak to the hadronic scale and then match the relativistic operators onto the non-relativistic effective theory [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 53" title="A.L. Fitzpatrick, W. Haxton, E. Katz, N. Lubbers, Y. Xu, The effective field theory of dark matter direct detection. JCAP 1302, 004 (2013). 
 arXiv:1203.3542
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR53" id="ref-link-section-d52098281e1230">53</a>] relevant for DM-nucleon scattering. We then calculate event rates in direct detection experiments to leading order in the chiral expansion, including the contributions from operators that are naively suppressed in the non-relativistic limit, and determine the resulting constraints using detailed likelihood functions for a large number of recent experiments. In the process, we include a number of nuisance parameters to account for uncertainties in nuclear form factors and the astrophysical distribution of DM.</p><p>Second, we consider the most recent constraints on DM annihilations using gamma rays and the Cosmic Microwave Background (CMB). To include the latter, we employ the recently released <span class="u-sans-serif">GAMBIT</span> module <span class="u-sans-serif">CosmoBit</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 54" title="GAMBIT Cosmology Workgroup: J.J. Renk, P. Stöcker et al., CosmoBit: a GAMBIT module for computing cosmological observables and likelihoods. JCAP 02, 022 (2021). 
 arXiv:2009.03286
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR54" id="ref-link-section-d52098281e1242">54</a>], which uses detailed spectra to calculate effective functions for the efficiency of the injected energy deposition and obtain constraints on the DM annihilation cross-section while varying cosmological parameters. For the calculation of annihilation cross-sections we make use of the new <span class="u-sans-serif">GAMBIT</span> Universal Model Machine (<span class="u-sans-serif">GUM</span>) [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 55" title="T.E. Gonzalo, GAMBIT: the global and modular BSM inference tool, in Tools for High Energy Physics and Cosmology (2021). 
 arXiv:2105.03165
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR55" id="ref-link-section-d52098281e1252">55</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 56" title="S. Bloor, T.E. Gonzalo et al., The GAMBIT universal model machine: from Lagrangians to likelihoods. 
 arXiv:2107.00030
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR56" id="ref-link-section-d52098281e1255">56</a>] to automatically generate the relevant code based on the EFT Lagrangian.</p><p>Third, we combine the above detailed astrophysical and cosmological constraints with a state-of-the-art implementation of LHC constraints on WIMP dark matter. A central concern for any study of EFTs is the range of validity of the EFT approach [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="I.M. Shoemaker, L. Vecchi, Unitarity and monojet bounds on models for DAMA, CoGeNT, and CRESST-II. Phys. Rev. D 86, 015023 (2012). 
 arXiv:1112.5457
 
 " href="#ref-CR57" id="ref-link-section-d52098281e1261">57</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="G. Busoni, A. De Simone, E. Morgante, A. Riotto, On the validity of the effective field theory for dark matter searches at the LHC. Phys. Lett. B 728, 412–421 (2014). 
 arXiv:1307.2253
 
 " href="#ref-CR58" id="ref-link-section-d52098281e1261_1">58</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="G. Busoni, A. De Simone, J. Gramling, E. Morgante, A. Riotto, On the validity of the effective field theory for dark matter searches at the LHC, part II: complete analysis for the 
 
 
 
 $$s$$
 
 s
 
 -channel. JCAP 06, 060 (2014). 
 arXiv:1402.1275
 
 " href="#ref-CR59" id="ref-link-section-d52098281e1261_2">59</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="G. Busoni, A. De Simone, T. Jacques, E. Morgante, A. Riotto, On the validity of the effective field theory for dark matter searches at the LHC part III: analysis for the 
 
 
 
 $$t$$
 
 t
 
 -channel. JCAP 09, 022 (2014). 
 arXiv:1405.3101
 
 " href="#ref-CR60" id="ref-link-section-d52098281e1261_3">60</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="M. Endo, Y. Yamamoto, Unitarity bounds on dark matter effective interactions at LHC. JHEP 06, 126 (2014). 
 arXiv:1403.6610
 
 " href="#ref-CR61" id="ref-link-section-d52098281e1261_4">61</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="N. Bell, G. Busoni, A. Kobakhidze, D.M. Long, M.A. Schmidt, Unitarisation of EFT amplitudes for dark matter searches at the LHC. JHEP 08, 125 (2016). 
 arXiv:1606.02722
 
 " href="#ref-CR62" id="ref-link-section-d52098281e1261_5">62</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="D. Racco, A. Wulzer, F. Zwirner, Robust collider limits on heavy-mediator Dark Matter. JHEP 05, 009 (2015). 
 arXiv:1502.04701
 
 " href="#ref-CR63" id="ref-link-section-d52098281e1261_6">63</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 64" title="S. Bruggisser, F. Riva, A. Urbano, The last gasp of dark matter effective theory. JHEP 11, 069 (2016). 
 arXiv:1607.02475
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR64" id="ref-link-section-d52098281e1264">64</a>]. This is particularly true when considering constraints from the LHC, which may probe energies above the assumed scale of new physics. A naive application of the EFT in such a case may lead to unphysical predictions, such as unitarity violation. Whenever this is the case it becomes essential to adopt some form of truncation to ensure that only reliable predictions are used to calculate experimental constraints.</p><p>In the present work we address these challenges in two key ways. First, we separate the scale of new physics <span class="mathjax-tex">${\Lambda }$</span> from the individual Wilson coefficients <img src="//media.springernature.com/lw13/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq3_HTML.gif" style="width:13px;max-width:none;" alt=""> (rather than scanning over a combination such as <img src="//media.springernature.com/lw41/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq4_HTML.gif" style="width:41px;max-width:none;" alt="">), such that the former can be directly interpreted as the scale where the EFT breaks down and the latter can be constrained by perturbativity. Second, we check the impact of a phenomenological nuisance parameter that describes the possible modification of LHC spectra at energies beyond the range of EFT validity. The nuisance parameter smoothly interpolates between an abrupt truncation and no truncation at all.</p><p>Our analysis reveals viable parameter regions for general WIMP models across a wide range of new physics scales, including very small values of <span class="mathjax-tex">${\Lambda }$</span> (<span class="mathjax-tex">${\Lambda }< 200 \, \text {GeV}$</span>), where there are no relevant LHC constraints and very large values of <span class="mathjax-tex">${\Lambda }$</span> (<span class="mathjax-tex">${\Lambda }> 1.5 \,\text {TeV}$</span>), where LHC constraints are largely robust. Of particular interest are the intermediate values of <span class="mathjax-tex">${\Lambda }$</span> (<span class="mathjax-tex">${\Lambda }\sim 700{\text {--}} 900 \, \text {GeV}$</span>), for which our DM EFT partly accommodates several small LHC data excesses that could be interesting to analyse in more detail in the context of specific UV completions or simplified models. However, our analysis also reveals that there cannot be a large hierarchy between <span class="mathjax-tex">${\Lambda }$</span> and the DM mass <span class="mathjax-tex">$m_\chi $</span>. In particular, even with the most general set of operators we consider, it is impossible to simultaneously have a small DM mass (<span class="mathjax-tex">$m_\chi \lesssim 100 \, \text {GeV}$</span>) and a large new physics scale (<span class="mathjax-tex">${\Lambda }> 200 \, \text {GeV}$</span>). In other words, for light DM to be consistent with all constraints, it is necessary for the new physics scale to be so low that the EFT approach breaks down for the calculation of LHC constraints. For heavier DM, on the other hand, thermal production of DM in the early universe would exceed the observed abundance whenever <span class="mathjax-tex">${\Lambda }$</span> is more than one order of magnitude larger than <span class="mathjax-tex">$m_\chi $</span> (up to the unitarity bound at a few hundred TeV [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 65" title="K. Griest, M. Kamionkowski, Unitarity limits on the mass and radius of dark matter particles. Phys. Rev. Lett. 64, 615 (1990)" href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR65" id="ref-link-section-d52098281e1598">65</a>], where the maximum possible value of <span class="mathjax-tex">${\Lambda }$</span> approaches <span class="mathjax-tex">$m_\chi $</span>).</p><p>This work is organised as follows. We introduce the DM EFT description in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec2">2</a>. In Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec6">3</a>, we discuss the constraints used in this study, and our methods for computing likelihoods and observables. We present our results in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec16">4</a>. Finally, we present our conclusions in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec25">5</a>. The samples from our scans and the corresponding <span class="u-sans-serif">GAMBIT</span> input files, and plotting scripts can be downloaded from <span class="u-sans-serif">Zenodo</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 66" title="GAMBIT Collaboration, Supplementary data: thermal WIMPs and the scale of new physics: global fits of dirac dark matter effective field theories (2021). 
 https://zenodo.org/record/4836397
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR66" id="ref-link-section-d52098281e1663">66</a>].</p></div></div></section><section data-title="Dark matter effective field theory"><div class="c-article-section" id="Sec2-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec2"><span class="c-article-section__title-number">2 </span>Dark matter effective field theory</h2><div class="c-article-section__content" id="Sec2-content"><p>In this study, we consider possible interactions of SM fields with a Dirac fermion DM field, <span class="mathjax-tex">$\chi $</span>, that is a singlet under the SM gauge group. For phenomenological reasons discussed in detail in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec6">3</a>, we focus on interactions between <span class="mathjax-tex">$\chi $</span> and the quarks or gluons of the SM. We assume that the mediators that generate these interactions are heavier than the scales probed by the experiments under consideration. Following the notation of Refs. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 67" title="F. Bishara, J. Brod, B. Grinstein, J. Zupan, DirectDM: a tool for dark matter direct detection. 
 arXiv:1708.02678
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR67" id="ref-link-section-d52098281e1711">67</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 68" title="J. Brod, A. Gootjes-Dreesbach, M. Tammaro, J. Zupan, Effective field theory for dark matter direct detection up to dimension seven. JHEP 10, 065 (2018). 
 arXiv:1710.10218
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR68" id="ref-link-section-d52098281e1714">68</a>], the interaction Lagrangian for the theory can be written as</p><div id="Equ1" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw151/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ1_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (1) </div></div><p>where <img src="//media.springernature.com/lw30/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq21_HTML.gif" style="width:30px;max-width:none;" alt=""> is the DM-SM operator, <span class="mathjax-tex">$d\ge 5$</span> is the mass dimension of the operator, <img src="//media.springernature.com/lw29/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq23_HTML.gif" style="width:29px;max-width:none;" alt=""> is the dimensionless Wilson coefficient associated to <img src="//media.springernature.com/lw30/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq24_HTML.gif" style="width:30px;max-width:none;" alt="">, and <span class="mathjax-tex">${\Lambda }$</span> is the scale of new physics (which can be identified with the mediator mass). The full Lagrangian for the theory is then</p><div id="Equ2" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw233/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ2_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (2) </div></div><p>such that the free parameters of the theory are the DM mass <span class="mathjax-tex">$m_\chi $</span>, the scale of new physics <span class="mathjax-tex">${\Lambda }$</span>, and the set of dimensionless Wilson coefficients <img src="//media.springernature.com/lw42/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq28_HTML.gif" style="width:42px;max-width:none;" alt="">.</p><p>For sufficiently large <span class="mathjax-tex">${\Lambda }$</span>, the phenomenology at small energies is dominated by the operators of lowest dimension, and we therefore limit ourselves to <span class="mathjax-tex">$d \le 7$</span>. However, even this leaves a relatively large set of operators. The DM EFT that is valid below the electroweak (EW) scale (with the Higgs, <i>W</i>, <i>Z</i> and the top quark integrated out) contains 2 dimension five, 4 dimension six, and 22 dimension seven operators (not counting flavour multiplicities), while the DM EFT above the EW scale for a singlet Dirac fermion DM has 4 dimension five, 12 dimension six, and 41 dimension seven operators (again, not counting flavour multiplicities) [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 68" title="J. Brod, A. Gootjes-Dreesbach, M. Tammaro, J. Zupan, Effective field theory for dark matter direct detection up to dimension seven. JHEP 10, 065 (2018). 
 arXiv:1710.10218
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR68" id="ref-link-section-d52098281e1904">68</a>]. The large set of possible operators poses a challenge for a global statistical analysis where bounds on <span class="mathjax-tex">${\Lambda }$</span> and <img src="//media.springernature.com/lw42/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq32_HTML.gif" style="width:42px;max-width:none;" alt=""> are derived from experimental observations (see Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec6">3</a> for details). An added complexity is that we consider both processes where the typical energy transfer is above the EW scale (such as collider searches and indirect detection) as well as processes in which the energy release is small (direct detection). The consistent implementation of these bounds requires the combination of both DM EFTs, together with the appropriate matching conditions between the two.</p><p>To make the problem tractable we focus in our numerical analysis on a subset of DM EFT operators - the dimension six operators involving DM, <span class="mathjax-tex">$\chi $</span>, and SM quark fields, <i>q</i>,</p><div id="Equ3" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw161/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ3_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (3) </div></div><div id="Equ4" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw177/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ4_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (4) </div></div><div id="Equ5" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw177/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ5_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (5) </div></div><div id="Equ6" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw192/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ6_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (6) </div></div><p>The difference between the DM EFT below the EW scale and the DM EFT above the EW scale is in this case very simple: above the EW scale the quark flavours run over all SM quarks, including the top quark, while below the EW scale the top quark is absent.</p><p>While the above set of operators does not span the full dimension six bases of the two DM EFTs, it does collect the most relevant operators. The full dimension six operator basis contains operators where quarks are replaced by the SM leptons. These are irrelevant for the collider and direct detection constraints we consider, and are thus omitted for simplicity. The basis of dimension six operators for the DM EFT above the EW scale contains, in addition, operators that are products of DM and Higgs currents. These are expected to be tightly constrained by direct detection to have very small coefficients such that they are irrelevant in other observables, and are thus also dropped for simplicity.</p><p>To explore to what extent the numerical analyses would change, if the set of considered DM EFT operators were enlarged, we also perform global fits including, in addition to the dimension six operators (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Equ3">3</a>)–(<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Equ6">6</a>), a set of dimension seven operators that comprise interactions with the gluon field either through the QCD field strength tensor <span class="mathjax-tex">$G^a_{\mu \nu }$</span> or its dual <span class="mathjax-tex">${\widetilde{G}}_{\mu \nu }=\frac{1}{2}\epsilon _{\mu \nu \rho \sigma }G^{\rho \sigma }$</span>, as well as operators constructed from scalar, pseudoscalar and tensor bilinears:</p><div id="Equ7" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw188/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ7_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (7) </div></div><div id="Equ8" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw210/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ8_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (8) </div></div><div id="Equ9" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw180/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ9_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (9) </div></div><div id="Equ10" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw201/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ10_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (10) </div></div><div id="Equ11" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw144/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ11_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (11) </div></div><div id="Equ12" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw165/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ12_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (12) </div></div><div id="Equ13" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw166/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ13_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (13) </div></div><div id="Equ14" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw187/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ14_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (14) </div></div><div id="Equ15" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw196/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ15_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (15) </div></div><div id="Equ16" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw224/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ16_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (16) </div></div><p>The definition of the operators describing interactions with the gluons, <img src="//media.springernature.com/lw32/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq36_HTML.gif" style="width:32px;max-width:none;" alt="">, includes a loop factor since in most new physics models these operators are generated at one loop. Similarly, the couplings to scalar and tensor quark bilinears, <img src="//media.springernature.com/lw50/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq37_HTML.gif" style="width:50px;max-width:none;" alt="">, include a conventional factor of the quark mass <span class="mathjax-tex">$m_q$</span>, since they have the same flavour structure as the quark mass terms (coupling left-handed and right-handed quark fields). The <span class="mathjax-tex">$m_q$</span> suppression of these operators is thus naturally encountered in new physics models that satisfy low energy flavour constraints, such as minimal flavour violation and its extensions. Note that, unless explicitly stated otherwise, <span class="mathjax-tex">$m_q$</span> always refers to the running mass in the modified minimal subtraction (<span class="mathjax-tex">$\overline{\mathrm{MS}}$</span>) scheme.</p><p>The complete dimension-seven basis below the EW scale contains eight additional operators with derivatives acting on the DM fields [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 68" title="J. Brod, A. Gootjes-Dreesbach, M. Tammaro, J. Zupan, Effective field theory for dark matter direct detection up to dimension seven. JHEP 10, 065 (2018). 
 arXiv:1710.10218
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR68" id="ref-link-section-d52098281e2313">68</a>]. To simplify the discussion we do not include these operators in our analysis, partially because they do not lead to new chiral structures in the SM currents. Moreover, the direct detection constraints on these additional operators are expressible in terms of the operators that we do include in the global fits due to the non-relativistic nature of the scattering process.</p><p>Note that the operators <img src="//media.springernature.com/lw50/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq42_HTML.gif" style="width:50px;max-width:none;" alt=""> are not invariant under EW gauge transformations, and are thus replaced in the DM EFT above the EW scale by operators of the form <span class="mathjax-tex">$({\bar{\chi }}\chi )({\bar{q}}_Lq_R)H$</span>, where <i>H</i> is the Higgs doublet. In all the processes we consider, <i>H</i> can be replaced by its vacuum expectation value – either because the emission of the Higgs boson is phase-space suppressed or suppressed by small Yukawa couplings, or both. This means that, up to renormalization group effects (to be discussed in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec3">2.1</a>), the operators <img src="//media.springernature.com/lw50/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq44_HTML.gif" style="width:50px;max-width:none;" alt=""> can also be used in our fitting procedure above the EW scale.</p><p>In principle, analogous operators to <img src="//media.springernature.com/lw50/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq45_HTML.gif" style="width:50px;max-width:none;" alt=""> exist for leptons instead of quarks [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 69" title="J. Kopp, V. Niro, T. Schwetz, J. Zupan, DAMA/LIBRA and leptonically interacting Dark Matter. Phys. Rev. D 80, 083502 (2009). 
 arXiv:0907.3159
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR69" id="ref-link-section-d52098281e2436">69</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 70" title="P.J. Fox, R. Harnik, J. Kopp, Y. Tsai, LEP shines light on dark matter. Phys. Rev. D 84, 014028 (2011). 
 arXiv:1103.0240
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR70" id="ref-link-section-d52098281e2439">70</a>] and weak gauge bosons instead of gluons [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="N. Weiner, I. Yavin, UV completions of magnetic inelastic and Rayleigh dark matter for the Fermi line(s). Phys. Rev. D 87, 023523 (2013). 
 arXiv:1209.1093
 
 " href="#ref-CR71" id="ref-link-section-d52098281e2442">71</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="M.T. Frandsen, U. Haisch, F. Kahlhoefer, P. Mertsch, K. Schmidt-Hoberg, Loop-induced dark matter direct detection signals from gamma-ray lines. JCAP 10, 033 (2012). 
 arXiv:1207.3971
 
 " href="#ref-CR72" id="ref-link-section-d52098281e2442_1">72</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 73" title="G. Paz, A.A. Petrov, M. Tammaro, J. Zupan, Shining dark matter in Xenon1T. Phys. Rev. D 103, L051703 (2021). 
 https://doi.org/10.1103/PhysRevD.103.L051703
 
 . 
 arXiv:2006.12462
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR73" id="ref-link-section-d52098281e2445">73</a>].<sup><a href="#Fn1"><span class="u-visually-hidden">Footnote </span>1</a></sup> In general, these play a much smaller role in the phenomenology and will not be considered here. Similarly, throughout this work the Wilson coefficients of any dimension five operators are set to zero at the UV scale.</p><p>The Wilson coefficients of the operators defined above depend implicitly on the energy scale of the process under consideration. In our fits, all Wilson coefficients are specified at the new physics scale <span class="mathjax-tex">${\Lambda }$</span>. If this scale is larger than the top mass, <span class="mathjax-tex">${\Lambda }> m_t$</span>, all six quarks are active degrees of freedom and the Wilson coefficients need to be specified for <span class="mathjax-tex">$q = u, d, s, c, b, t$</span>. For <span class="mathjax-tex">${\Lambda }< m_t$</span>, the top quarks are integrated out, and only the Wilson coefficients for <span class="mathjax-tex">$q = u, d, s, c, b$</span> need to be specified. This is done automatically in our fitting procedures, such that effectively both EFTs are used in the fit, according to the numerical value of the scale <span class="mathjax-tex">${\Lambda }$</span>.</p><p>Although, a priori, the Wilson coefficients for each quark flavour are independent, we will restrict ourselves to the assumption of minimal flavour violation (which implies <img src="//media.springernature.com/lw133/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq52_HTML.gif" style="width:133px;max-width:none;" alt=""> and <img src="//media.springernature.com/lw133/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq53_HTML.gif" style="width:133px;max-width:none;" alt="">), and the assumption of isospin invariance (which implies <img src="//media.springernature.com/lw81/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq54_HTML.gif" style="width:81px;max-width:none;" alt="">).<sup><a href="#Fn2"><span class="u-visually-hidden">Footnote </span>2</a></sup> Hence, each operator comes with only one free parameter in addition to the global parameters <span class="mathjax-tex">${\Lambda }$</span> and <span class="mathjax-tex">$m_\chi $</span>. Under these assumptions, the two EFTs above and below the EW scale have the same number of free parameters.</p><h3 class="c-article__sub-heading" id="Sec3"><span class="c-article-section__title-number">2.1 </span>Running and mixing</h3><p>For many applications, the RG running of the Wilson coefficients (i.e. their dependence on the energy scale <span class="mathjax-tex">$\mu $</span>) can be neglected. In fact, the operators <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq59_HTML.gif" style="width:31px;max-width:none;" alt="">, <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq60_HTML.gif" style="width:31px;max-width:none;" alt="">, <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq61_HTML.gif" style="width:31px;max-width:none;" alt=""> and <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq62_HTML.gif" style="width:31px;max-width:none;" alt=""> have vanishing anomalous dimension, while <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq63_HTML.gif" style="width:31px;max-width:none;" alt="">, <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq64_HTML.gif" style="width:31px;max-width:none;" alt="">, <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq65_HTML.gif" style="width:31px;max-width:none;" alt="">, <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq66_HTML.gif" style="width:31px;max-width:none;" alt=""> as well as <img src="//media.springernature.com/lw32/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq67_HTML.gif" style="width:32px;max-width:none;" alt=""> exhibit no running at one-loop order in QCD [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 77" title="R.J. Hill, M.P. Solon, Standard model anatomy of WIMP dark matter direct detection II: QCD analysis and hadronic matrix elements. Phys. Rev. D 91, 043505 (2015). 
 arXiv:1409.8290
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR77" id="ref-link-section-d52098281e2831">77</a>]. Nevertheless, there are two cases when the effects of running can be important: </p><ol class="u-list-style-none"> <li> <span class="u-custom-list-number">1.</span> <p><b>Mixing:</b> Different operators can mix with each other under RG evolution, such that operators assumed negligible at one scale may give a relevant contribution at a different scale. This is particularly important in the context of direct detection, because for certain operators the DM-nucleon scattering cross-section is strongly suppressed in the non-relativistic limit. In such a case, the dominant contribution to direct detection may arise from operators induced only at the loop level [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 78" title="F. Bishara, J. Brod, B. Grinstein, J. Zupan, Renormalization group effects in dark matter interactions. JHEP 03, 089 (2020). 
 arXiv:1809.03506
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR78" id="ref-link-section-d52098281e2847">78</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 79" title="J. Brod, B. Grinstein, E. Stamou, J. Zupan, Weak mixing below the weak scale in dark-matter direct detection. JHEP 02, 174 (2018). 
 arXiv:1801.04240
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR79" id="ref-link-section-d52098281e2850">79</a>]. In our case, the dominant effects arise from the top quark Yukawa and are discussed below.</p> </li> <li> <span class="u-custom-list-number">2.</span> <p><b>Threshold corrections:</b> Whenever the scale <span class="mathjax-tex">$\mu $</span> drops below the mass of one of the quarks, the number of active degrees of freedom is reduced and a finite correction to various operators arises. In our context, the only effect is the matching of the operators <img src="//media.springernature.com/lw43/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq69_HTML.gif" style="width:43px;max-width:none;" alt=""> onto the operators <img src="//media.springernature.com/lw32/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq70_HTML.gif" style="width:32px;max-width:none;" alt=""> at the heavy quark thresholds, which is given by </p><div id="Equ17" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw137/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ17_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (17) </div></div><p> Mixing of the tensor operators <img src="//media.springernature.com/lw78/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq71_HTML.gif" style="width:78px;max-width:none;" alt=""> above the EW scale and subsequent matching gives rise to the dimension-five dipole operators </p><div id="Equ18" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw175/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ18_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (18) </div></div><div id="Equ19" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw199/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ19_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (19) </div></div><p> where <span class="mathjax-tex">$F_{\mu \nu }$</span> is the electromagnetic field strength tensor and <i>e</i> is the electromagnetic charge. These operators give an important contribution to direct detection experiments and are thus kept.<sup><a href="#Fn3"><span class="u-visually-hidden">Footnote </span>3</a></sup></p> </li> </ol><p>In the present work we include these effects as follows. To calculate the Wilson coefficients at the hadronic scale <span class="mathjax-tex">$\mu = 2\,\text {GeV}$</span> (relevant for direct detection) we make use of the public code <span class="u-sans-serif">DirectDM</span> <span class="u-sans-serif">v2.2.0</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 67" title="F. Bishara, J. Brod, B. Grinstein, J. Zupan, DirectDM: a tool for dark matter direct detection. 
 arXiv:1708.02678
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR67" id="ref-link-section-d52098281e3036">67</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 68" title="J. Brod, A. Gootjes-Dreesbach, M. Tammaro, J. Zupan, Effective field theory for dark matter direct detection up to dimension seven. JHEP 10, 065 (2018). 
 arXiv:1710.10218
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR68" id="ref-link-section-d52098281e3039">68</a>], which calculates the RG evolution of the operators defined above, including threshold corrections and mixing effects. The code furthermore performs a matching of the resulting operators at <span class="mathjax-tex">$\mu = 2\,\text {GeV}$</span> onto the basis of non-relativistic effective operators relevant for DM direct detection (see Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec7">3.1</a>).</p><p><span class="u-sans-serif">DirectDM</span> currently requires as input the Wilson coefficients in the five-flavour scheme given at the scale <span class="mathjax-tex">$m_Z = 91.1876\,\text {GeV}$</span>. For <span class="mathjax-tex">${\Lambda }< m_t$</span> (five-flavour EFT), we can therefore directly pass the Wilson coefficients defined above to <span class="u-sans-serif">DirectDM</span>. For <span class="mathjax-tex">${\Lambda }> m_t$</span> (six-flavour EFT), there are three additional effects that are considered. First, as pointed out in Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 80" title="U. Haisch, F. Kahlhoefer, On the importance of loop-induced spin-independent interactions for dark matter direct detection. JCAP 1304, 050 (2013). 
 arXiv:1302.4454
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR80" id="ref-link-section-d52098281e3175">80</a>], the operators <img src="//media.springernature.com/lw46/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq80_HTML.gif" style="width:46px;max-width:none;" alt=""> give a contribution to the dipole operators <img src="//media.springernature.com/lw30/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq81_HTML.gif" style="width:30px;max-width:none;" alt=""> at the one-loop level, which is given by<sup><a href="#Fn4"><span class="u-visually-hidden">Footnote </span>4</a></sup></p><div id="Equ20" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw279/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ20_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (20) </div></div><p>Second, as pointed out first in Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 81" title="A. Crivellin, F. D’Eramo, M. Procura, New constraints on dark matter effective theories from standard model loops. Phys. Rev. Lett. 112, 191304 (2014). 
 arXiv:1402.1173
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR81" id="ref-link-section-d52098281e3310">81</a>], the operator with an axial-vector top-quark current <img src="//media.springernature.com/lw29/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq84_HTML.gif" style="width:29px;max-width:none;" alt=""> mixes into the operators <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq85_HTML.gif" style="width:31px;max-width:none;" alt=""> with light quark vector currents. The relevant effects are given by [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 78" title="F. Bishara, J. Brod, B. Grinstein, J. Zupan, Renormalization group effects in dark matter interactions. JHEP 03, 089 (2020). 
 arXiv:1809.03506
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR78" id="ref-link-section-d52098281e3330">78</a>]</p><div id="Equ21" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw313/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ21_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (21) </div></div><p>after integrating out the <i>Z</i> boson at the weak scale. Here, <span class="mathjax-tex">$s_w\equiv \sin \theta _w$</span> with <span class="mathjax-tex">$\theta _w$</span> the weak mixing angle, and <span class="mathjax-tex">$v=246\,$</span>GeV is the Higgs field vacuum expectation value. The flavour universal UV contributions <img src="//media.springernature.com/lw69/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq89_HTML.gif" style="width:69px;max-width:none;" alt=""> largely compensate the mixing effect in the fit; the remnant effect, due to the isospin-breaking <i>Z</i> couplings, is small.</p><p>Third, in order to match the EFT with six active quark flavours onto the five-flavour scheme, we need to integrate out the top quark and apply the top quark threshold corrections given in Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Equ17">17</a>). We neglect any other effects of RG evolution between the scales <span class="mathjax-tex">${\Lambda }$</span> and <span class="mathjax-tex">$m_Z$</span>, i.e. all Wilson coefficients other than <img src="//media.springernature.com/lw30/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq92_HTML.gif" style="width:30px;max-width:none;" alt=""> and <img src="//media.springernature.com/lw32/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq93_HTML.gif" style="width:32px;max-width:none;" alt=""> are directly passed to <span class="u-sans-serif">DirectDM</span>.<sup><a href="#Fn5"><span class="u-visually-hidden">Footnote </span>5</a></sup></p><p>For the purpose of calculating the LHC constraints, we neglect the effects of running and do not consider loop-induced mixing between different operators, which is a good approximation for the operators <img src="//media.springernature.com/lw43/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq94_HTML.gif" style="width:43px;max-width:none;" alt=""> and <img src="//media.springernature.com/lw32/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq95_HTML.gif" style="width:32px;max-width:none;" alt="">. For the operators <img src="//media.springernature.com/lw50/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq96_HTML.gif" style="width:50px;max-width:none;" alt=""> mixing effects are known to be important in principle [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 82" title="U. Haisch, F. Kahlhoefer, J. Unwin, The impact of heavy-quark loops on LHC dark matter searches. JHEP 07, 125 (2013). 
 arXiv:1208.4605
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR82" id="ref-link-section-d52098281e3546">82</a>], but these operators are currently unconstrained by the LHC in the parameter region where the EFT is valid (see Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec4">2.2</a>). Likewise we also calculate DM annihilation cross-sections at tree level. In particular, in these calculations we neglect the running of the strong coupling <span class="mathjax-tex">$(\alpha _s)$</span> and use the pole quark masses <span class="mathjax-tex">$(m_q^{\text {pole}})$</span> instead of the running quark masses. Moreover, we neglect a small loop-level contribution from the operators <img src="//media.springernature.com/lw43/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq99_HTML.gif" style="width:43px;max-width:none;" alt=""> to the operators <img src="//media.springernature.com/lw32/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq100_HTML.gif" style="width:32px;max-width:none;" alt="">.</p><h3 class="c-article__sub-heading" id="Sec4"><span class="c-article-section__title-number">2.2 </span>EFT validity</h3><p>A central concern when employing an EFT to capture the effects of new physics is that the scale of new physics must be sufficiently large compared to the energy scales of interest for the EFT description to be valid. Unfortunately, the point at which the EFT breaks down is difficult to determine from the low-energy theory alone. Considerations of unitarity violation make it possible to determine the scale where the EFT becomes unphysical, but in many cases the EFT description already fails at lower energies, in particular if the UV completion is weakly coupled.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-1" data-title="Fig. 1"><figure><figcaption><b id="Fig1" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 1</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/1" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig1_HTML.png?as=webp"><img aria-describedby="Fig1" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig1_HTML.png" alt="figure 1" loading="lazy" width="685" height="368"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-1-desc"><p>Illustration of our approach for studying DM EFTs compared to a more naive approach, in which one only uses the experiment that yields the strongest bound on <span class="mathjax-tex">$C / {\Lambda }^2$</span>. The resulting exclusion is indicated by the red shaded region. By independently varying <span class="mathjax-tex">${\Lambda }$</span>, we can include additional information from experiments that give weaker bounds on <span class="mathjax-tex">$C / {\Lambda }^2$</span> but for which the EFT has a larger range of validity. The additional exclusion obtained in this way is indicated by the blue shaded region. The region of parameter space that corresponds to the non-perturbative values of Wilson coefficient <i>C</i> is excluded in either approach (shaded brown)</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/1" data-track-dest="link:Figure1 Full size image" aria-label="Full size image figure 1" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>To address this issue in the present study, we simultaneously vary the overall scale <span class="mathjax-tex">${\Lambda }$</span>, which corresponds to the energy where new degrees of freedom become relevant and the EFT description breaks down, and the Wilson coefficients <img src="//media.springernature.com/lw29/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq105_HTML.gif" style="width:29px;max-width:none;" alt=""> for each operator. Doing so introduces a degeneracy, because cross sections are invariant under the rescaling <span class="mathjax-tex">${\Lambda }\rightarrow \alpha {\Lambda }$</span> and <img src="//media.springernature.com/lw121/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq107_HTML.gif" style="width:121px;max-width:none;" alt="">. However, the advantage of this approach is that the parameter <span class="mathjax-tex">${\Lambda }$</span> can be used to determine which constraints can be trusted in the EFT limit. This is illustrated in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig1">1</a>, which compares our approach of varying <span class="mathjax-tex">${\Lambda }$</span> and <img src="//media.springernature.com/lw29/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq110_HTML.gif" style="width:29px;max-width:none;" alt=""> separately to the naive approach where only <img src="//media.springernature.com/lw75/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq111_HTML.gif" style="width:75px;max-width:none;" alt=""> is constrained.</p><p>We emphasize that this approach assumes the same new-physics scale for all effective operators, even though they may be generated through different mechanisms, and hence at different scales, in the UV. In practice, one should think of <span class="mathjax-tex">${\Lambda }$</span> as the minimum of all of these scales, i.e. the energy at which new degrees of freedom first become relevant. These new degrees of freedom may not contribute to all processes, such that some effective operators may provide an accurate description even at energies above <span class="mathjax-tex">${\Lambda }$</span>. Whether or not this is the case cannot be determined from the low-energy viewpoint, such that we conservatively limit the EFT validity to energies below <span class="mathjax-tex">${\Lambda }$</span>.</p><p>For the purpose of direct detection constraints, the only requirement on <span class="mathjax-tex">${\Lambda }$</span> is that it is larger than the hadronic scale, so that the effective operators can be written in terms of free quarks and gluons. This is the case for <span class="mathjax-tex">${\Lambda } > rsim 2\,\text {GeV}$</span>, which will always be satisfied in the present study. However, in order to evaluate direct detection constraints, it is necessary to determine the relic abundance of DM particles, which depends on the cross-sections for the processes <span class="mathjax-tex">$\chi \chi \rightarrow q q$</span> or <span class="mathjax-tex">$\chi \chi \rightarrow g g$</span>, just as in the case of indirect detection constraints (see Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec9">3.3</a>). For this calculation to be meaningful in the EFT framework, we require <span class="mathjax-tex">${\Lambda }> 2 m_\chi $</span>. Parameter points with smaller values of <span class="mathjax-tex">${\Lambda }$</span> will thus be invalidated. A dedicated study of direct detection constraints for <span class="mathjax-tex">${\Lambda }< 2 m_\chi $</span> will be left for future work.</p><p>In the context of LHC searches for DM, EFT validity requires that the invariant mass of the DM pair produced in a collision satisfies <span class="mathjax-tex">$m_{\chi \chi } < {\Lambda }$</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 83" title="A. Berlin, T. Lin, L.-T. Wang, Mono-Higgs detection of dark matter at the LHC. JHEP 06, 078 (2014). 
 arXiv:1402.7074
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR83" id="ref-link-section-d52098281e4160">83</a>]. To obtain robust constraints, only events with smaller energy transfer should be included in the calculation of likelihoods. The problem with this prescription is that <span class="mathjax-tex">$m_{\chi \chi }$</span> does not directly correspond to any observable quantity (such as the missing energy <img src="//media.springernature.com/lw21/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq124_HTML.gif" style="width:21px;max-width:none;" alt=""> of the event) and hence the impact of varying <span class="mathjax-tex">${\Lambda }$</span> on predicted LHC spectra is difficult to assess. One possible way to address this issue would be to generate new LHC events for each parameter point and include only those events with small enough <span class="mathjax-tex">$m_{\chi \chi }$</span> in the likelihood calculation, but this is not computationally feasible in the context of a global scan.</p><p>In the present work, we adopt the following simpler approach: Rather than comparing <span class="mathjax-tex">${\Lambda }$</span> to the invariant mass of the DM pair, we compare it to the typical overall energy scale of the event, which can be estimated by the amount of missing energy produced. In other words, we do not modify the missing energy spectrum for <img src="//media.springernature.com/lw57/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq128_HTML.gif" style="width:57px;max-width:none;" alt=""> and only apply the EFT validity requirement for larger values of <img src="//media.springernature.com/lw21/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq129_HTML.gif" style="width:21px;max-width:none;" alt="">. This approach is less conservative than the one advocated, for instance in Refs. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 63" title="D. Racco, A. Wulzer, F. Zwirner, Robust collider limits on heavy-mediator Dark Matter. JHEP 05, 009 (2015). 
 arXiv:1502.04701
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR63" id="ref-link-section-d52098281e4281">63</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 64" title="S. Bruggisser, F. Riva, A. Urbano, The last gasp of dark matter effective theory. JHEP 11, 069 (2016). 
 arXiv:1607.02475
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR64" id="ref-link-section-d52098281e4284">64</a>], where the energy scale of the event is taken to be the partonic centre-of-mass energy <span class="mathjax-tex">$\sqrt{{\hat{s}}}$</span>, but it has the crucial advantage that it can be applied <i>after</i> event generation, since the differential cross-section with respect to missing energy <img src="//media.springernature.com/lw56/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq131_HTML.gif" style="width:56px;max-width:none;" alt=""> is exactly the quantity that is directly compared to data.<sup><a href="#Fn6"><span class="u-visually-hidden">Footnote </span>6</a></sup></p><p>In the following, we will consider two different prescriptions for how to impose the EFT validity. The first one is to introduce a hard cut-off, i.e. to set <img src="//media.springernature.com/lw88/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq138_HTML.gif" style="width:88px;max-width:none;" alt=""> for <img src="//media.springernature.com/lw57/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq139_HTML.gif" style="width:57px;max-width:none;" alt="">. The second, more realistic, prescription is to introduce a smooth cut-off that leads to a non-zero but steeply falling missing energy spectrum above <span class="mathjax-tex">${\Lambda }$</span>. For this we make the replacement</p><div id="Equ22" class="c-article-equation"><div class="c-article-equation__content"><img src="//media.springernature.com/lw172/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Equ22_HTML.png" class="u-display-block" alt=""></div><div class="c-article-equation__number"> (22) </div></div><p>for <img src="//media.springernature.com/lw57/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq141_HTML.gif" style="width:57px;max-width:none;" alt="">. Here <i>a</i> is a free parameter that depends on the specific UV completion. The limits <span class="mathjax-tex">$ a \rightarrow 0 $</span> and <span class="mathjax-tex">$a \rightarrow \infty $</span> correspond to no truncation and an abrupt truncation above the cut-off, respectively. For the case that the EFT results from the exchange of an <i>s</i>-channel mediator with mass close to <span class="mathjax-tex">${\Lambda }$</span>, one finds <span class="mathjax-tex">$a \approx 2$</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 30" title="O. Buchmueller, M.J. Dolan, C. McCabe, Beyond effective field theory for dark matter searches at the LHC. JHEP 01, 025 (2014). 
 arXiv:1308.6799
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR30" id="ref-link-section-d52098281e4553">30</a>]. Rather than taking inspiration from a specific UV completion, we will instead keep <i>a</i> as a free parameter in the interval [0, 4] and find the value that gives the best fit to data at each parameter point. This approach typically leads to conservative LHC bounds in the sense that much stronger exclusions may be obtained in specific UV completions, if the heavy particles that generate the effective DM interactions can be directly produced at the LHC. However, this truncation procedure can lead to unrealistic spectral shapes with sharp features that may be tuned to fit fluctuations in the data. As will be discussed in more detail in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec16">4</a>, any explanation of data excesses through this approach must be interpreted with care.</p><p>Without upper bounds on the Wilson coefficients, any requirement on EFT validity could be satisfied by making both <span class="mathjax-tex">${\Lambda }$</span> and the Wilson coefficients arbitrarily large. We therefore require <img src="//media.springernature.com/lw71/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq147_HTML.gif" style="width:71px;max-width:none;" alt="">, which is necessary for a perturbative UV completion and ensures that there is no unitarity violation in the validity range of the EFT [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 62" title="N. Bell, G. Busoni, A. Kobakhidze, D.M. Long, M.A. Schmidt, Unitarisation of EFT amplitudes for dark matter searches at the LHC. JHEP 08, 125 (2016). 
 arXiv:1606.02722
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR62" id="ref-link-section-d52098281e4591">62</a>].</p><p>One drawback of this prescription is that the EFT validity requirement depends on the normalisation of the effective operators. For example, we have written <img src="//media.springernature.com/lw32/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq148_HTML.gif" style="width:32px;max-width:none;" alt=""> with a prefactor <span class="mathjax-tex">$\alpha _s / (12\pi )$</span> and <img src="//media.springernature.com/lw32/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq150_HTML.gif" style="width:32px;max-width:none;" alt=""> with a prefactor <span class="mathjax-tex">$\alpha _s / (8\pi )$</span> to reflect the fact that in many UV completions, these operators would be generated at the one-loop level. If these operators are instead generated at tree level (e.g. from a strongly interacting theory), it would be more appropriate to write the prefactor as <span class="mathjax-tex">$4\pi \alpha _s$</span>. With the latter convention any constraint on the new physics scale <span class="mathjax-tex">${\Lambda }$</span> becomes stronger by a factor <span class="mathjax-tex">$(48\pi ^2)^{1/3} \approx 5.3$</span> for <img src="//media.springernature.com/lw32/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq155_HTML.gif" style="width:32px;max-width:none;" alt=""> and by a factor <span class="mathjax-tex">$(32\pi ^2)^{1/3} \approx 4.6$</span> for <img src="//media.springernature.com/lw32/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq157_HTML.gif" style="width:32px;max-width:none;" alt="">, meaning that much larger values of <span class="mathjax-tex">${\Lambda }$</span> are experimentally testable and the range of EFT validity is substantially increased. We have confirmed explicitly that the results presented in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec16">4</a> do not depend on the specific definition of the Wilson coefficients for <img src="//media.springernature.com/lw32/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq159_HTML.gif" style="width:32px;max-width:none;" alt="">.<sup><a href="#Fn7"><span class="u-visually-hidden">Footnote </span>7</a></sup></p><h3 class="c-article__sub-heading" id="Sec5"><span class="c-article-section__title-number">2.3 </span>Parameter ranges</h3><p>In this study we focus on the following parameter regions. In order to be able to neglect QCD resonances in the process <span class="mathjax-tex">$\chi {\bar{\chi }} \rightarrow q {\bar{q}}$</span>, we restrict ourselves to <span class="mathjax-tex">$m_\chi > 5\,\text {GeV}$</span>. In order to have a sufficiently large separation of scales between the new physics scale <span class="mathjax-tex">${\Lambda }$</span> and the hadronic scale, we also require <span class="mathjax-tex">${\Lambda }> 20\,\text {GeV}$</span>. As discussed in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec4">2.2</a>, we furthermore impose the bound <img src="//media.springernature.com/lw80/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq166_HTML.gif" style="width:80px;max-width:none;" alt=""> on all Wilson coefficients and the bound <span class="mathjax-tex">${\Lambda }> 2 m_\chi $</span>. The upper bounds on <span class="mathjax-tex">$m_\chi $</span> and <span class="mathjax-tex">${\Lambda }$</span> depend on the details of the scans that we perform and will be discussed in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec16">4</a>.</p></div></div></section><section data-title="Constraints"><div class="c-article-section" id="Sec6-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec6"><span class="c-article-section__title-number">3 </span>Constraints</h2><div class="c-article-section__content" id="Sec6-content"><p>In this section we describe the constraints relevant for our model. A summary of all likelihoods included in our scans is provided in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Tab1">1</a>. For each likelihood that directly constrains the interactions of the DM particle we also quote the background-only log-likelihood <span class="mathjax-tex">$\ln {\mathcal {L}}^{\text {bg}}$</span> obtained when setting all Wilson coefficients to zero. For the remaining likelihoods we instead quote the maximum achievable value of the log-likelihood <span class="mathjax-tex">$\ln {\mathcal {L}}^{\text {max}}$</span>. The sum of all these contributions, <span class="mathjax-tex">$\ln {\mathcal {L}}^{\text {ideal}} = -105.3$</span> will be used to calculate log-likelihood differences below.</p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-1"><figure><figcaption class="c-article-table__figcaption"><b id="Tab1" data-test="table-caption">Table 1 Likelihoods included in our scans and their respective values for the background-only hypothesis. For each likelihood that directly constrains the interactions of the DM particle we also quote the background-only log-likelihood <span class="mathjax-tex">$\ln {\mathcal {L}}^{\text {bg}}$</span> obtained when setting all Wilson coefficients to zero. For the remaining likelihoods we instead quote the maximum achievable value of the log-likelihood <span class="mathjax-tex">$\ln {\mathcal {L}}^{\text {max}}$</span></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-09712-6/tables/1" aria-label="Full size table 1"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><h3 class="c-article__sub-heading" id="Sec7"><span class="c-article-section__title-number">3.1 </span>Direct detection</h3><p>Direct detection experiments search for the scattering of DM particles from the Galactic halo off nuclei in an ultra-pure target by measuring the energy <span class="mathjax-tex">$E_{\text {R}}$</span> of recoiling nuclei. The differential event rate with respect to recoil energy is given by</p><div id="Equ23" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} \frac{{\text {d}}R}{{\text {d}}E_{\text {R}}} = \frac{\rho _0}{m_T \, m_\chi } \int _{v_{\text {min}}}^\infty v f(v) \frac{{\text {d}} \sigma }{\text {d} E_{{\text {R}}}} {\text {d}}^3 v\; , \end{aligned}$$</span></div><div class="c-article-equation__number"> (23) </div></div><p>where <span class="mathjax-tex">$\rho _0$</span> is the local DM density, <span class="mathjax-tex">$m_T$</span> is the target nucleus mass, <i>f</i>(<i>v</i>) is the local DM velocity distribution and</p><div id="Equ24" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} v_{\text {min}}(E_{\text {R}}) = \sqrt{\frac{m_T E_{\text {R}}}{2 \, \mu ^2}} \end{aligned}$$</span></div><div class="c-article-equation__number"> (24) </div></div><p>is the minimal DM velocity to cause a recoil carrying away a kinetic energy <span class="mathjax-tex">$E_{\text {R}}$</span>, where <span class="mathjax-tex">$\mu = m_T \, m_\chi / (m_T + m_\chi )$</span> is the reduced mass of the DM-nucleus system.</p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-2"><figure><figcaption class="c-article-table__figcaption"><b id="Tab2" data-test="table-caption">Table 2 A full list of dimension-6 and 7 operators included in this study, and the types of interactions they induce. For the DM-nucleon scattering cross-section, we distinguish between spin-independent (SI) and spin-dependent (SD) interactions, with the former receiving a large coherent enhancement and the latter vanishing for nuclei with zero spin. We use “unsuppressed” (“suppressed”) to denote tree-level contributions that do not vanish (that vanish) in the zero-velocity limit, while “loop-induced” implies that an unsuppressed interaction is induced at the one-loop level. For the annihilation cross-section we use “<i>s</i>-wave” (“<i>p</i>-wave”) to denote annihilations that do not vanish (that vanish) in the zero-velocity limit. Note that if the <i>s</i>-wave contribution is helicity suppressed (i.e. proportional to <span class="mathjax-tex">$m_q^2 / m_\chi ^2$</span>), the <i>p</i>-wave contribution may dominate in the relic density calculation</b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-09712-6/tables/2" aria-label="Full size table 2"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>The local DM density and velocity distribution are not very well known and introduce sizeable uncertainties in the prediction of experimental signals (see the discussion of nuisance parameters in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec15">3.6</a>). Nevertheless, the greatest challenge in the present context is the calculation of the differential scattering cross-section <span class="mathjax-tex">$\text {d}\sigma / \text {d}E_{\text {R}}$</span>. For this purpose, one needs to map the effective interactions between relativistic DM particles and quarks or gluons defined above onto effective interactions between non-relativistic DM particles and nucleons <span class="mathjax-tex">$N = p,n$</span>. The EFT of non-relativistic interactions can be written as</p><div id="Equ25" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} {\mathcal {L}}_{\text {NR}} = \sum _{i,N} c_i^N(q^2) \, {\mathcal {O}}^N_i, \end{aligned}$$</span></div><div class="c-article-equation__number"> (25) </div></div><p>where the operators <span class="mathjax-tex">${\mathcal {O}}^N_i$</span> depend only on the DM spin <span class="mathjax-tex">$\mathbf {S}_\chi $</span>, the nucleon spin <span class="mathjax-tex">$\mathbf {S}_N$</span>, the momentum transfer <span class="mathjax-tex">$\mathbf {q}$</span> and the DM-nucleon relative velocity <span class="mathjax-tex">$\mathbf {v}$</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 4" title="J. Fan, M. Reece, L.-T. Wang, Non-relativistic effective theory of dark matter direct detection. JCAP 1011, 042 (2010). 
 arXiv:1008.1591
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR4" id="ref-link-section-d52098281e7570">4</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 53" title="A.L. Fitzpatrick, W. Haxton, E. Katz, N. Lubbers, Y. Xu, The effective field theory of dark matter direct detection. JCAP 1302, 004 (2013). 
 arXiv:1203.3542
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR53" id="ref-link-section-d52098281e7573">53</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 99" title="N. Anand, A.L. Fitzpatrick, W.C. Haxton, Weakly interacting massive particle-nucleus elastic scattering response. Phys. Rev. C 89, 065501 (2014). 
 arXiv:1308.6288
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR99" id="ref-link-section-d52098281e7577">99</a>].</p><p>The non-relativistic operators can be divided into four categories according to whether or not they depend on the nucleon spin <span class="mathjax-tex">$\mathbf {S}_N$</span>, such that scattering is suppressed for nuclei with vanishing spin, and whether or not they depend on <span class="mathjax-tex">$\mathbf {q}$</span> and/or <span class="mathjax-tex">$\mathbf {v}$</span>, such that scattering is suppressed in the non-relativistic limit. Specifically, <span class="mathjax-tex">${\mathcal {O}}^N_1$</span> leads to spin-independent (SI) unsuppressed scattering, <span class="mathjax-tex">${\mathcal {O}}^N_4$</span> leads to spin-dependent (SD) unsuppressed scattering, <span class="mathjax-tex">${\mathcal {O}}^N_5$</span>, <span class="mathjax-tex">${\mathcal {O}}^N_8$</span>, <span class="mathjax-tex">${\mathcal {O}}^N_{11}$</span> lead to SI momentum-suppressed scattering and <span class="mathjax-tex">${\mathcal {O}}^N_6$</span>, <span class="mathjax-tex">${\mathcal {O}}^N_7$</span>, <span class="mathjax-tex">${\mathcal {O}}^N_9$</span>, <span class="mathjax-tex">${\mathcal {O}}^N_{10}$</span>, <span class="mathjax-tex">${\mathcal {O}}^N_{12}$</span> lead to SD momentum-suppressed scattering, which is typically unobservable. For the relativistic operators included in this study we give the dominant type of interaction they induce in the non-relativistic limit in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Tab2">2</a>.</p><p>The coefficients <span class="mathjax-tex">$c_i^N(q^2)$</span> can be directly calculated from the Wilson coefficients of the relativistic operators at <span class="mathjax-tex">$\mu = 2\,\text {GeV}$</span>. The explicit dependence on the momentum transfer <span class="mathjax-tex">$q = \sqrt{2 m_T E_{\text {R}}}$</span> is a result of two effects. First, under RG evolution some of the effective DM-quark operators mix into the DM dipole operators <img src="//media.springernature.com/lw30/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq239_HTML.gif" style="width:30px;max-width:none;" alt=""> (see Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Equ20">20</a>)). These operators then induce long-range interactions, i.e. contributions to the <span class="mathjax-tex">$c_i^N(q^2)$</span> that scale as <span class="mathjax-tex">$q^{-2}$</span>. Since the momentum transfer can be very small in direct detection experiments, these contributions can be important in spite of their loop suppression. Second, the coefficients include nuclear form factors, obtained by evaluating expectation values of quark currents like <span class="mathjax-tex">$\langle N' | {\overline{q}} \gamma ^\mu q | N \rangle $</span>. These form factors can be calculated in chiral perturbation theory and exhibit a pion pole for axial and pseudoscalar currents, i.e. a divergence for <span class="mathjax-tex">$q \rightarrow m_\pi $</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 100" title="F. Bishara, J. Brod, B. Grinstein, J. Zupan, Chiral effective theory of dark matter direct detection. JCAP 1702, 009 (2017). 
 arXiv:1611.00368
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR100" id="ref-link-section-d52098281e8213">100</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 101" title="F. Bishara, J. Brod, B. Grinstein, J. Zupan, From quarks to nucleons in dark matter direct detection. JHEP 11, 059 (2017). 
 arXiv:1707.06998
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR101" id="ref-link-section-d52098281e8216">101</a>].</p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-3"><figure><figcaption class="c-article-table__figcaption"><b id="Tab3" data-test="table-caption">Table 3 The hadronic input parameters as used in <span class="u-sans-serif">DirectDM</span> <span class="u-sans-serif">v2.2.0</span></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-09712-6/tables/3" aria-label="Full size table 3"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>All of these effects are fully taken into account in <span class="mathjax-tex">$\textsf {DirectDM} $</span>, which calculates the coefficients <span class="mathjax-tex">$c_i^N(q^2)$</span> for given Wilson coefficients <img src="//media.springernature.com/lw29/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq279_HTML.gif" style="width:29px;max-width:none;" alt=""> at a higher scale (see App. A). These coefficients are then passed onto <span class="u-sans-serif">DDCalc v2.2.0</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 52" title="GAMBIT Dark Matter Workgroup: T. Bringmann, J. Conrad et al., DarkBit: a GAMBIT module for computing dark matter observables and likelihoods. Eur. Phys. J. C 77, 831 (2017). 
 arXiv:1705.07920
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR52" id="ref-link-section-d52098281e9671">52</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 110" title="GAMBIT Collaboration: P. Athron et al., Global analyses of Higgs portal singlet dark matter models using GAMBIT. Eur. Phys. J. C 79, 38 (2019). 
 arXiv:1808.10465
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR110" id="ref-link-section-d52098281e9675">110</a>], which calculates the differential cross-section for each operator <span class="mathjax-tex">${\mathcal {O}}^N_i$</span> (including interference) and target element of interest. <span class="u-sans-serif">DDCalc</span> also performs the velocity integrals needed for the calculation of the differential event rate, and the convolution with energy resolution and detector acceptance needed to predict signals in specific experiments:</p><div id="Equ26" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} N_p = M \, T_{\text {exp}} \int \phi (E_{\text {R}}) \, \frac{\text {d}R}{\text {d}E_{\text {R}}} \, \text {d}E_{\text {R}}, \end{aligned}$$</span></div><div class="c-article-equation__number"> (26) </div></div><p>where <i>M</i> is the detector mass, <span class="mathjax-tex">$T_{\text {exp}}$</span> is the exposure time and <span class="mathjax-tex">$\phi (E_{\text {R}})$</span> is the acceptance function.</p><p>By combining <span class="u-sans-serif">DirectDM</span> and <span class="u-sans-serif">DDCalc</span>, we can obtain likelihoods for a wide range of direct detection experiments. In the present analysis, we include constraints from the most recent XENON1T analysis [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 93" title="XENON: E. Aprile et al., Dark matter search results from a one ton-year exposure of XENON1T. Phys. Rev. Lett. 121, 111302 (2018). 
 arXiv:1805.12562
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR93" id="ref-link-section-d52098281e9888">93</a>], LUX 2016 [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 88" title="LUX: D.S. Akerib et al., Results from a search for dark matter in the complete LUX exposure. Phys. Rev. Lett. 118, 021303 (2017). 
 arXiv:1608.07648
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR88" id="ref-link-section-d52098281e9891">88</a>], PandaX 2016 [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 91" title="PandaX-II: A. Tan et al., Dark matter results from first 98.7 days of data from the PandaX-II experiment. Phys. Rev. Lett. 117, 121303 (2016). 
 arXiv:1607.07400
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR91" id="ref-link-section-d52098281e9894">91</a>] and 2017 [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 92" title="PandaX-II: X. Cui et al., Dark matter results from 54-ton-day exposure of PandaX-II experiment. Phys. Rev. Lett. 119, 181302 (2017). 
 arXiv:1708.06917
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR92" id="ref-link-section-d52098281e9898">92</a>] analyses, CDMSlite [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 84" title="SuperCDMS: R. Agnese et al., New results from the search for low-mass weakly interacting massive particles with the CDMS low ionization threshold experiment. Phys. Rev. Lett. 116, 071301 (2016). 
 arXiv:1509.02448
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR84" id="ref-link-section-d52098281e9901">84</a>], CRESST-II [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 85" title="CRESST: G. Angloher et al., Results on light dark matter particles with a low-threshold CRESST-II detector. Eur. Phys. J. C 76, 25 (2016). 
 arXiv:1509.01515
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR85" id="ref-link-section-d52098281e9904">85</a>] and CRESST-III [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 86" title="CRESST: A.H. Abdelhameed et al., First results from the CRESST-III low-mass dark matter program. Phys. Rev. D 100, 102002 (2019). 
 arXiv:1904.00498
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR86" id="ref-link-section-d52098281e9907">86</a>], PICO-60 2017 [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 89" title="PICO: C. Amole et al., Dark matter search results from the PICO-60 C
 
 
 
 $$_3$$
 
 
 
 3
 
 
 F
 
 
 
 $$_8$$
 
 
 
 8
 
 
 bubble chamber. Phys. Rev. Lett. 118, 251301 (2017). 
 arXiv:1702.07666
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR89" id="ref-link-section-d52098281e9910">89</a>] and 2019 [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 90" title="PICO: C. Amole et al., Dark matter search results from the complete exposure of the PICO-60 C
 
 
 
 $$_3$$
 
 
 
 3
 
 
 F
 
 
 
 $$_8$$
 
 
 
 8
 
 
 bubble chamber. Phys. Rev. D 100, 022001 (2019). 
 arXiv:1902.04031
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR90" id="ref-link-section-d52098281e9913">90</a>], and DarkSide-50 [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 87" title="P. Agnes et al., DarkSide-50 532-day dark matter search with low-radioactivity argon. Phys. Rev. D 98, 102006 (2018). 
 https://doi.org/10.1103/PhysRevD.98.102006
 
 . 
 arXiv:1802.07198
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR87" id="ref-link-section-d52098281e9917">87</a>].</p><p>The hadronic inputs to <span class="u-sans-serif">DirectDM</span> <span class="u-sans-serif">v2.2.0</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 67" title="F. Bishara, J. Brod, B. Grinstein, J. Zupan, DirectDM: a tool for dark matter direct detection. 
 arXiv:1708.02678
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR67" id="ref-link-section-d52098281e9929">67</a>] were updated with the most recent <span class="mathjax-tex">$N_f=2+1$</span> lattice QCD results, following the FLAG quality requirements [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 107" title="Flavour Lattice Averaging Group: S. Aoki et al., FLAG review 2019: Flavour Lattice Averaging Group (FLAG). Eur. Phys. J. C 80, 113 (2020). 
 arXiv:1902.08191
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR107" id="ref-link-section-d52098281e9965">107</a>], see Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Tab3">3</a>. All the inputs are evaluated at <span class="mathjax-tex">$\mu =2$</span> GeV. The hadronic matrix elements for protons and neutrons are related using isospin conservation.</p><p>For operators with vector quark currents, the least well known are the hadronic matrix elements involving the strange quark, while the matrix elements for operators with <i>u</i>, <i>d</i> quark vector currents have negligible errors to the precision we are working with. Since the strange quark vector current vanishes at <span class="mathjax-tex">$q^2=0$</span>, the first non-vanishing contribution is obtained only at next-to-leading order in the chiral expansion, and depends on the strange quark charge radius, <span class="mathjax-tex">$r_s^2 = -0.0045(14)\,$</span>fm<span class="mathjax-tex">$^2$</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 104" title="D. Djukanovic, K. Ottnad, J. Wilhelm, H. Wittig, Strange electromagnetic form factors of the nucleon with 
 
 
 
 $$N_f = 2 + 1{\cal{O}}(a)$$
 
 
 
 N
 f
 
 =
 2
 +
 1
 O
 
 (
 a
 )
 
 
 
 -improved Wilson fermions. Phys. Rev. Lett. 123, 212001 (2019). 
 arXiv:1903.12566
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR104" id="ref-link-section-d52098281e10104">104</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 105" title="R.S. Sufian, Y.-B. Yang et al., Strange quark magnetic moment of the nucleon at the physical point. Phys. Rev. Lett. 118, 042001 (2017). 
 arXiv:1606.07075
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR105" id="ref-link-section-d52098281e10107">105</a>]. For the nuclear magnetic moment induced by the strange quark, <span class="mathjax-tex">$\mu _s= -0.036(21)$</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 104" title="D. Djukanovic, K. Ottnad, J. Wilhelm, H. Wittig, Strange electromagnetic form factors of the nucleon with 
 
 
 
 $$N_f = 2 + 1{\cal{O}}(a)$$
 
 
 
 N
 f
 
 =
 2
 +
 1
 O
 
 (
 a
 )
 
 
 
 -improved Wilson fermions. Phys. Rev. Lett. 123, 212001 (2019). 
 arXiv:1903.12566
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR104" id="ref-link-section-d52098281e10152">104</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 105" title="R.S. Sufian, Y.-B. Yang et al., Strange quark magnetic moment of the nucleon at the physical point. Phys. Rev. Lett. 118, 042001 (2017). 
 arXiv:1606.07075
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR105" id="ref-link-section-d52098281e10155">105</a>], we inflate the errors according to the Particle Data Group prescription.</p><p>The scalar form factors at zero recoil are obtained from expressions in Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 103" title="A. Crivellin, M. Hoferichter, M. Procura, Accurate evaluation of hadronic uncertainties in spin-independent WIMP-nucleon scattering: disentangling two- and three-flavor effects. Phys. Rev. D 89, 054021 (2014). 
 arXiv:1312.4951
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR103" id="ref-link-section-d52098281e10161">103</a>], namely</p><div id="Equ27" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} \sigma _{u(d)}^N = \frac{\sigma _{\pi N}}{2} (1 \mp \xi )\pm Bc_5 \, (m_d-m_u)\left( 1 \mp \frac{1}{\xi }\right) , \end{aligned}$$</span></div><div class="c-article-equation__number"> (27) </div></div><p>where the upper (lower) sign is for the proton (neutron). We use a rather conservative estimate <span class="mathjax-tex">$\sigma _{\pi N}=(50\pm 15)$</span> MeV [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 101" title="F. Bishara, J. Brod, B. Grinstein, J. Zupan, From quarks to nucleons in dark matter direct detection. JHEP 11, 059 (2017). 
 arXiv:1707.06998
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR101" id="ref-link-section-d52098281e10352">101</a>] that covers the spread between the lattice QCD [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="QCDSF-UKQCD: R. Horsley, Y. Nakamura et al., Hyperon sigma terms for 2 + 1 quark flavours. Phys. Rev. D 85, 034506 (2012). 
 arXiv:1110.4971
 
 " href="#ref-CR111" id="ref-link-section-d52098281e10355">111</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="S. Durr et al., Lattice computation of the nucleon scalar quark contents at the physical point. Phys. Rev. Lett. 116, 172001 (2016). 
 arXiv:1510.08013
 
 " href="#ref-CR112" id="ref-link-section-d52098281e10355_1">112</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="xQCD: Y.-B. Yang, A. Alexandru, T. Draper, J. Liang, K.-F. Liu, 
 
 
 
 $$\pi $$
 
 π
 
 N and strangeness sigma terms at the physical point with chiral fermions. Phys. Rev. D 94, 054503 (2016). 
 arXiv:1511.09089
 
 " href="#ref-CR113" id="ref-link-section-d52098281e10355_2">113</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="ETM: A. Abdel-Rehim, C. Alexandrou et al., Direct evaluation of the quark content of nucleons from lattice QCD at the physical point. Phys. Rev. Lett. 116, 252001 (2016). 
 arXiv:1601.01624
 
 " href="#ref-CR114" id="ref-link-section-d52098281e10355_3">114</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="RQCD: G.S. Bali, S. Collins et al., Direct determinations of the nucleon and pion terms at nearly physical quark masses. Phys. Rev. D 93, 094504 (2016). 
 arXiv:1603.00827
 
 " href="#ref-CR115" id="ref-link-section-d52098281e10355_4">115</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="C. Alexandrou, S. Bacchio et al., Nucleon axial, tensor, and scalar charges and -terms in lattice QCD. Phys. Rev. D 102, 054517 (2020). 
 arXiv:1909.00485
 
 " href="#ref-CR116" id="ref-link-section-d52098281e10355_5">116</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="JLQCD: N. Yamanaka, S. Hashimoto, T. Kaneko, H. Ohki, Nucleon charges with dynamical overlap fermions. Phys. Rev. D 98, 054516 (2018). 
 arXiv:1805.10507
 
 " href="#ref-CR117" id="ref-link-section-d52098281e10355_6">117</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 118" title="S. Borsanyi, Z. Fodor et al., Ab-initio calculation of the proton and the neutron’s scalar couplings for new physics searches. 
 arXiv:2007.03319
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR118" id="ref-link-section-d52098281e10359">118</a>] and pionic atom determinations [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 113" title="xQCD: Y.-B. Yang, A. Alexandru, T. Draper, J. Liang, K.-F. Liu, 
 
 
 
 $$\pi $$
 
 π
 
 N and strangeness sigma terms at the physical point with chiral fermions. Phys. Rev. D 94, 054503 (2016). 
 arXiv:1511.09089
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR113" id="ref-link-section-d52098281e10362">113</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 114" title="ETM: A. Abdel-Rehim, C. Alexandrou et al., Direct evaluation of the quark content of nucleons from lattice QCD at the physical point. Phys. Rev. Lett. 116, 252001 (2016). 
 arXiv:1601.01624
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR114" id="ref-link-section-d52098281e10365">114</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 117" title="JLQCD: N. Yamanaka, S. Hashimoto, T. Kaneko, H. Ohki, Nucleon charges with dynamical overlap fermions. Phys. Rev. D 98, 054516 (2018). 
 arXiv:1805.10507
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR117" id="ref-link-section-d52098281e10368">117</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="J.M. Alarcon, J. Martin Camalich, J.A. Oller, The chiral representation of the 
 
 
 
 $$\pi N$$
 
 
 π
 N
 
 
 scattering amplitude and the pion-nucleon sigma term. Phys. Rev. D 85, 051503 (2012). 
 arXiv:1110.3797
 
 " href="#ref-CR119" id="ref-link-section-d52098281e10371">119</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="M. Hoferichter, J. Ruiz de Elvira, B. Kubis, U.-G. Meissner, High-precision determination of the pion-nucleon term from Roy–Steiner equations. Phys. Rev. Lett. 115, 092301 (2015). 
 arXiv:1506.04142
 
 " href="#ref-CR120" id="ref-link-section-d52098281e10371_1">120</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="V. Dmitrašinović, H.-X. Chen, A. Hosaka, Baryon fields with 
 
 
 
 $$U_L(3)$$
 
 
 
 U
 L
 
 
 (
 3
 )
 
 
 
 Ö 
 
 
 
 $$U_R(3)$$
 
 
 
 U
 R
 
 
 (
 3
 )
 
 
 
 chiral symmetry. V. Pion-nucleon and kaon-nucleon 
 
 
 
 $${{\varSigma }}$$
 
 Σ
 
 terms. Phys. Rev. C 93, 065208 (2016). 
 arXiv:1812.03414
 
 " href="#ref-CR121" id="ref-link-section-d52098281e10371_2">121</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="J. Ruiz de Elvira, M. Hoferichter, B. Kubis, U.-G. Meissner, Extracting the -term from low-energy pion-nucleon scattering. J. Phys. G 45, 024001 (2018). 
 arXiv:1706.01465
 
 " href="#ref-CR122" id="ref-link-section-d52098281e10371_3">122</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 123" title="E. Friedman, A. Gal, The pion-nucleon 
 
 
 
 $${\sigma }$$
 
 
 σ
 
 
 term from pionic atoms. Phys. Lett. B 792, 340–344 (2019). 
 arXiv:1901.03130
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR123" id="ref-link-section-d52098281e10374">123</a>]. The other two parameters are <span class="mathjax-tex">$\xi \equiv (m_d-m_u)/(m_d + m_u)= 0.36\, \pm 0.04$</span> and <span class="mathjax-tex">$B c_5 \, (m_d-m_u)=(-0.51\pm 0.08)$</span> MeV [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 103" title="A. Crivellin, M. Hoferichter, M. Procura, Accurate evaluation of hadronic uncertainties in spin-independent WIMP-nucleon scattering: disentangling two- and three-flavor effects. Phys. Rev. D 89, 054021 (2014). 
 arXiv:1312.4951
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR103" id="ref-link-section-d52098281e10539">103</a>].</p><p>The matrix elements of tensor currents are described by three sets of form factors, but only two, <span class="mathjax-tex">$g_{T}^{q}$</span> and <span class="mathjax-tex">$B_{T,10}^{q/N} (0)$</span>, enter the chirally leading expressions. For <span class="mathjax-tex">$g_{T}^{q}$</span>, the only <span class="mathjax-tex">$N_f=2+1$</span> result from Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 117" title="JLQCD: N. Yamanaka, S. Hashimoto, T. Kaneko, H. Ohki, Nucleon charges with dynamical overlap fermions. Phys. Rev. D 98, 054516 (2018). 
 arXiv:1805.10507
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR117" id="ref-link-section-d52098281e10685">117</a>] does not satisfy the FLAG quality requirements, so we use the <span class="mathjax-tex">$N_f=2+1+1$</span> results from Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 106" title="R. Gupta, B. Yoon et al., Flavor diagonal tensor charges of the nucleon from (2 + 1 + 1)-flavor lattice QCD. Phys. Rev. D 98, 091501 (2018). 
 arXiv:1808.07597
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR106" id="ref-link-section-d52098281e10727">106</a>] instead; the difference between the <span class="mathjax-tex">$N_f=2+1$</span> and <span class="mathjax-tex">$N_f=2+1+1$</span> results is expected to be small. For <span class="mathjax-tex">$B_{T,10}^{q/N}(0)$</span>, we use the results from the constituent quark model in Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 109" title="B. Pasquini, M. Pincetti, S. Boffi, Chiral-odd generalized parton distributions in constituent quark models. Phys. Rev. D 72, 094029 (2005). 
 arXiv:hep-ph/0510376
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR109" id="ref-link-section-d52098281e10854">109</a>].</p><h3 class="c-article__sub-heading" id="Sec8"><span class="c-article-section__title-number">3.2 </span>Relic abundance of DM</h3><p>The Early Universe time evolution of the number density of the <span class="mathjax-tex">$\chi $</span> particles, <span class="mathjax-tex">$n_\chi $</span>, is governed by the Boltzmann equation [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 124" title="P. Gondolo, G. Gelmini, Cosmic abundances of stable particles: improved analysis. Nucl. Phys. A 360, 145–179 (1991)" href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR124" id="ref-link-section-d52098281e10904">124</a>]</p><div id="Equ28" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} \frac{dn_\chi }{dt} + 3Hn_\chi = -\langle \sigma v_\text {rel}\rangle \left( n_\chi n_{{{\bar{\chi }}}}-n_{\chi ,\text {eq}}n_{{{\bar{\chi }}},\text {eq}}\right) , \end{aligned}$$</span></div><div class="c-article-equation__number"> (28) </div></div><p>where <span class="mathjax-tex">$n_{\chi ,\text {eq}}$</span> is the number density in equilibrium, <i>H</i>(<i>t</i>) is the Hubble rate and <span class="mathjax-tex">$\langle \sigma v_{\text {{rel}}}\rangle $</span> is the thermally averaged cross-section times the relative (Møller) velocity, given by</p><div id="Equ29" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} \langle \sigma v_\text {rel}\rangle = \int ^{\infty }_{4m_\chi ^2} \!ds \, \frac{\sqrt{s-4m_\chi ^2}(s-2m_\chi ^2)\,K_1 \left( \sqrt{s}/T\right) }{8m_\chi ^4 \,T K_2^2\left( m_\chi /T\right) } \,\sigma v_{\mathrm{lab}}, \end{aligned}$$</span></div><div class="c-article-equation__number"> (29) </div></div><p>where <span class="mathjax-tex">$K_{1,2}$</span> are the modified Bessel functions and <span class="mathjax-tex">$v_{\mathrm{lab}}$</span> is the velocity of one of the annihilating (anti-)DM particles in the rest frame of the other (for a discussion, see also Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 125" title="T. Binder, T. Bringmann, M. Gustafsson, A. Hryczuk, Early kinetic decoupling of dark matter: when the standard way of calculating the thermal relic density fails. Phys. Rev. D 96, 115010 (2017). 
 arXiv:1706.07433
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR125" id="ref-link-section-d52098281e11405">125</a>]). We stress that there is no additional factor of 1/2 in the above equations. However, the fact that DM consists of Dirac particles implies that the total contribution to the observed DM density is given by <span class="mathjax-tex">$n_\chi +n_{{{\bar{\chi }}}}=2n_\chi $</span> (disregarding the possibility of an initial asymmetry [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 126" title="D.E. Kaplan, M.A. Luty, K.M. Zurek, Asymmetric dark matter. Phys. Rev. D 79, 115016 (2009). 
 arXiv:0901.4117
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR126" id="ref-link-section-d52098281e11466">126</a>]).</p><p>We compute tree-level annihilation cross-sections using <span class="u-sans-serif">CalcHEP</span> <span class="u-sans-serif">v3.6.27</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 127" title="A. Pukhov, CalcHEP 2.3: MSSM, structure functions, event generation, batchs, and generation of matrix elements for other packages. 
 arXiv:hep-ph/0412191
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR127" id="ref-link-section-d52098281e11478">127</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 128" title="A. Belyaev, N.D. Christensen, A. Pukhov, CalcHEP 3.4 for collider physics within and beyond the Standard Model. Comput. Phys. Commun. 184, 1729–1769 (2013). 
 arXiv:1207.6082
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR128" id="ref-link-section-d52098281e11481">128</a>], where the implementation of the four-fermion interactions is generated by <span class="u-sans-serif">GUM</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 55" title="T.E. Gonzalo, GAMBIT: the global and modular BSM inference tool, in Tools for High Energy Physics and Cosmology (2021). 
 arXiv:2105.03165
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR55" id="ref-link-section-d52098281e11488">55</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 56" title="S. Bloor, T.E. Gonzalo et al., The GAMBIT universal model machine: from Lagrangians to likelihoods. 
 arXiv:2107.00030
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR56" id="ref-link-section-d52098281e11491">56</a>] from <span class="u-sans-serif">UFO</span> files via the tool <span class="u-sans-serif">ufo_to_mdl</span> (described in Appendix B). To ensure the EFT picture is valid, we invalidate points where <span class="mathjax-tex">${\Lambda }\le 2 m_\chi $</span>. We obtain the relic density of <span class="mathjax-tex">$\chi $</span> by numerically solving Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Equ28">28</a>) at each parameter point, assuming the standard cosmological history<sup><a href="#Fn8"><span class="u-visually-hidden">Footnote </span>8</a></sup> and using the routines implemented in <span class="u-sans-serif">DarkSUSY</span> <span class="u-sans-serif">v6.2.2</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 130" title="T. Bringmann, J. Edsjö, P. Gondolo, P. Ullio, L. Bergström, DarkSUSY 6: an advanced tool to compute dark matter properties numerically. JCAP 1807, 033 (2018). 
 arXiv:1802.03399
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR130" id="ref-link-section-d52098281e11568">130</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 131" title="P. Gondolo, J. Edsjo et al., DarkSUSY: computing supersymmetric dark matter properties numerically. JCAP 0407, 008 (2004). 
 arXiv:astro-ph/0406204
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR131" id="ref-link-section-d52098281e11571">131</a>] via <span class="u-sans-serif">DarkBit</span>. We then compare the prediction to the relic density constraint from <i>Planck</i> 2018: <span class="mathjax-tex">${\varOmega }_{\text {DM}}\,h^2 = 0.120 \pm 0.001$</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 98" title="Planck: N. Aghanim et al., Planck 2018 results. VI. Cosmological parameters. Astron. Astrophys. 641, A6 (2020). 
 arXiv:1807.06209
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR98" id="ref-link-section-d52098281e11624">98</a>]. We include a <span class="mathjax-tex">$1\%$</span> theoretical error on the computed values of the relic density, which we combine in quadrature with the observed error on the <i>Planck</i> measured value. More details on this prescription can be found in Refs. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 48" title="GAMBIT Collaboration: P. Athron, C. Balázs et al., GAMBIT: the global and modular beyond-the-standard-model inference tool. Eur. Phys. J. C 77, 784 (2017). 
 arXiv:1705.07908
 
 . Addendum in [190]" href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR48" id="ref-link-section-d52098281e11653">48</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 52" title="GAMBIT Dark Matter Workgroup: T. Bringmann, J. Conrad et al., DarkBit: a GAMBIT module for computing dark matter observables and likelihoods. Eur. Phys. J. C 77, 831 (2017). 
 arXiv:1705.07920
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR52" id="ref-link-section-d52098281e11656">52</a>].</p><p>We note that our uncertainty estimate does not include uncertainties in the calculation of the annihilation cross-section very close to quark thresholds, which may be considerably larger. Moreover, our approach does not capture the potential effect of additional degrees of freedom on <span class="mathjax-tex">$\langle \sigma v_\text {rel}\rangle $</span> during freeze-out. The resulting effects, such as resonances or coannihilations could both increase and decrease the resulting value of <span class="mathjax-tex">${\varOmega }_\chi $</span> (see e.g. Refs. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 132" title="N.F. Bell, Y. Cai, A.D. Medina, Co-annihilating dark matter: effective operator analysis and collider phenomenology. Phys. Rev. D 89, 115001 (2014). 
 arXiv:1311.6169
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR132" id="ref-link-section-d52098281e11717">132</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 133" title="M.J. Baker et al., The coannihilation codex. JHEP 12, 120 (2015). 
 arXiv:1510.03434
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR133" id="ref-link-section-d52098281e11720">133</a>]), so the relic density constraint should be interpreted with care for <span class="mathjax-tex">${\Lambda }\sim 2m_\chi $</span>, i.e. close to the EFT validity boundary (see Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec4">2.2</a>).</p><p>The very nature of the EFT construction implies additional degrees of freedom above the energy scale <span class="mathjax-tex">${\Lambda }$</span>. Given the potential for a rich dark sector containing <span class="mathjax-tex">$\chi $</span>, and in particular, the possibility of additional DM candidates not captured by the EFT, we will by default <i>not</i> demand that the particle <span class="mathjax-tex">$\chi $</span> constitutes all of the observed DM, i.e. we allow for the possibility of other DM species to contribute to the observed relic density. In practice, this means that we modify the relic density constraint in such a way that the likelihood is flat if the predicted value is smaller than the observed one. In this case, we rescale all predicted direct and indirect detection signals by</p><div id="Equ30" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} f_\chi \equiv ({\varOmega }_\chi + {\varOmega }_{{{\bar{\chi }}}})/{\varOmega }_{\text {DM}} = 2 {\varOmega }_\chi / {\varOmega }_{\text {DM}} \end{aligned}$$</span></div><div class="c-article-equation__number"> (30) </div></div><p>and <span class="mathjax-tex">$f_\chi ^2$</span>, respectively. In doing so, we assume that the fraction <span class="mathjax-tex">$f_\chi $</span> is the same in all astrophysical systems and that any additional DM population does <i>not</i> contribute to signals in these experiments. In a second set of scans we then impose a stricter requirement, namely that the DM particle under consideration saturates the DM relic abundance (<span class="mathjax-tex">$f_\chi \approx 1$</span>) rather than imposing the relic density as an upper bound (<span class="mathjax-tex">$f_\chi \le 1$</span>).<sup><a href="#Fn9"><span class="u-visually-hidden">Footnote </span>9</a></sup></p><h3 class="c-article__sub-heading" id="Sec9"><span class="c-article-section__title-number">3.3 </span>Indirect detection with gamma rays</h3><p>If DM is held in thermal equilibrium in the early universe via collisions with SM particles, then it can still annihilate today, especially in regions of high DM density. As with the relic abundance calculation, in order for the effective picture to hold for DM annihilation, we must impose <span class="mathjax-tex">${\Lambda }> 2 m_\chi $</span>.</p><p>Gamma rays from dwarf spheroidal galaxies (dSphs) are a particularly robust way of constraining annihilation signals from DM [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 134" title="T. Bringmann, C. Weniger, Gamma ray signals from dark matter: concepts, status and prospects. Phys. Dark Universe 1, 194–217 (2012). 
 arXiv:1208.5481
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR134" id="ref-link-section-d52098281e12180">134</a>]. In general, for a given energy bin <i>i</i>, the DM-induced <span class="mathjax-tex">$\gamma $</span>-ray flux from target <i>k</i> can be written in the factorised form <span class="mathjax-tex">${\varPhi }_i \cdot J_k$</span>, where details of the particle physics processes are encoded in <span class="mathjax-tex">${\varPhi }_i$</span>, and details of the astrophysics are encoded in <span class="mathjax-tex">$J_k$</span>. See the <span class="u-sans-serif">DarkBit</span> manual [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 52" title="GAMBIT Dark Matter Workgroup: T. Bringmann, J. Conrad et al., DarkBit: a GAMBIT module for computing dark matter observables and likelihoods. Eur. Phys. J. C 77, 831 (2017). 
 arXiv:1705.07920
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR52" id="ref-link-section-d52098281e12288">52</a>] for more details.</p><p>In general, only operators that lead to <i>s</i>-wave annihilation (<img src="//media.springernature.com/lw152/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq328_HTML.gif" style="width:152px;max-width:none;" alt="">) give rise to observable gamma-ray signals; see for instance, Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Tab2">2</a>. For the operators <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq329_HTML.gif" style="width:31px;max-width:none;" alt=""> and <img src="//media.springernature.com/lw63/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq330_HTML.gif" style="width:63px;max-width:none;" alt="">, the leading contribution to the annihilation cross-section is <i>p</i>-wave suppressed, i.e. proportional to <span class="mathjax-tex">$v_{\text {rel}}^2$</span>. As DM in dSphs is extremely cold, with <span class="mathjax-tex">$\langle v^2\rangle ^{1/2}\sim 10^{-4}$</span>, this factor is very small, and the resulting limits are exceedingly weak. We therefore neglect <i>p</i>-wave contributions to all annihilation processes here.</p><p>For <i>s</i>-wave annihilation, one obtains</p><div id="Equ31" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} {\varPhi }_i&= \frac{f_\chi ^2}{4} \sum _{j} \frac{(\sigma v)_{0,j}}{4\pi m_\chi ^2}\int _{{\varDelta } E_i} dE \, \frac{dN_{\gamma ,j}}{dE}, \end{aligned}$$</span></div><div class="c-article-equation__number"> (31) </div></div><p>where <span class="mathjax-tex">$f_\chi $</span> is the DM fraction defined in Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Equ30">30</a>), <span class="mathjax-tex">$(\sigma v)_{0,j}$</span> denotes the zero-velocity limit of the cross-section for <span class="mathjax-tex">$\chi {{\bar{\chi }}}\rightarrow j$</span> and <span class="mathjax-tex">$N_{\gamma ,j}$</span> is the number of photons, per annihilation, resulting from the final state channel <i>j</i>. The prefactor 1/4 accounts for the Dirac nature of the DM particles (under the assumption that <span class="mathjax-tex">$n_\chi =n_{{{\bar{\chi }}}}$</span>). Again, we use <span class="u-sans-serif">CalcHEP</span> to compute annihilation cross-sections, with the <span class="u-sans-serif">CalcHEP</span> model files generated by <span class="u-sans-serif">ufo_to_mdl</span> via <span class="u-sans-serif">GUM</span> (see Appendix B). The photon yields <span class="mathjax-tex">${dN_{\gamma ,j}}/{dE}$</span> used in <span class="u-sans-serif">DarkBit</span> are based on tabulated <span class="u-sans-serif">Pythia</span> runs, as provided by <span class="u-sans-serif">DarkSUSY</span>.</p><p>The <i>J</i>-factor for each dSph <i>k</i> is simply the line-of-sight integral over the DM distribution assuming an NFW density profile and the solid angle <span class="mathjax-tex">${\varOmega }$</span>,</p><div id="Equ32" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} J_k&= \int _{{\varDelta }{\varOmega }_k} d{\varOmega } \int _{\text {l.o.s.}} ds \, \rho _{\mathrm{DM}}^2\simeq D_k^{-2} \int d^3x\,\rho _{\mathrm{DM}}^2, \end{aligned}$$</span></div><div class="c-article-equation__number"> (32) </div></div><p>where <span class="mathjax-tex">$D_k$</span> is the distance to the dSph. In our analysis we use the <span class="u-monospace">Pass-8</span> combined analysis of 15 dSphs after 6 years of <i>Fermi</i>-LAT data [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 96" title="Fermi-LAT: M. Ackermann et al., Searching for dark matter annihilation from Milky Way dwarf spheroidal galaxies with six years of Fermi large area telescope data. Phys. Rev. Lett. 115, 231301 (2015). 
 arXiv:1503.02641
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR96" id="ref-link-section-d52098281e13032">96</a>]. We use the <span class="u-sans-serif">gamLike</span> <span class="u-sans-serif">v1.0.1</span> interface within <span class="u-sans-serif">DarkBit</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 52" title="GAMBIT Dark Matter Workgroup: T. Bringmann, J. Conrad et al., DarkBit: a GAMBIT module for computing dark matter observables and likelihoods. Eur. Phys. J. C 77, 831 (2017). 
 arXiv:1705.07920
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR52" id="ref-link-section-d52098281e13045">52</a>] to compute the likelihood for the gamma-ray observations, <span class="mathjax-tex">$\ln {\mathcal {L}}_{\mathrm{exp}}$</span>, constructed from the product <span class="mathjax-tex">${\varPhi }_i \cdot J_k$</span> and summed over all targets and energy bins,</p><div id="Equ33" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} \ln {\mathcal {L}}_{\mathrm{exp}} = \sum ^{\mathrm{N_{dSphs}}}_{k=1} \sum ^{\mathrm{N_{eBins}}}_{i=1} \ln {\mathcal {L}}_{ki}\left( {\varPhi }_i \cdot J_k\right) . \end{aligned}$$</span></div><div class="c-article-equation__number"> (33) </div></div><p>We also include a contribution from profiling over the <i>J</i>-factors of each dSph, <span class="mathjax-tex">$\ln {\mathcal {L}}_J = \sum _k \ln {\mathcal {L}}(J_k)$</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 52" title="GAMBIT Dark Matter Workgroup: T. Bringmann, J. Conrad et al., DarkBit: a GAMBIT module for computing dark matter observables and likelihoods. Eur. Phys. J. C 77, 831 (2017). 
 arXiv:1705.07920
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR52" id="ref-link-section-d52098281e13301">52</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 96" title="Fermi-LAT: M. Ackermann et al., Searching for dark matter annihilation from Milky Way dwarf spheroidal galaxies with six years of Fermi large area telescope data. Phys. Rev. Lett. 115, 231301 (2015). 
 arXiv:1503.02641
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR96" id="ref-link-section-d52098281e13304">96</a>], such that the full likelihood reads</p><div id="Equ34" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} \ln {\mathcal {L}}_{\mathrm{dSphs}}^{\mathrm{prof.}} = \underset{\{J_k\}}{\text {max}}\left( \ln {\mathcal {L}}_{\mathrm{exp}} + \ln {\mathcal {L}}_J \right) . \end{aligned}$$</span></div><div class="c-article-equation__number"> (34) </div></div><p>Gamma rays from the Galactic centre region provide a promising complementary way of constraining a signal from annihilating DM. While the <i>J</i>-factor is expected to be significantly higher than for dSphs, however, this conclusion is largely based on the result of numerical simulations of gravitational clustering rather than on the direct analysis of kinematical data. The reason for this is that the gravitational potential within the solar circle is dominated by baryons, not by DM, which adds additional uncertainty due to a dominant component of astrophysical gamma rays from this target region. As a result, Galactic centre observations with <i>Fermi</i>-LAT are somewhat less competitive than the dSph limits discussed above [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 135" title="Fermi-LAT: M. Ackermann et al., The Fermi Galactic Center GeV excess and implications for dark matter. Astrophys. J. 840, 43 (2017). 
 arXiv:1704.03910
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR135" id="ref-link-section-d52098281e13419">135</a>]. The upcoming Cherenkov Telescope Array (CTA), on the other hand, has a good chance of probing thermally produced DM up to particle masses of several TeV [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 136" title="CTA: A. Acharyya et al., Sensitivity of the Cherenkov Telescope Array to a dark matter signal from the Galactic Centre. JCAP 01, 057 (2021). 
 arXiv:2007.16129
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR136" id="ref-link-section-d52098281e13423">136</a>]. We will not include the projected CTA likelihoods in our scans, but indicate the reach of CTA when discussing our results.</p><h3 class="c-article__sub-heading" id="Sec10"><span class="c-article-section__title-number">3.4 </span>Other indirect detection constraints</h3><h4 class="c-article__sub-heading c-article__sub-heading--small" id="Sec11"><span class="c-article-section__title-number">3.4.1 </span>Solar capture</h4><p>The presence of non-zero elastic scattering cross-sections with nuclei combined with self-annihilation to heavy SM states leads to an additional, unique signature of DM in the form of high-energy neutrinos from the Sun. If Milky Way DM scatters with solar nuclei and loses enough kinetic energy to fall below the local escape velocity, it will become gravitationally bound. As long as it is above the evaporation mass threshold <span class="mathjax-tex">$\simeq 4$</span> GeV, captured DM will thermalize in a small region near the solar centre, and annihilate to SM products which then produce neutrinos via regular decay processes. These are distinct from the neutrinos from Solar fusion, as they are expected to have much higher energies than the <span class="mathjax-tex">$\sim $</span> MeV scales of fusion processes. Leading constraints have been obtained by Super-Kamiokande down to a few GeV [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 137" title="Super-Kamiokande: K. Choi et al., Search for neutrinos from annihilation of captured low-mass dark matter particles in the Sun by Super-Kamiokande. Phys. Rev. Lett. 114, 141301 (2015). 
 arXiv:1503.04858
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR137" id="ref-link-section-d52098281e13478">137</a>], and by the IceCube South Pole Neutrino Observatory, between 20 and 10<span class="mathjax-tex">$^4$</span> GeV [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 138" title="IceCube: M.G. Aartsen et al., Search for annihilating dark matter in the Sun with 3 years of IceCube data. Eur. Phys. J. C 77, 146 (2017). 
 arXiv:1612.05949
 
 [Erratum: Eur. Phys. J. C 79, 214 (2019)]" href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR138" id="ref-link-section-d52098281e13503">138</a>]. For typical annihilation cross-sections, the captured DM population reaches an equilibrium that is determined by the capture rate. For each likelihood evaluation, we obtain the non-relativistic effective operators (Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Equ25">25</a>)) as described in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec7">3.1</a>, using <span class="u-sans-serif">DirectDM</span> to obtain the non-relativistic Wilson coefficients. These are passed to the public code <span class="u-sans-serif">Capt’n General</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 139" title="N. Avis Kozar, A. Caddell, L. Fraser-Leach, P. Scott, A.C. Vincent, Capt’n General: a generalized stellar dark matter capture and heat transport code (2021). 
 arXiv:2105.06810
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR139" id="ref-link-section-d52098281e13519">139</a>], which computes the DM capture rate via the integral over the solar radius <i>r</i> and DM halo velocity <i>u</i>:</p><div id="Equ35" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} C_\odot (t) = 4\pi \int _0^{R_\odot } r^2 \int _0^\infty \frac{f(u)}{u} \, w {\varOmega }(w,r) \, d u \, d r, \end{aligned}$$</span></div><div class="c-article-equation__number"> (35) </div></div><p>where <span class="mathjax-tex">$w(r) = \sqrt{u^2 + v^2_{{\text {esc}},\odot }(r)}$</span> is the DM velocity at position <i>r</i>, and</p><div id="Equ36" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} {\varOmega }(w)&= w \sum _i n_i(r,t) \frac{\mu _{i,+}^2}{\mu _i}{\varTheta }\left( \frac{\mu _i v^2}{\mu _{i,-}^2} - u^2 \right) \nonumber \\&\quad \times \int _{m_\chi u^2/2}^{m_\chi w^2 \mu _i/2\mu _{i,+}^2} \frac{d\sigma _{i}}{dE_{\text {R}}} \, d E_{\text {R}} , \end{aligned}$$</span></div><div class="c-article-equation__number"> (36) </div></div><p>is the probability of scattering from velocity <i>w</i> to a velocity less than the local Solar escape velocity <span class="mathjax-tex">$v_{\text {esc},\odot }(r)$</span>, <span class="mathjax-tex">${d\sigma _{i}}/{dE_{\text {R}}}$</span> is the DM-<i>nucleus</i> scattering cross-section, <span class="mathjax-tex">$n_i(r)$</span> is the number density of species <i>i</i> with atomic mass <span class="mathjax-tex">$m_{N,i}$</span>, and <span class="mathjax-tex">$\mu _i = m_\chi /m_{N,i}$</span>. Version 2.1 of <span class="u-sans-serif">Capt’n General</span> uses the method described in detail in Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 140" title="R. Catena, B. Schwabe, Form factors for dark matter capture by the Sun in effective theories. JCAP 04, 042 (2015). 
 arXiv:1501.03729
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR140" id="ref-link-section-d52098281e14257">140</a>], separating the DM-nucleus cross-section into factors proportional to non-relativistic Wilson coefficients, powers of <i>w</i> and exchanged momentum <i>q</i>, and operator-dependent <i>nuclear response functions</i> computed in Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 140" title="R. Catena, B. Schwabe, Form factors for dark matter capture by the Sun in effective theories. JCAP 04, 042 (2015). 
 arXiv:1501.03729
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR140" id="ref-link-section-d52098281e14270">140</a>] for the 16 most abundant elements in the Sun. Solar parameters are based on the Barcelona Group’s AGSS09ph Standard Solar Model [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 141" title="N. Vinyoles, A.M. Serenelli et al., A new generation of standard solar models. Astrophys. J. 835, 202 (2017). 
 arXiv:1611.09867
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR141" id="ref-link-section-d52098281e14273">141</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 142" title="M. Asplund, N. Grevesse, A.J. Sauval, P. Scott, The chemical composition of the Sun. ARA&A 47, 481–522 (2009). 
 arXiv:0909.0948
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR142" id="ref-link-section-d52098281e14276">142</a>].</p><p>Annihilation cross-sections are computed as described in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec8">3.2</a>, via <span class="u-sans-serif">CalcHEP</span>. Once the equilibrium population of DM in the Sun has been obtained, cross-sections and annihilation rates are passed to <span class="u-sans-serif">DarkSUSY</span>, which computes the neutrino yields as a function of energy. These are finally passed to <span class="u-sans-serif">nulike</span> <span class="u-sans-serif">v1.0.9</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 143" title="IceCube Collaboration: M.G. Aartsen, R. Abbasi et al., Search for dark matter annihilations in the Sun with the 79-String IceCube detector. Phys. Rev. Lett. 110, 131302 (2013). 
 arXiv:1212.4097
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR143" id="ref-link-section-d52098281e14298">143</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 144" title="P. Scott, C. Savage, J. Edsjö, The IceCube Collaboration: R. Abbasi et al., Use of event-level neutrino telescope data in global fits for theories of new physics. JCAP 11, 57 (2012). 
 arXiv:1207.0810
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR144" id="ref-link-section-d52098281e14301">144</a>], which computes event-level likelihoods based on a re-analysis of the 79-string IceCube search for DM annihilation in the Sun [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 97" title="IceCube Collaboration: M.G. Aartsen et al., Improved limits on dark matter annihilation in the Sun with the 79-string IceCube detector and implications for supersymmetry. JCAP 04, 022 (2016). 
 arXiv:1601.00653
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR97" id="ref-link-section-d52098281e14304">97</a>].</p><h4 class="c-article__sub-heading c-article__sub-heading--small" id="Sec12"><span class="c-article-section__title-number">3.4.2 </span>Cosmic microwave background</h4><p>Additional constraints on the DM annihilation cross-section arise from the early universe, more specifically from observations of the Cosmic Microwave Background (CMB). Annihilating DM particles inject energy into the primordial plasma, which affects the reionisation history and alters the optical depth <span class="mathjax-tex">$\tau $</span>. The magnitude of this effect depends on the specific annihilation channel and how efficiently the injected energy is deposited. These details can be encoded in an effective efficiency coefficient <span class="mathjax-tex">$f_{\text {eff}}$</span>, which depends on the injected yields of photons, electrons and positrons, and thus on the DM mass and its branching ratios into different final states [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 145" title="T.R. Slatyer, Indirect dark matter signatures in the cosmic dark ages. I. Generalizing the bound on s-wave dark matter annihilation from Planck results. Phys. Rev. D 93, 023527 (2016). 
 arXiv:1506.03811
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR145" id="ref-link-section-d52098281e14354">145</a>]. The CMB is then sensitive to the following parameter combination:</p><div id="Equ37" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} p_{\text {ann}} \equiv f_\chi ^2 f_{\text {eff}} \frac{\langle \sigma v_{\text {rel}} \rangle }{m_\chi }, \end{aligned}$$</span></div><div class="c-article-equation__number"> (37) </div></div><p>where <span class="mathjax-tex">$\langle \sigma v_{\text {rel}} \rangle \approx (\sigma v)_0$</span> to a very good approximation during recombination; we thus also neglect <i>p</i>-wave contributions to all annihilation processes here.</p><p>In order to calculate <span class="mathjax-tex">$p_{\text {ann}}$</span> for a given parameter point, one first needs to calculate the injected spectrum of photons, electrons and positrons and then convolve the result with suitable transfer functions that link the energy injection rate to the energy deposition rate [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 146" title="T.R. Slatyer, Indirect dark matter signatures in the cosmic dark ages II. Ionization, heating and photon production from arbitrary energy injections. Phys. Rev. D 93, 023521 (2016). 
 arXiv:1506.03812
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR146" id="ref-link-section-d52098281e14530">146</a>]. The first part of this calculation has been automated within <span class="u-sans-serif">DarkSUSY</span> and is accessible via <span class="u-sans-serif">DarkBit</span>. The second part relies on <span class="u-sans-serif">DarkAges</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 147" title="P. Stöcker, M. Krämer, J. Lesgourgues, V. Poulin, Exotic energy injection with ExoCLASS: application to the Higgs portal model and evaporating black holes. JCAP 1803, 018 (2018). 
 arXiv:1801.01871
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR147" id="ref-link-section-d52098281e14543">147</a>] (which is part of the <span class="u-sans-serif">ExoCLASS</span> branch of <span class="u-sans-serif">CLASS</span>) and is accessible via <span class="u-sans-serif">CosmoBit</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 54" title="GAMBIT Cosmology Workgroup: J.J. Renk, P. Stöcker et al., CosmoBit: a GAMBIT module for computing cosmological observables and likelihoods. JCAP 02, 022 (2021). 
 arXiv:2009.03286
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR54" id="ref-link-section-d52098281e14555">54</a>], see Appendix C for further details.<sup><a href="#Fn10"><span class="u-visually-hidden">Footnote </span>10</a></sup></p><p>As the <i>Planck</i> collaboration only quotes the 95% credible interval for <span class="mathjax-tex">$p_{\text {ann}}$</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 98" title="Planck: N. Aghanim et al., Planck 2018 results. VI. Cosmological parameters. Astron. Astrophys. 641, A6 (2020). 
 arXiv:1807.06209
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR98" id="ref-link-section-d52098281e14705">98</a>], the remaining challenge is to obtain a likelihood for <span class="mathjax-tex">$p_{\text {ann}}$</span> from cosmological data. Although this likelihood can, in principle, be calculated for each parameter point individually using the <span class="u-sans-serif">CosmoBit</span> interface to <span class="u-sans-serif">CLASS</span> and the <i>Planck</i> likelihoods, carrying out such a large number of calculations would be prohibitively slow, in particular if the cosmological parameters of the <span class="mathjax-tex">${\Lambda }$</span>CDM model are to be varied simultaneously. In the present work, we therefore adopt a simpler approach, where we first calculate the likelihood when varying <span class="mathjax-tex">$p_{\text {ann}}$</span> (while profiling over the <span class="mathjax-tex">${\Lambda }$</span>CDM and cosmological nuisance parameters). This approach yields</p><div id="Equ38" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} {\mathcal {L}}(p_{\text {ann}}) = {\mathcal {L}}_0 \exp \left[ - \left( \frac{p_{\text {ann}}^{28} + 0.48}{2.45} \right) ^2 \right] , \end{aligned}$$</span></div><div class="c-article-equation__number"> (38) </div></div><p>where <span class="mathjax-tex">$p_{\text {ann}}^{28} \equiv p_{\text {ann}} / \left( 10^{-28} \, \text {cm}^3~\text {s}^{-1}~\text {GeV}^{-1} \right) $</span>. In arriving at this result, we have included the <i>Planck</i> TT,TE,EE+lowE+lensing likelihoods (using the ‘lite’ likelihood for multipoles <span class="mathjax-tex">$ \ell \ge 30 $</span>, which only require one additional nuisance parameter [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 148" title="Planck: N. Aghanim et al., Planck 2018 results. V. CMB power spectra and likelihoods. Astron. Astrophys. 641, A5 (2020). 
 arXiv:1907.12875
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR148" id="ref-link-section-d52098281e15027">148</a>]), as well as the BAO data of 6dF [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 149" title="F. Beutler, C. Blake et al., The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant. MNRAS 416, 3017–3032 (2011). 
 arXiv:1106.3366
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR149" id="ref-link-section-d52098281e15030">149</a>], SDSS DR7 MGS [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 150" title="A.J. Ross, L. Samushia et al., The clustering of the SDSS DR7 main Galaxy sample—I. A 4 per cent distance measure at z = 0.15. MNRAS 449, 835–847 (2015). 
 arXiv:1409.3242
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR150" id="ref-link-section-d52098281e15033">150</a>], and the SDSS BOSS DR12 galaxy sample [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 151" title="BOSS: S. Alam et al., The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample. MNRAS 470, 2617–2652 (2017). 
 arXiv:1607.03155
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR151" id="ref-link-section-d52098281e15037">151</a>]. This profile likelihood, which reproduces the 95% credible interval obtained by the <i>Planck</i> collaboration [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 98" title="Planck: N. Aghanim et al., Planck 2018 results. VI. Cosmological parameters. Astron. Astrophys. 641, A6 (2020). 
 arXiv:1807.06209
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR98" id="ref-link-section-d52098281e15043">98</a>], can then be used in all subsequent scans, so that only <span class="mathjax-tex">$p_{\text {ann}}$</span> needs to be calculated for each parameter point and it is no longer necessary to call <span class="u-sans-serif">CLASS</span> or <span class="u-sans-serif">plc</span>.</p><h4 class="c-article__sub-heading c-article__sub-heading--small" id="Sec13"><span class="c-article-section__title-number">3.4.3 </span>Charged cosmic rays</h4><p>Finally, DM particles annihilating in the Galactic halo also produce positrons, antiprotons and, to a lesser degree, heavier anti-nuclei that could in principle be observed in the spectrum of charged cosmic rays. Positrons quickly lose their energy through synchrotron radiation, and are thus a robust probe of exotic contributions from the <i>local</i> Galactic environment; the resulting bounds on DM annihilating to quarks or gluons are, however, much weaker than the other indirect detection constraints discussed here [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 152" title="J. Kopp, Constraints on dark matter annihilation from AMS-02 results. Phys. Rev. D 88, 076013 (2013). 
 arXiv:1304.1184
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR152" id="ref-link-section-d52098281e15085">152</a>].<sup><a href="#Fn11"><span class="u-visually-hidden">Footnote </span>11</a></sup> Anti-nuclei, on the other hand, probe a significant fraction of the entire Galactic halo because energy losses are much less efficient in this case. For antiprotons, this generally leads to competitive constraints on DM annihilation signals [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="L. Bergstrom, J. Edsjo, P. Ullio, Cosmic anti-protons as a probe for supersymmetric dark matter? Astrophys. J. 526, 215–235 (1999). 
 arXiv:astro-ph/9902012
 
 " href="#ref-CR155" id="ref-link-section-d52098281e15108">155</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="T. Bringmann, P. Salati, The galactic antiproton spectrum at high energies: background expectation vs. exotic contributions. Phys. Rev. D 75, 083006 (2007). 
 arXiv:astro-ph/0612514
 
 " href="#ref-CR156" id="ref-link-section-d52098281e15108_1">156</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 157" title="A. Cuoco, M. Krämer, M. Korsmeier, Novel dark matter constraints from antiprotons in light of AMS-02. Phys. Rev. Lett. 118, 191102 191102 (2017). 
 arXiv:1610.03071
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR157" id="ref-link-section-d52098281e15111">157</a>], but it also means that such bounds necessarily strongly depend on uncertainties relating to modelling the production and propagation of cosmic rays in the Galactic halo. In addition to the dozen (or more) free parameters in the diffusion-reacceleration equations, there exist significant uncertainties on the energy dependence of the nuclear cross-sections responsible for the conventional antiproton flux [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 158" title="J. Heisig, M. Korsmeier, M.W. Winkler, Dark matter or correlated errors: systematics of the AMS-02 antiproton excess. Phys. Rev. Res. 2, 043017 (2020). 
 arXiv:2005.04237
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR158" id="ref-link-section-d52098281e15115">158</a>] and possible correlated systematics [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 159" title="M. Boudaud, Y. Génolini et al., AMS-02 antiprotons’ consistency with a secondary astrophysical origin. Phys. Rev. Res. 2, 023022 (2020). 
 arXiv:1906.07119
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR159" id="ref-link-section-d52098281e15118">159</a>]. A full statistical analysis, which would require a treatment of the large number of (effective) propagation parameters as nuisance parameters in our scans, is prohibitive in terms of computational costs [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 160" title="G. Jóhannesson et al., Bayesian analysis of cosmic-ray propagation: evidence against homogeneous diffusion. Astrophys. J. 824, 16 (2016). 
 arXiv:1602.02243
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR160" id="ref-link-section-d52098281e15121">160</a>] and hence beyond the scope of this work.</p><h3 class="c-article__sub-heading" id="Sec14"><span class="c-article-section__title-number">3.5 </span>Collider physics</h3><p>The effective operators defined in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec2">2</a> allow for the pair production of WIMPs in the proton–proton collisions at the LHC. If one of the incoming partons radiates a jet through initial state radiation (ISR), one can observe the process <span class="mathjax-tex">$pp \rightarrow \chi \chi j$</span> as a single jet associated with missing transverse energy (<img src="//media.springernature.com/lw21/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq370_HTML.gif" style="width:21px;max-width:none;" alt="">). In this study, we include the CMS [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 95" title="CMS: A.M. Sirunyan et al., Search for new physics in final states with an energetic jet or a hadronically decaying 
 
 
 
 $$W$$
 
 W
 
 or 
 
 
 
 $$Z$$
 
 Z
 
 boson and transverse momentum imbalance at 
 
 
 
 $$\sqrt{s}=13\,\text{TeV}$$
 
 
 
 s
 
 =
 13
 
 TeV
 
 
 . Phys. Rev. D 97, 092005 (2018). 
 arXiv:1712.02345
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR95" id="ref-link-section-d52098281e15176">95</a>] and ATLAS [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 94" title="ATLAS: G. Aad et al., Search for new phenomena in events with an energetic jet and missing transverse momentum in 
 
 
 
 $$pp$$
 
 
 pp
 
 
 collisions at 
 
 
 
 $$\sqrt{s} = 13$$
 
 
 
 s
 
 =
 13
 
 
 TeV with the ATLAS detector. 
 arXiv:2102.10874
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR94" id="ref-link-section-d52098281e15179">94</a>] monojet analyses based on <span class="mathjax-tex">$36\,\mathrm {fb}^{-1}$</span> and <span class="mathjax-tex">$139\,\mathrm {fb}^{-1}$</span> of data from Run II, respectively. ATLAS and CMS have performed a number of further searches for other types of ISR, leading for example to mono-photon signatures, but these are known to give weaker bounds on DM EFTs than monojet searches [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 24" title="N. Zhou, D. Berge, D. Whiteson, Mono-everything: combined limits on dark matter production at colliders from multiple final states. Phys. Rev. D 87, 095013 (2013). 
 arXiv:1302.3619
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR24" id="ref-link-section-d52098281e15259">24</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 161" title="M. Bauer, M. Klassen, V. Tenorth, Universal properties of pseudoscalar mediators in dark matter extensions of 2HDMs. JHEP 07, 107 (2018). 
 arXiv:1712.06597
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR161" id="ref-link-section-d52098281e15262">161</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 162" title="A.J. Brennan, M.F. McDonald, J. Gramling, T.D. Jacques, Collide and conquer: constraints on simplified dark matter models using mono-X collider searches. JHEP 05, 112 (2016). 
 arXiv:1603.01366
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR162" id="ref-link-section-d52098281e15265">162</a>].</p><p>The expected number of events in a given bin of the <img src="//media.springernature.com/lw21/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq373_HTML.gif" style="width:21px;max-width:none;" alt=""> distribution is</p><div id="Equ49" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} N = L\times \sigma \times (\epsilon A), \end{aligned}$$</span></div></div><p>where <span class="mathjax-tex">$L =36\,{\text {fb}}^{-1}$</span> or <span class="mathjax-tex">$139\,{\text {fb}}^{-1}$</span> is the total integrated luminosity, <span class="mathjax-tex">$\sigma $</span> the total production cross-section and the factor <span class="mathjax-tex">$(\epsilon A)$</span> is the efficiency times acceptance for passing the kinematic selection requirements for the analysis. Both <span class="mathjax-tex">$\sigma $</span> and <span class="mathjax-tex">$(\epsilon A)$</span> can be obtained via Monte Carlo simulation, but given the dimensionality of the DM EFT parameter space it is computationally too expensive to perform these simulations on the fly during the parameter scan, as would be the standard approach to collider simulations within <span class="u-sans-serif">ColliderBit</span> in <span class="u-sans-serif">GAMBIT</span>.</p><p>Starting from <span class="u-sans-serif">UFO</span> files generated using <span class="u-sans-serif">FeynRules</span> <span class="u-sans-serif">v2.0</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 163" title="A. Alloul, N.D. Christensen, C. Degrande, C. Duhr, B. Fuks, FeynRules 2.0—a complete toolbox for tree-level phenomenology. Comput. Phys. Commun. 185, 2250–2300 (2014). 
 arXiv:1310.1921
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR163" id="ref-link-section-d52098281e15521">163</a>], we have therefore produced separate interpolations of <span class="mathjax-tex">$\sigma $</span> and <span class="mathjax-tex">$\epsilon A$</span> based on the output of Monte Carlo simulations with <span class="u-sans-serif">MadGraph_aMC@NLO</span> <span class="u-sans-serif">v2.6.6</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 164" title="J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, T. Stelzer, MadGraph 5: going beyond. JHEP 06, 128 (2011). 
 arXiv:1106.0522
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR164" id="ref-link-section-d52098281e15570">164</a>] (<span class="u-sans-serif">v2.9.2</span>) for the CMS (ATLAS) analysis, interfaced to <span class="u-sans-serif">Pythia</span> <span class="u-sans-serif">v8.1</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 165" title="T. Sjostrand, S. Mrenna, P.Z. Skands, A brief introduction to PYTHIA 8.1. Comput. Phys. Commun. 178, 852–867 (2008). 
 arXiv:0710.3820
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR165" id="ref-link-section-d52098281e15583">165</a>] for parton showering and hadronization. The matching between <span class="u-sans-serif">MadGraph</span> and <span class="u-sans-serif">Pythia</span> is performed according to the CKKW prescription, and the detector response is simulated using <span class="u-sans-serif">Delphes</span> <span class="u-sans-serif">v3.4.2</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 166" title="DELPHES 3: J. de Favereau, C. Delaere et al., DELPHES 3, a modular framework for fast simulation of a generic collider experiment. JHEP 02, 057 (2014). 
 arXiv:1307.6346
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR166" id="ref-link-section-d52098281e15599">166</a>]. The <span class="u-sans-serif">ColliderBit</span> code extension that enables <span class="mathjax-tex">$\sigma $</span> and <span class="mathjax-tex">$(\epsilon A)$</span> interpolations to be used as an alternative to direct Monte Carlo simulation will be generalised and documented in the next major version of <span class="u-sans-serif">ColliderBit</span>.</p><p>We only include the dimension-6 and 7 EFT operators (<img src="//media.springernature.com/lw28/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq384_HTML.gif" style="width:28px;max-width:none;" alt=""> and <img src="//media.springernature.com/lw58/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq385_HTML.gif" style="width:58px;max-width:none;" alt="">) which are relevant for collider searches. Other operators give a negligible contribution due to either being suppressed by the parton distribution functions (in the case of heavy quarks), or by a factor of the fermion mass (small in the case of light quarks).</p><p>To reduce the computation time for our study, we generate events in discrete grids of the Wilson coefficients and DM mass. Separate grids are defined for each set of operators that do not interfere, such that the total number of events will simply be the sum of the contributions calculated from each grid. At dimension-6, there is interference between operators <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq386_HTML.gif" style="width:31px;max-width:none;" alt="">/<img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq387_HTML.gif" style="width:31px;max-width:none;" alt=""> and <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq388_HTML.gif" style="width:31px;max-width:none;" alt="">/<img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq389_HTML.gif" style="width:31px;max-width:none;" alt="">. For these Wilson coefficients, we parametrize the tabulated grids in terms of a mixing angle <span class="mathjax-tex">$\theta $</span>, defined via <img src="//media.springernature.com/lw83/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq391_HTML.gif" style="width:83px;max-width:none;" alt=""> and <img src="//media.springernature.com/lw85/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq392_HTML.gif" style="width:85px;max-width:none;" alt="">.</p><p>The CMS and ATLAS analyses have 22 and 13 exclusive signal regions, respectively, corresponding to the individual bins in the missing transverse energy distributions. As discussed below, the publicly available information makes it possible to combine all signal regions for the CMS analysis, while for the ATLAS analysis, only a single signal region can be used at once. To maximize the sensitivity of the ATLAS analysis, we combine the three highest missing energy bins, for which systematic uncertainties in the background estimation (and hence their correlations) are negligible, such that the highest bin in our analysis corresponds to all events with <img src="//media.springernature.com/lw112/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq393_HTML.gif" style="width:112px;max-width:none;" alt="">.<sup><a href="#Fn12"><span class="u-visually-hidden">Footnote </span>12</a></sup> Once the predicted yields for all bins have been evaluated, taking into account the EFT validity constraint as described in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec4">2.2</a>, we compute a likelihood for each analysis as follows.</p><p>For the CMS analysis, we follow the “simplified likelihood” method [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 167" title="CMS Collaboration, Simplified likelihood for the re-interpretation of public CMS results. CMS-NOTE-2017-001 (2017)" href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR167" id="ref-link-section-d52098281e15789">167</a>], since the required covariance matrix was published by CMS. In this approach, the full experimental likelihood function is approximated by a standard convolved Poisson–Gaussian form, with the systematic uncertainties on the background predictions treated as correlated Gaussian distributions:</p><div id="Equ39" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} {\mathcal {L}}_{{\text {CMS}}}({\varvec{s}}, {\varvec{\gamma }})= & {} \prod _{i=1}^{22} \left[ \frac{(s_i + b_i + \gamma _i)^{n_i} \, e^{-(s_i + b_i + \gamma _i)}}{n_i!} \right] \nonumber \\&\quad \times \frac{1}{\sqrt{\det 2\pi {\varSigma }}} e^{-\frac{1}{2} {\varvec{\gamma }}^T {\varvec{{\varSigma }^{-1}}} {\varvec{\gamma }}}. \end{aligned}$$</span></div><div class="c-article-equation__number"> (39) </div></div><p>For each signal region <i>i</i>, the observed yield, expected signal yield and expected background yield are given by <span class="mathjax-tex">$n_i$</span>, <span class="mathjax-tex">$s_i$</span> and <span class="mathjax-tex">$b_i$</span>, respectively. The deviation from the nominal expected yield due to systematic uncertainties is given by <span class="mathjax-tex">$\gamma _i$</span>. The correlations between the different <span class="mathjax-tex">$\gamma _i$</span> are encoded in the covariance matrix <span class="mathjax-tex">${\varvec{{\varSigma }}}$</span> provided by CMS, where we also add the signal yield uncertainties in quadrature along the diagonal. We follow the procedure in Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 167" title="CMS Collaboration, Simplified likelihood for the re-interpretation of public CMS results. CMS-NOTE-2017-001 (2017)" href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR167" id="ref-link-section-d52098281e16224">167</a>] in treating the <span class="mathjax-tex">$\gamma _i$</span> nuisance parameters as linear corrections to the expected yields. For every point in our scans of the DM EFT parameter space, we profile Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Equ39">39</a>) over the 22 nuisance parameters in <span class="mathjax-tex">${\varvec{\gamma }}$</span> to obtain a likelihood solely in terms of the set of DM EFT signal estimates <span class="mathjax-tex">${\varvec{s}}$</span>:</p><div id="Equ40" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} {\mathcal {L}}_{{\text {CMS}}}({\varvec{s}}) \equiv {\mathcal {L}}_{{\text {CMS}}}({\varvec{s}}, \hat{\hat{{\varvec{\gamma }}}}). \end{aligned}$$</span></div><div class="c-article-equation__number"> (40) </div></div><p>In the case of the ATLAS analysis, for which such a covariance matrix is not available, the conservative course of action is to calculate a likelihood using only the signal region with the best expected sensitivity. The ATLAS likelihood is therefore given by</p><div id="Equ41" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} {\mathcal {L}}_{{\text {ATLAS}}}(s_i) \equiv {\mathcal {L}}_{{\text {ATLAS}}}(s_i, \hat{\hat{\gamma _i}}) \, , \end{aligned}$$</span></div><div class="c-article-equation__number"> (41) </div></div><p>where <span class="mathjax-tex">${\mathcal {L}}_{{\text {ATLAS}}}(s_i, \hat{\hat{\gamma _i}})$</span> is the single-bin equivalent of Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Equ39">39</a>), and <i>i</i> refers to the signal region with the best expected sensitivity, i.e. the signal region that would give the lowest likelihood in the case <span class="mathjax-tex">$n_i = b_i$</span>.</p><p>The total LHC log-likelihood is then given by <span class="mathjax-tex">$\ln {\mathcal {L}}_{{\text {LHC}}} = \ln {\mathcal {L}}_{{\text {CMS}}} + \ln {\mathcal {L}}_{{\text {ATLAS}}}$</span>. However, due to the per-point signal region selection required in the evaluation of <span class="mathjax-tex">$\ln {\mathcal {L}}_{{\text {ATLAS}}}$</span>, the variation in typical yields between the different signal regions would manifest as a large variation in the effective likelihood normalization between different parameter points. To avoid this we follow the standard approach in <span class="u-sans-serif">ColliderBit</span> of using the log-likelihood difference</p><div id="Equ42" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} {\varDelta } \ln {\mathcal {L}}_{{\text {LHC}}} = \ln {\mathcal {L}}_{{\text {LHC}}}(\mathbf{s}) - \ln {\mathcal {L}}_{{\text {LHC}}}(\mathbf{s}=\mathbf{0}) \end{aligned}$$</span></div><div class="c-article-equation__number"> (42) </div></div><p>as the LHC log-likelihood contribution in the parameter scan [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 168" title="GAMBIT Collider Workgroup: C. Balázs, A. Buckley et al., ColliderBit: a GAMBIT module for the calculation of high-energy collider observables and likelihoods. Eur. Phys. J. C 77, 795 (2017). 
 arXiv:1705.07919
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR168" id="ref-link-section-d52098281e16795">168</a>].</p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-4"><figure><figcaption class="c-article-table__figcaption"><b id="Tab4" data-test="table-caption">Table 4 A list of nuisance parameters that are varied simultaneously with the DM EFT model parameters in our scans (the hadronic parameters are given at <span class="mathjax-tex">$\mu =2$</span> GeV). All parameters are scanned over their <span class="mathjax-tex">$3\sigma $</span> range using flat parametrisation. For more details on the respective nuisance likelihoods, see Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec15">3.6</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-09712-6/tables/4" aria-label="Full size table 4"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>When presenting the results of a global fit we identify the maximum-likelihood point <span class="mathjax-tex">${\varvec{{\Theta }}}_{\text {best-fit}}$</span> in the DM EFT parameter space and map out the <span class="mathjax-tex">$1\sigma $</span> and <span class="mathjax-tex">$2\sigma $</span> confidence regions defined using the likelihood ratio <span class="mathjax-tex">${\mathcal {L}}({\varvec{{\Theta }}}) / {\mathcal {L}}({\varvec{{\Theta }}}_{\text {best-fit}})$</span>. Thus, in cases where some region of the DM EFT parameter space can accommodate a modest excess in the collider data, other DM EFT parameter regions that might still perform better than the SM, or that are experimentally indistinguishable from SM, can appear as excluded. While this is perfectly reasonable, given that the comparison is to the best-fit DM EFT point and not to the SM expectation, it is also interesting to study the global fit results under the assumption that mild excesses in the collider data indeed do not originate from a true new physics signal. A simple and pragmatic approach is then to replace <span class="mathjax-tex">${\varDelta } \ln {\mathcal {L}}_{{\text {LHC}}}$</span> with a capped version,</p><div id="Equ43" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} {\varDelta } \ln {\mathcal {L}}_{{\text {LHC}}}^{\text {cap}}(\mathbf{s}) = \min [ {\varDelta } \ln {\mathcal {L}}_{{\text {LHC}}}(\mathbf{s}), {\varDelta } \ln {\mathcal {L}}_{{\text {LHC}}}(\mathbf{s}=\mathbf{0})]. \end{aligned}$$</span></div><div class="c-article-equation__number"> (43) </div></div><p>This will assign the same log-likelihood value, <span class="mathjax-tex">${\varDelta } \ln {\mathcal {L}}_{{\text {LHC}}}^{\text {cap}} = 0$</span>, for all DM EFT parameter points whose prediction fit the collider data as well as, or better than, the SM prediction (<span class="mathjax-tex">$\mathbf{s} = \mathbf{0}$</span>) does. Thus, analogous to how exclusion limits from LHC searches are constructed to only exclude new physics scenarios that predict too <i>many</i> signal events, the capped likelihood only penalizes parameter points for performing worse than the background-only scenario. The result obtained from using <span class="mathjax-tex">${\varDelta } \ln {\mathcal {L}}_{{\text {LHC}}}^{\text {cap}}$</span> in a fit is therefore close to the result one would obtain by constructing a joint exclusion limit for the LHC searches, and applying this limit as a hard cut on the parameter space favoured by the other observables. The main difference is that the capped LHC likelihood incorporates a continuous likelihood penalty.<sup><a href="#Fn13"><span class="u-visually-hidden">Footnote </span>13</a></sup> A more detailed introduction to the capped likelihood construction can be found in Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 169" title="GAMBIT Collaboration: P. Athron et al., Combined collider constraints on neutralinos and charginos. Eur. Phys. J. C 79, 395 (2019). 
 arXiv:1809.02097
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR169" id="ref-link-section-d52098281e18004">169</a>].</p><p>Below we will present some results using this capped LHC likelihood, and some using the full LHC likelihood in Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Equ42">42</a>). In light of the discussion above, the two sets of results should be interpreted as answering slightly different questions: The fit results with the full LHC likelihood show what DM EFT scenario is in best agreement with the complete set of current data, and how much worse other DM EFT scenarios perform in comparison. The results with the capped LHC likelihood map out the DM EFT parameter space that is preferred by the non-collider observables and not excluded by a combination of the LHC searches.</p><h3 class="c-article__sub-heading" id="Sec15"><span class="c-article-section__title-number">3.6 </span>Nuisance parameter likelihoods</h3><p>In our scans we also vary a set of relevant nuisance parameters related to the DM observables and SM measurements. Most of these nuisance parameters are directly constrained by dedicated measurements, which we include through appropriate likelihood functions. In some cases, however, several conflicting measurements exist, indicating additional systematic uncertainties in the methodology. In these cases we constrain the nuisance parameters through effective likelihoods intended to give a conservative constraint on the allowed ranges. The nuisance parameters and <span class="mathjax-tex">$3\sigma $</span> ranges used in this study are summarised in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Tab4">4</a>. We briefly cover each nuisance likelihood in turn below.</p><p>We follow the default prescription in <span class="u-sans-serif">DarkBit</span> for the local DM density <span class="mathjax-tex">$\rho _0$</span>, where the likelihood is given by a log-normal distribution with central value <span class="mathjax-tex">$\rho _0 = 0.40$</span> GeV cm<span class="mathjax-tex">$^{-3}$</span> and error <span class="mathjax-tex">$\sigma _{\rho _0}=0.15$</span> GeV cm<span class="mathjax-tex">$^{-3}$</span>. We scan over an asymmetric range in <span class="mathjax-tex">$\rho _0$</span> to reflect the log-normal distribution – see Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 52" title="GAMBIT Dark Matter Workgroup: T. Bringmann, J. Conrad et al., DarkBit: a GAMBIT module for computing dark matter observables and likelihoods. Eur. Phys. J. C 77, 831 (2017). 
 arXiv:1705.07920
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR52" id="ref-link-section-d52098281e18214">52</a>] for more details.</p><p>We follow the same treatment of the Milky Way halo as in the <span class="u-sans-serif">GAMBIT</span> Higgs portal study [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 110" title="GAMBIT Collaboration: P. Athron et al., Global analyses of Higgs portal singlet dark matter models using GAMBIT. Eur. Phys. J. C 79, 38 (2019). 
 arXiv:1808.10465
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR110" id="ref-link-section-d52098281e18223">110</a>]. We utilise Gaussian likelihoods for parameters describing the Maxwell-Boltzmann velocity distribution, specifically the peak of the distribution <span class="mathjax-tex">$v_{\mathrm{peak}} = 240\, \pm \,8$</span> km s<span class="mathjax-tex">$^{-1}$</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 170" title="M.J. Reid et al., Trigonometric parallaxes of high mass star forming regions: the structure and kinematics of the Milky Way. Astrophys. J. 783, 130 (2014). 
 arXiv:1401.5377
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR170" id="ref-link-section-d52098281e18292">170</a>], and the galactic escape velocity <span class="mathjax-tex">$v_{\mathrm{esc}} = 528 \pm 25$</span> km s<span class="mathjax-tex">$^{-1}$</span>, based on the <i>Gaia</i> data [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 171" title="A.J. Deason, A. Fattahi et al., The local high-velocity tail and the galactic escape speed. MNRAS 485, 3514–3526 (2019). 
 arXiv:1901.02016
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR171" id="ref-link-section-d52098281e18360">171</a>].</p><p>We employ a Gaussian likelihood for the running top quark mass in the <span class="mathjax-tex">$\overline{\text {MS}}$</span> scheme with a central value <span class="mathjax-tex">$m_t (m_t) = 162.9$</span> GeV and an error 2.0 GeV [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 172" title="ATLAS: G. Aad et al., Measurement of the top-quark mass in 
 
 
 
 $$t{\bar{t}}+1$$
 
 
 t
 
 
 t
 
 
 ¯
 
 
 +
 1
 
 
 -jet events collected with the ATLAS detector in 
 
 
 
 $$pp$$
 
 
 pp
 
 
 collisions at 
 
 
 
 $$\sqrt{s}=8$$
 
 
 
 s
 
 =
 8
 
 
 TeV. JHEP 11, 150 (2019). 
 arXiv:1905.02302
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR172" id="ref-link-section-d52098281e18433">172</a>].<sup><a href="#Fn14"><span class="u-visually-hidden">Footnote </span>14</a></sup> The top pole mass <span class="mathjax-tex">$(m_t^\text {pole})$</span> is then computed using the following formula:</p><div id="Equ44" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} m_t^{\text {pole}} = m_t (m_t) \left[ 1 + \dfrac{4}{3} \dfrac{\alpha _s (m_Z)}{\pi } \right] . \end{aligned}$$</span></div><div class="c-article-equation__number"> (44) </div></div><p>We use only the one-loop QCD corrections in this shift in order to be consistent with the procedure carried out in Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 172" title="ATLAS: G. Aad et al., Measurement of the top-quark mass in 
 
 
 
 $$t{\bar{t}}+1$$
 
 
 t
 
 
 t
 
 
 ¯
 
 
 +
 1
 
 
 -jet events collected with the ATLAS detector in 
 
 
 
 $$pp$$
 
 
 pp
 
 
 collisions at 
 
 
 
 $$\sqrt{s}=8$$
 
 
 
 s
 
 =
 8
 
 
 TeV. JHEP 11, 150 (2019). 
 arXiv:1905.02302
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR172" id="ref-link-section-d52098281e18666">172</a>]. We have checked that the above expression gives the expected result for the top pole mass and matches well with Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 172" title="ATLAS: G. Aad et al., Measurement of the top-quark mass in 
 
 
 
 $$t{\bar{t}}+1$$
 
 
 t
 
 
 t
 
 
 ¯
 
 
 +
 1
 
 
 -jet events collected with the ATLAS detector in 
 
 
 
 $$pp$$
 
 
 pp
 
 
 collisions at 
 
 
 
 $$\sqrt{s}=8$$
 
 
 
 s
 
 =
 8
 
 
 TeV. JHEP 11, 150 (2019). 
 arXiv:1905.02302
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR172" id="ref-link-section-d52098281e18669">172</a>].</p><p>For direct detection, we employ nuisance parameter likelihoods for a number of hadronic input parameters that are used to evaluate form factors at the nuclear scale. Specifically, we use a product of four Gaussian likelihoods to include the constraints on <span class="mathjax-tex">$\sigma _{\pi N}$</span>, <span class="mathjax-tex">${\varDelta } s$</span>, <span class="mathjax-tex">$g_T^s$</span> and <span class="mathjax-tex">$r_s^2$</span> quoted in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Tab3">3</a>. The remaining hadronic input parameters are fixed to the central values given in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Tab3">3</a>.</p></div></div></section><section data-title="Results"><div class="c-article-section" id="Sec16-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec16"><span class="c-article-section__title-number">4 </span>Results</h2><div class="c-article-section__content" id="Sec16-content"><p>We now present the results obtained from comprehensive scans of the parameter space introduced above. These scans were carried out with the differential evolution sampler <span class="u-sans-serif">Diver v1.4.0</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 173" title="GAMBIT Scanner Workgroup: G.D. Martinez, J. McKay et al., Comparison of statistical sampling methods with ScannerBit, the GAMBIT scanning module. Eur. Phys. J. C 77, 761 (2017). 
 arXiv:1705.07959
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR173" id="ref-link-section-d52098281e18792">173</a>] using a population of <span class="mathjax-tex">$5 \times 10^4$</span> and a convergence threshold of either <span class="mathjax-tex">$10^{-5}$</span> or <span class="mathjax-tex">$3 \times 10^{-5}$</span>. As we will analyse our scan results using profile likelihood maps, the sole aim of the scans is to map out the likelihood function in sufficient detail across the high-likelihood regions of parameter space. In particular, no statistical interpretation is associated with the density of parameter samples, and we can therefore combine samples from scans that use different metrics on the parameter space. To ensure that all parameter regions are properly explored, we perform two different types of scans:</p><ul class="u-list-style-dash"> <li> <p><b>Full:</b> We explore DM masses up to the unitarity bound (<span class="mathjax-tex">$5 \, \text {GeV}< m_\chi < 150\,\text {TeV}$</span> and <span class="mathjax-tex">$20 \, \text {GeV}< {\Lambda }< 300 \, \text {TeV}$</span>).<sup><a href="#Fn15"><span class="u-visually-hidden">Footnote </span>15</a></sup> In these scans, <span class="mathjax-tex">$m_\chi $</span> and <span class="mathjax-tex">${\Lambda }$</span> are scanned on a logarithmic scale, while the Wilson coefficients are scanned on both a linear and a logarithmic scale (i.e. we combine the samples from both scanning strategies to achieve a thorough exploration of the whole parameter space).</p> </li> <li> <p><b>Restricted:</b> We consider the parameter region where experimental constraints are most relevant (<span class="mathjax-tex">$m_\chi < 500\,\text {GeV}$</span> and <span class="mathjax-tex">${\Lambda }< 2 \, \text {TeV}$</span>). In these scans the DM mass is scanned on a linear scale, the scale <span class="mathjax-tex">${\Lambda }$</span> on a logarithmic scale and the Wilson coefficients on a scale that is logarithmic on <span class="mathjax-tex">$[-4\pi ,-10^{-6}]$</span>, linear on <span class="mathjax-tex">$[-10^{-6},10^{-6}]$</span> and logarithmic on <span class="mathjax-tex">$[10^{-6},4\pi ]$</span>. This approach was found to achieve the optimum resolution of the LHC constraints while simultaneously ensuring that enough viable samples are also found for small <span class="mathjax-tex">${\Lambda }$</span> when some or all of the Wilson coefficients are tightly constrained.</p> </li> </ul><p>All nuisance parameters are scanned on a linear scale. In the first set of scans, we fix the Wilson coefficients for all dimension-7 operators to zero, so that there are 6 model parameters and 8 nuisance parameters. The second set of scans then includes all 14 Wilson coefficients, bringing the total number of parameters up to 24.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-2" data-title="Fig. 2"><figure><figcaption><b id="Fig2" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 2</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/2" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig2_HTML.png?as=webp"><img aria-describedby="Fig2" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig2_HTML.png" alt="figure 2" loading="lazy" width="685" height="272"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-2-desc"><p>Profile likelihood in the <span class="mathjax-tex">$m_\chi $</span>–<span class="mathjax-tex">${\Lambda }$</span> plane when considering only dimension-6 operators and capping the LHC likelihood at the value of the background-only hypothesis. The white contours indicate the <span class="mathjax-tex">$1\sigma $</span> and <span class="mathjax-tex">$2\sigma $</span> confidence regions and the best-fit point is indicated by the white star. The shaded region (corresponding to <span class="mathjax-tex">${\Lambda }\le 2 m_\chi $</span>) is excluded by the EFT validity requirement. In the right panel, the parameter ranges have been restricted to the most interesting region. Note that the position of the best-fit points in the two panels is somewhat arbitrary, as there is a degeneracy between <span class="mathjax-tex">${\Lambda }$</span> and <span class="mathjax-tex">${\mathcal {C}}_{3,4}^{(6)}$</span> and hence the likelihood is essentially constant across the entire yellow region (see also Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig4">4</a>)</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/2" data-track-dest="link:Figure2 Full size image" aria-label="Full size image figure 2" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-3" data-title="Fig. 3"><figure><figcaption><b id="Fig3" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 3</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/3" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig3_HTML.png?as=webp"><img aria-describedby="Fig3" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig3_HTML.png" alt="figure 3" loading="lazy" width="685" height="1764"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-3-desc"><p>Profile likelihood in terms of the DM mass, the relic density and the rescaled annihilation cross-section. As in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig2">2</a>, we consider only dimension-6 operators and cap the LHC likelihood at the value of the background-only hypothesis. The solid red line in the middle panel denotes the “initial construction” projection sensitivity of Cherenkov Telescope Array (CTA) towards the Galactic Centre (GC) for the <span class="mathjax-tex">$b{\bar{b}}$</span> final state [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 136" title="CTA: A. Acharyya et al., Sensitivity of the Cherenkov Telescope Array to a dark matter signal from the Galactic Centre. JCAP 01, 057 (2021). 
 arXiv:2007.16129
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR136" id="ref-link-section-d52098281e19611">136</a>]</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/3" data-track-dest="link:Figure3 Full size image" aria-label="Full size image figure 3" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>We furthermore consider a number of variations in the constraints that we include in our scans:</p><ul class="u-list-style-dash"> <li> <p>We perform scans where the DM particle is allowed to be a sub-component (<span class="mathjax-tex">$f_\chi \le 1$</span>) and scans where we require that the DM relic density be saturated (<span class="mathjax-tex">$f_\chi \approx 1$</span>), see Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec8">3.2</a>;</p> </li> <li> <p>We perform scans with both the capped LHC likelihood and the full LHC likelihood (see Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec14">3.5</a>);</p> </li> <li> <p>When considering the full LHC likelihood, we furthermore apply two different prescriptions for imposing the EFT validity: a hard cut-off and a smooth cut-off (see Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec4">2.2</a>).</p> </li> </ul><p>Unless explicitly stated otherwise, our default choices for the discussion below are to allow a DM sub-component and consider the capped LHC likelihood with a hard cut-off.</p><h3 class="c-article__sub-heading" id="Sec17"><span class="c-article-section__title-number">4.1 </span>Capped LHC likelihood</h3><p>Let us begin with the case that the LHC likelihood is capped, i.e. it cannot exceed the likelihood of the background-only hypothesis. We first consider only dimension-6 operators with different requirements for the DM relic density, and then also include dimension-7 operators.</p><h4 class="c-article__sub-heading c-article__sub-heading--small" id="Sec18"><span class="c-article-section__title-number">4.1.1 </span>Dimension-6 operators only (relic density upper bound)</h4><p>Our main results for this case are shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig2">2</a> in terms of the DM mass and the new physics scale <span class="mathjax-tex">${\Lambda }$</span>. The left panel corresponds to the full parameter range, whereas the right panel provides a closer look at the most interesting parameter region. We find a large viable parameter space but also a number of notable features. For large values of <span class="mathjax-tex">$m_\chi $</span> and <span class="mathjax-tex">${\Lambda }$</span>, the allowed parameter space is determined by the EFT validity requirement <span class="mathjax-tex">${\Lambda }> 2 m_\chi $</span> and the relic density requirement which, combined with the perturbativity bound on the Wilson coefficients, implies an upper bound on <span class="mathjax-tex">${\Lambda }$</span> for given <span class="mathjax-tex">$m_\chi $</span>. These different constraints are compatible only for <span class="mathjax-tex">$m_\chi < 150 \, \text {TeV}$</span>, implying an upper bound on the scale of new physics of <span class="mathjax-tex">${\Lambda }< 300 \, \text {TeV}$</span>. This limit corresponds to the well-known unitarity bound for thermal freeze-out [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 65" title="K. Griest, M. Kamionkowski, Unitarity limits on the mass and radius of dark matter particles. Phys. Rev. Lett. 64, 615 (1990)" href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR65" id="ref-link-section-d52098281e19923">65</a>].</p><p>The zoomed-in version in the right panel reveals a number of additional features. In the top-left corner (small <span class="mathjax-tex">$m_\chi $</span>, large <span class="mathjax-tex">${\Lambda }$</span>), there are strong constraints from the LHC, which make it impossible to satisfy the relic density requirement. These constraints become weaker as <span class="mathjax-tex">${\Lambda }$</span> decreases and the EFT can only be trusted for smaller values of <img src="//media.springernature.com/lw21/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq496_HTML.gif" style="width:21px;max-width:none;" alt="">. The various sharp features correspond to the points where <span class="mathjax-tex">${\Lambda }$</span> crosses the boundary of a specific <img src="//media.springernature.com/lw21/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq498_HTML.gif" style="width:21px;max-width:none;" alt=""> bin, leading to a jump in the likelihood. In our conservative approach, LHC constraints are completely absent for <span class="mathjax-tex">${\Lambda }< 200 \, \text {GeV}$</span>. Finally, we find that there is a slight upward fluctuation in <i>Fermi</i>-LAT data, which can be fitted for <span class="mathjax-tex">$m_\chi = 5.0 \,\text {GeV}$</span> and <span class="mathjax-tex">$f_\chi ^2 \langle \sigma v \rangle _0 = 1.1 \times 10^{-27} \, \text {cm}^3~ \text {s}^{-1}$</span>.<sup><a href="#Fn16"><span class="u-visually-hidden">Footnote </span>16</a></sup></p><p>We emphasize that a great advantage of our approach is that we treat the new-physics scale <span class="mathjax-tex">${\Lambda }$</span> as an independent parameter, which is kept explicit in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig2">2</a> (rather than being profiled out like the individual Wilson coefficients). This makes it possible in a straight-forward way to distinguish those parameter regions where the EFT predictions can be considered robust and those parameter regions where additional constraints may apply. As discussed in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec4">2.2</a>, the EFT is expected to be valid if <span class="mathjax-tex">${\Lambda }$</span> is sufficiently greater than the largest <span class="mathjax-tex">$p_T$</span> bin considered in the LHC analyses, i.e. <span class="mathjax-tex">${\Lambda }> 1.3 \, \text {TeV}$</span>. Conversely, for <span class="mathjax-tex">${\Lambda }< 200 \, \text {GeV}$</span> we conservatively suppress constraints from the LHC, such that the viable parameter regions found in this range must be interpreted with great care. For intermediate values of <span class="mathjax-tex">${\Lambda }$</span>, LHC constraints are being applied but may depend on the specific UV completion. Which of these parameter regions is considered most interesting depends on the specific context and is left to the reader.</p><p>A complementary perspective is provided in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig3">3</a>, which shows the allowed parameter regions in terms of the DM mass, the relic density and the rescaled annihilation cross-section. A number of additional features become apparent in these plots. First, for <span class="mathjax-tex">$m_\chi \lesssim 100\,\text {GeV}$</span> it is impossible to saturate the observed DM relic density, <span class="mathjax-tex">${\varOmega }_{\text {DM}} h^2 = 0.12$</span>, due to the combined constraints from direct and indirect detection experiments. However, these constraints are suppressed for DM sub-components, such that it is possible to have very small relic densities in this mass region. For <span class="mathjax-tex">$m_\chi > 100 \, \text {GeV}$</span> (corresponding to <span class="mathjax-tex">${\Lambda }> 200 \, \text {GeV}$</span>), on the other hand, constraints from the LHC become relevant, which are not suppressed for DM sub-components. These constraints are then again relaxed for <span class="mathjax-tex">$m_\chi > rsim 1 \, \text {TeV}$</span> as the LHC energy becomes insufficient to produce a pair of DM particles.</p><p>For <span class="mathjax-tex">$m_\chi \lesssim 1 \, \text {TeV}$</span>, we find that there is a direct correspondence between <span class="mathjax-tex">${\varOmega }_\chi h^2$</span> and the rescaled annihilation cross-section <span class="mathjax-tex">$f_\chi ^2 \langle \sigma v \rangle _0$</span>. This is because the operators that induce <i>p</i>-wave annihilations (in particular <span class="mathjax-tex">${\mathcal {C}}^{(6)}_2$</span>) are strongly constrained by the LHC and direct detection experiments, and the annihilation cross-section is therefore always dominated by the <i>s</i>-wave contribution. For larger DM masses, it becomes possible for the <i>p</i>-wave contribution to dominate the relic density calculation, such that the total annihilation cross-section is velocity-dependent and becomes tiny in the present universe. While indirect detection experiments presently cannot probe the relevant parameter space for TeV-scale DM, it is worth stressing that CTA will be able to do so for operators that induce <i>s</i>-wave annihilation. We illustrate this in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig3">3</a> by indicating the sensitivity of CTA to a DM signal from the galactic center [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 136" title="CTA: A. Acharyya et al., Sensitivity of the Cherenkov Telescope Array to a dark matter signal from the Galactic Centre. JCAP 01, 057 (2021). 
 arXiv:2007.16129
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR136" id="ref-link-section-d52098281e20661">136</a>] (for simplicity based on the assumption of <span class="mathjax-tex">$b{\bar{b}}$</span> final states, noting that <i>any</i> hadronic DM annihilation channel results in very similar gamma-ray spectra at these energies). We note that the CTA sensitivity indicated in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig3">3</a> is based on assuming a standard Einasto profile as expected for WIMP DM; if the DM density in the galactic center is instead roughly constant, the sensitivity can worsen by up to about one order of magnitude [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 136" title="CTA: A. Acharyya et al., Sensitivity of the Cherenkov Telescope Array to a dark matter signal from the Galactic Centre. JCAP 01, 057 (2021). 
 arXiv:2007.16129
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR136" id="ref-link-section-d52098281e20705">136</a>].</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-4" data-title="Fig. 4"><figure><figcaption><b id="Fig4" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 4</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/4" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig4_HTML.png?as=webp"><img aria-describedby="Fig4" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig4_HTML.png" alt="figure 4" loading="lazy" width="685" height="269"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-4-desc"><p>Profile likelihood in the <span class="mathjax-tex">${\Lambda }$</span>–<span class="mathjax-tex">${\mathcal {C}}^{(6)}_4$</span> plane (left) and the <span class="mathjax-tex">${\Lambda }$</span>–<span class="mathjax-tex">${\mathcal {C}}^{(6)}_3$</span> plane (right) for the restricted parameter ranges. As in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig2">2</a>, we only consider dimension-6 operators and cap the LHC likelihood at the value of the background-only hypothesis. The contour lines show the <span class="mathjax-tex">$1\sigma $</span> and <span class="mathjax-tex">$2\sigma $</span> confidence regions. Note that the position of the best-fit points (white stars) in the two panels is somewhat arbitrary, as there is a degeneracy between <span class="mathjax-tex">${\Lambda }$</span> and <span class="mathjax-tex">${\mathcal {C}}_{3,4}^{(6)}$</span> and hence the likelihood is essentially constant across the entire yellow region</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/4" data-track-dest="link:Figure4 Full size image" aria-label="Full size image figure 4" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>Let us finally consider the allowed parameter space in terms of the Wilson coefficients. The coefficient <span class="mathjax-tex">${\mathcal {C}}^{(6)}_1$</span> gives rise to spin-independent scattering, which is very strongly constrained by direct detection experiments. Thus, this coefficient is required to be so small that it cannot give a sizeable contribution to any other process. The coefficient <span class="mathjax-tex">${\mathcal {C}}^{(6)}_4$</span>, on the other hand, gives rise to spin-dependent interactions, for which constraints are significantly weaker. We show the allowed parameter regions for this coefficient in the left panel of Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig4">4</a>. The observed mirror symmetry results from the fact that all experimental predictions (and hence the likelihoods) are invariant under a global sign change of all Wilson coefficients. For <span class="mathjax-tex">${\Lambda }< 200\,\text {GeV}$</span>, all constraints are furthermore invariant under the rescaling <span class="mathjax-tex">${\mathcal {C}} \rightarrow \alpha ^2 {\mathcal {C}}$</span>, <span class="mathjax-tex">${\Lambda }\rightarrow \alpha {\Lambda }$</span>, which explains why the allowed parameter region grows with increasing <span class="mathjax-tex">${\Lambda }$</span>. For <span class="mathjax-tex">${\Lambda }> 200 \, \text {GeV}$</span>, LHC constraints become relevant and strongly constrain the magnitude of the coefficient. Very similar results are obtained for the coefficient <span class="mathjax-tex">${\mathcal {C}}^{(6)}_2$</span>, which gives rise to a momentum-suppressed spin-independent scattering (see Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Tab2">2</a>).</p><p>In the right panel of Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig4">4</a>, we show the allowed parameter region in terms of <span class="mathjax-tex">${\mathcal {C}}^{(6)}_3$</span>, which induces scattering that is <i>simultaneously</i> momentum-suppressed and spin-dependent, such that direct detection constraints are very weak. Correspondingly, we find that this coefficient is largely unconstrained for <span class="mathjax-tex">${\Lambda }< 200\,\text {GeV}$</span>. We also identify this coefficient as giving the main contribution for fitting the <i>Fermi</i>-LAT excess. For larger values of <span class="mathjax-tex">${\Lambda }$</span>, on the other hand, the constraints are very similar to the ones for <span class="mathjax-tex">${\mathcal {C}}^{(6)}_{2,4}$</span> as the LHC only has limited sensitivity to distinguish the spin structure of the operators.</p><h4 class="c-article__sub-heading c-article__sub-heading--small" id="Sec19"><span class="c-article-section__title-number">4.1.2 </span>Dimension-6 operators only (relic density saturated)</h4><p>Next we consider the case where the relic density constraint is imposed not only as an upper limit but as an actual measurement, i.e., the DM particle under consideration is required to account for all of the DM in the universe via the effective interactions that we consider. We show in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig5">5</a> the allowed parameter space in the restricted <span class="mathjax-tex">$m_\chi $</span>–<span class="mathjax-tex">${\Lambda }$</span> plane when considering a capped LHC likelihood, i.e. the same likelihoods as in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig2">2</a> apart from the modified relic density requirement. As expected from the top row of Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig3">3</a>, it is not possible to saturate the observed relic density for <span class="mathjax-tex">$m_\chi \lesssim 100 \, \text {GeV}$</span>. The reason is that for such small DM masses the relic density requirement is incompatible with <i>Fermi</i>-LAT and CMB bounds on the annihilation cross-section for operators that predict dominantly <i>s</i>-wave annihilation (<img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq541_HTML.gif" style="width:31px;max-width:none;" alt=""> and <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq542_HTML.gif" style="width:31px;max-width:none;" alt="">), and incompatible with direct detection and LHC constraints for <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq543_HTML.gif" style="width:31px;max-width:none;" alt=""> and <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq544_HTML.gif" style="width:31px;max-width:none;" alt="">.</p><p>Constraints from direct and indirect detection experiments are also responsible for the preference for larger DM masses visible in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig5">5</a>. In particular, the <i>Fermi</i>-LAT likelihood pushes the best-fit point towards the boundary <span class="mathjax-tex">$m_\chi = 500 \, \text {GeV}$</span>. We find the likelihood of the best-fit point to be slightly worse than for the background-only hypothesis: <span class="mathjax-tex">$2 {\varDelta } \ln {\mathcal {L}} \equiv 2(\ln {\mathcal {L}}^{\text {best-fit}} - \ln {\mathcal {L}}^{\text {ideal}}) = -0.5$</span>. Extending the range of the scan to larger DM masses would allow the model to fully evade the <i>Fermi</i>-LAT constraint. This would shift the best-fit point and the allowed parameter regions to slightly larger DM masses without changing the remaining conclusions (see also Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig3">3</a>).</p><p>For a complementary view of the parameter space, we show in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig6">6</a> the predicted number of signal events in the next-generation direct detection experiment LZ [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 174" title="LUX-ZEPLIN: D.S. Akerib et al., Projected WIMP sensitivity of the LUX-ZEPLIN dark matter experiment. Phys. Rev. D 101, 052002 (2020). 
 arXiv:1802.06039
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR174" id="ref-link-section-d52098281e21602">174</a>] as a function of the DM mass. Due to the various different operators contributing to the DM-nucleus scattering, the predicted number of signal events is a more useful quantity to consider than the DM-nucleon scattering cross-section at zero momentum transfer. The predicted number of events corresponds to nuclear recoil energies in the search window <span class="mathjax-tex">$[6 \, \text {keV}, 30 \, \text {keV}]$</span> and assumes an exposure of <span class="mathjax-tex">$5.6 \times 10^6 \, \text {kg\,days}$</span> and 50% acceptance for nuclear recoils (see Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 110" title="GAMBIT Collaboration: P. Athron et al., Global analyses of Higgs portal singlet dark matter models using GAMBIT. Eur. Phys. J. C 79, 38 (2019). 
 arXiv:1808.10465
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR110" id="ref-link-section-d52098281e21677">110</a>] for details on our implementation of LZ).</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-5" data-title="Fig. 5"><figure><figcaption><b id="Fig5" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 5</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/5" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig5_HTML.png?as=webp"><img aria-describedby="Fig5" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig5_HTML.png" alt="figure 5" loading="lazy" width="685" height="562"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-5-desc"><p>Same as the right panel of Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig2">2</a> but requiring the DM relic density to be saturated (rather than imposing an upper bound only)</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/5" data-track-dest="link:Figure5 Full size image" aria-label="Full size image figure 5" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>We find that of the order of 10 events are predicted around the best-fit point, which requires a non-zero contribution from the operator <img src="//media.springernature.com/lw29/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq549_HTML.gif" style="width:29px;max-width:none;" alt=""> leading to spin-independent (but momentum-suppressed) scattering. However, the predicted number of events varies significantly within the allowed region of parameter space and can be as small as 0.1 at 68% confidence level. In this case the main contribution arises from the mixing of the operator <img src="//media.springernature.com/lw29/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq550_HTML.gif" style="width:29px;max-width:none;" alt=""> into the operator <img src="//media.springernature.com/lw29/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq551_HTML.gif" style="width:29px;max-width:none;" alt=""> as given in Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Equ21">21</a>).<sup><a href="#Fn17"><span class="u-visually-hidden">Footnote </span>17</a></sup> While such an event number is too low to be detected with next-generation experiments, it is still well above the neutrino background and should be observable with more ambitious future detectors such as DARWIN [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 175" title="DARWIN: J. Aalbers et al., DARWIN: towards the ultimate dark matter detector. JCAP 11, 017 (2016). 
 arXiv:1606.07001
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR175" id="ref-link-section-d52098281e21739">175</a>] or DarkSide-20k [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 176" title="C.E. Aalseth et al., DarkSide-20k: a 20 tonne two-phase LAr TPC for direct dark matter detection at LNGS. Eur. Phys. J. Plus 133, 131 (2018). 
 arXiv:1707.08145
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR176" id="ref-link-section-d52098281e21742">176</a>].</p><p>Another interesting approach would be to not perform a relic density calculation at all and simply assume that <span class="mathjax-tex">$f_\chi = 1$</span> is achieved through some modification of early universe cosmology. In this case it would also be possible to consider <span class="mathjax-tex">${\Lambda }< 2 m_\chi $</span> since the calculation of the annihilation cross-section is unnecessary. However, since none of the other likelihoods that we consider give a strong preference for a DM signal, there would then be no lower bound on the interaction strength of the DM particle, i.e. it would be possible for all Wilson coefficients to vanish simultaneously. Hence we expect all combinations of <span class="mathjax-tex">$m_\chi $</span> and <span class="mathjax-tex">${\Lambda }$</span> to be viable in this approach, and we do not explore this direction further in the present work.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-6" data-title="Fig. 6"><figure><figcaption><b id="Fig6" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 6</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/6" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig6_HTML.png?as=webp"><img aria-describedby="Fig6" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig6_HTML.png" alt="figure 6" loading="lazy" width="685" height="565"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-6-desc"><p>Profile likelihood in terms of <span class="mathjax-tex">$m_\chi $</span> and the predicted number of signal events in the LZ experiment when <span class="mathjax-tex">$\chi $</span> accounts for all of the observed DM abundance (as in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig5">5</a>)</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/6" data-track-dest="link:Figure6 Full size image" aria-label="Full size image figure 6" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-7" data-title="Fig. 7"><figure><figcaption><b id="Fig7" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 7</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/7" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig7_HTML.png?as=webp"><img aria-describedby="Fig7" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig7_HTML.png" alt="figure 7" loading="lazy" width="685" height="263"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-7-desc"><p>Profile likelihood in the <span class="mathjax-tex">$m_\chi $</span>–<span class="mathjax-tex">${\Lambda }$</span> plane (left) and in terms of <span class="mathjax-tex">$m_\chi $</span> and the predicted relic density (right) when considering all dimension-6 and dimension-7 operators, and capping the LHC likelihood at the value of the background-only hypothesis. The white contours show the <span class="mathjax-tex">$1\sigma $</span> and <span class="mathjax-tex">$2\sigma $</span> confidence regions and the white star marks the best-fit point. For comparison, we also show the <span class="mathjax-tex">$1\sigma $</span> and <span class="mathjax-tex">$2\sigma $</span> confidence region contours (dashed grey lines) and best-fit point (grey star) for the case of dimension-6 operators only in the right panel (see also Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig3">3</a>)</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/7" data-track-dest="link:Figure7 Full size image" aria-label="Full size image figure 7" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><h4 class="c-article__sub-heading c-article__sub-heading--small" id="Sec20"><span class="c-article-section__title-number">4.1.3 </span>Operators up to dimension 7 (relic density upper bound)</h4><p>We now turn to the case where we simultaneously consider all dimension-6 operators as well as the dimension-7 operators involving DM particles and quarks or gluons introduced in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec2">2</a>. We remind the reader that we neglect additional dimension-7 operators involving Higgs bosons that would arise in theories respecting unbroken electroweak symmetry (which are phenomenologically irrelevant) as well as operators with derivative interactions (which largely give redundant information). Even with these restrictions our analysis requires 24-dimensional (16 model + 8 nuisance) parameter scans.</p><p>In Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig7">7</a>, we show the allowed regions in the <span class="mathjax-tex">$m_\chi $</span>-<span class="mathjax-tex">${\Lambda }$</span> plane (left) and in the <span class="mathjax-tex">$m_\chi $</span>–<span class="mathjax-tex">${\varOmega }_\chi h^2$</span> plane (right) when using the capped LHC likelihood. As before, we find that the parameter region at small <span class="mathjax-tex">$m_\chi $</span> and <span class="mathjax-tex">${\Lambda }$</span> can fit the slight <i>Fermi</i>-LAT excess with best-fit values: <span class="mathjax-tex">$m_\chi = 5.5$</span> GeV and <span class="mathjax-tex">$f_\chi ^2 \langle \sigma v \rangle _0 = 1.9 \times 10^{-27}$</span> cm<span class="mathjax-tex">$^{3}$</span> s<span class="mathjax-tex">$^{-1}$</span>.</p><p>As the inclusion of additional parameters can only increase the profile likelihood, we expect the allowed regions of parameter space to be larger than the ones found above. Interestingly, the differences between the left panel of Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig7">7</a> and the right panel of Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig2">2</a> are rather minimal. In other words, the inclusion of the 10 additional dimension-7 operators does not open up new parameter space in terms of <span class="mathjax-tex">$m_\chi $</span> and <span class="mathjax-tex">${\Lambda }$</span>. This is of course expected for the parameter region with large <span class="mathjax-tex">$m_\chi $</span> and small <span class="mathjax-tex">${\Lambda }$</span> (bottom-right), which is excluded by the EFT validity constraint but surprising for the region with small <span class="mathjax-tex">$m_\chi $</span> and large <span class="mathjax-tex">${\Lambda }$</span> (top-left), which is excluded by the combination of the LHC constraints and the relic density requirement.</p><p>The reason why this parameter space remains inaccessible is that the gluon operators <img src="//media.springernature.com/lw32/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq581_HTML.gif" style="width:32px;max-width:none;" alt=""> are strongly constrained by the LHC for <span class="mathjax-tex">${\Lambda }> 200 \, \text {GeV}$</span> and can therefore not contribute significantly to the annihilation cross-section. The quark operators <img src="//media.springernature.com/lw50/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq583_HTML.gif" style="width:50px;max-width:none;" alt="">, on the other hand, are unconstrained by the LHC, but for <span class="mathjax-tex">$m_\chi < m_t$</span>, the resulting annihilation cross-section is suppressed by a factor <span class="mathjax-tex">$m_b^2 m_\chi ^2 / {\Lambda }^6$</span>, and therefore too small to produce a relic abundance that evades the upper bound from the relic density requirement given the perturbativity bound on the Wilson coefficients.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-8" data-title="Fig. 8"><figure><figcaption><b id="Fig8" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 8</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/8" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig8_HTML.png?as=webp"><img aria-describedby="Fig8" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig8_HTML.png" alt="figure 8" loading="lazy" width="685" height="263"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-8-desc"><p>Profile likelihood in the <span class="mathjax-tex">$m_\chi $</span>–<span class="mathjax-tex">${\Lambda }$</span> parameter plane when considering only dimension-6 operators and including the full LHC likelihood. In the left (right) panel, we impose a hard (smooth) cut-off in the predicted missing energy spectrum for <img src="//media.springernature.com/lw57/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq588_HTML.gif" style="width:57px;max-width:none;" alt=""> (see text for details)</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/8" data-track-dest="link:Figure8 Full size image" aria-label="Full size image figure 8" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-9" data-title="Fig. 9"><figure><figcaption><b id="Fig9" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 9</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/9" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig9_HTML.png?as=webp"><img aria-describedby="Fig9" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig9_HTML.png" alt="figure 9" loading="lazy" width="685" height="491"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-9-desc"><p><i>Top panel:</i> Examples of missing energy spectra for the CMS monojet search [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 95" title="CMS: A.M. Sirunyan et al., Search for new physics in final states with an energetic jet or a hadronically decaying 
 
 
 
 $$W$$
 
 W
 
 or 
 
 
 
 $$Z$$
 
 Z
 
 boson and transverse momentum imbalance at 
 
 
 
 $$\sqrt{s}=13\,\text{TeV}$$
 
 
 
 s
 
 =
 13
 
 TeV
 
 
 . Phys. Rev. D 97, 092005 (2018). 
 arXiv:1712.02345
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR95" id="ref-link-section-d52098281e22721">95</a>], illustrating different choices for imposing an EFT validity requirement on the signal prediction. For <img src="//media.springernature.com/lw57/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq589_HTML.gif" style="width:57px;max-width:none;" alt="">, we scale the <img src="//media.springernature.com/lw21/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq590_HTML.gif" style="width:21px;max-width:none;" alt=""> signal spectrum with the factor <img src="//media.springernature.com/lw72/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq591_HTML.gif" style="width:72px;max-width:none;" alt=""> as described in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec4">2.2</a>. The green distributions show the resulting signal predictions for four different choices of <i>a</i>, from <span class="mathjax-tex">$a = 0$</span> (lightest green), corresponding to no modification of the spectrum, to <span class="mathjax-tex">$a \rightarrow \infty $</span> (darkest green), which removes any signal contribution in <img src="//media.springernature.com/lw21/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq594_HTML.gif" style="width:21px;max-width:none;" alt=""> bins above <img src="//media.springernature.com/lw57/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq595_HTML.gif" style="width:57px;max-width:none;" alt="">. The SM background prediction (purple) and the observed event counts (black points) are taken from Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 95" title="CMS: A.M. Sirunyan et al., Search for new physics in final states with an energetic jet or a hadronically decaying 
 
 
 
 $$W$$
 
 W
 
 or 
 
 
 
 $$Z$$
 
 Z
 
 boson and transverse momentum imbalance at 
 
 
 
 $$\sqrt{s}=13\,\text{TeV}$$
 
 
 
 s
 
 =
 13
 
 TeV
 
 
 . Phys. Rev. D 97, 092005 (2018). 
 arXiv:1712.02345
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR95" id="ref-link-section-d52098281e22820">95</a>]. The last bin, starting at <img src="//media.springernature.com/lw112/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq596_HTML.gif" style="width:112px;max-width:none;" alt="">, contains any overflow and is thus not normalised to a given bin width. <i>Bottom panel:</i> A small bar chart per bin showing the pulls, defined as <span class="mathjax-tex">$(\text {data} - \text {prediction}) / \text {uncertainty}$</span>, resulting from adding the indicated signal prediction on top of the SM background prediction. The uncertainty includes the background uncertainty, signal uncertainty and statistical data uncertainty, added in quadrature. The purple bars show the pulls when only including the SM background prediction. The <span class="mathjax-tex">$\chi ^2$</span> values in the top panel legend correspond to the sum of the squared pulls in each case. These values are intended for illustration only, i.e. they do not correspond directly to <span class="mathjax-tex">$-2\ln {\mathcal {L}}_{{\text {CMS}}}$</span> where <span class="mathjax-tex">${\mathcal {L}}_{{\text {CMS}}}$</span> is defined in Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Equ39">39</a>)</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/9" data-track-dest="link:Figure9 Full size image" aria-label="Full size image figure 9" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>Comparing the right panel of Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig7">7</a> to the allowed parameter regions from Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig3">3</a> (indicated by the grey dashed lines) does however reveal a number of differences. First of all, it is now possible to saturate the relic density bound for small <span class="mathjax-tex">$m_\chi $</span> (and small <span class="mathjax-tex">${\Lambda }$</span>), thanks to the contribution of <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq603_HTML.gif" style="width:31px;max-width:none;" alt=""> and <img src="//media.springernature.com/lw31/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq604_HTML.gif" style="width:31px;max-width:none;" alt="">, which both give suppressed signals in direct and indirect detection experiments and are therefore largely unconstrained. Moreover, for <span class="mathjax-tex">$m_\chi > m_t$</span>, we find that the predicted relic abundance can be substantially smaller than for the case with only dimension-6 operators, thanks to the contribution from the dimension-7 DM-quark operators <img src="//media.springernature.com/lw50/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq606_HTML.gif" style="width:50px;max-width:none;" alt="">. The additional freedom in the annihilation cross-section also implies that the impact of imposing a strict relic density requirement is reduced compared to the case of dimension-6 operators only and will therefore not be discussed in further detail here.</p><p>We emphasize that global fits with 24 free parameters are computationally quite challenging, in particular when the best-fit region is not strongly constrained by data. As a result the contours in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig7">7</a> are less smooth than for the case of dimension-6 operators only. This is particularly obvious in the right panel for DM masses around <span class="mathjax-tex">$150\,\text {GeV}$</span>. In this region many operators are strongly constrained by LHC data while annihilations into top quarks are kinematically forbidden. This makes it challenging to find parameter points that satisfy the relic density constraint, leading to comparably poor sampling. We have confirmed explicitly that this is not a physical effect, i.e. the allowed parameter region should be smooth and extend to <span class="mathjax-tex">${\varOmega }_\chi h^2 = 0.12$</span> everywhere.</p><h3 class="c-article__sub-heading" id="Sec21"><span class="c-article-section__title-number">4.2 </span>Full LHC likelihood</h3><h4 class="c-article__sub-heading c-article__sub-heading--small" id="Sec22"><span class="c-article-section__title-number">4.2.1 </span>Dimension-6 operators only (relic density upper bound)</h4><p>We now move onto the case where the full (rather than capped) LHC likelihood is included in the scans. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig8">8</a> shows the allowed parameter regions in terms of <span class="mathjax-tex">$m_\chi $</span> and <span class="mathjax-tex">${\Lambda }$</span> for the case where we introduce a hard cut-off in the missing energy spectrum for <img src="//media.springernature.com/lw57/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq611_HTML.gif" style="width:57px;max-width:none;" alt=""> (left panel), and the case where we introduce a smooth cut-off (right panel), as discussed in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Sec4">2.2</a>. We see that in both cases, the results differ from Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig2">2</a>, i.e. there is a preference for higher <span class="mathjax-tex">${\Lambda }$</span> values. This preference arises due to data excesses in a few high-<img src="//media.springernature.com/lw21/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq613_HTML.gif" style="width:21px;max-width:none;" alt=""> bins in the ATLAS and CMS monojet searches.</p><p>The difference in the above two results can be understood as follows. For <img src="//media.springernature.com/lw57/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq614_HTML.gif" style="width:57px;max-width:none;" alt="">, the missing energy spectrum arising from DM is harder than the background, while for <img src="//media.springernature.com/lw57/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq615_HTML.gif" style="width:57px;max-width:none;" alt="">, we either set it to zero or assume that it drops rapidly. Thus, the ratio of signal-to-background is largest for <img src="//media.springernature.com/lw57/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq616_HTML.gif" style="width:57px;max-width:none;" alt="">, enabling our model to (partially) fit local excesses in the data. This is illustrated in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig9">9</a>, which shows the missing energy spectra for background and signal in CMS when applying different EFT validity prescriptions. As seen in the distribution of pulls in the bottom panel, the CMS search observes a couple of <span class="mathjax-tex">$1\sigma $</span>–<span class="mathjax-tex">$2\sigma $</span> data excesses in bins around <img src="//media.springernature.com/lw93/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq619_HTML.gif" style="width:93px;max-width:none;" alt=""> (purple bars). By including a DM signal prediction on top of the SM background, these excesses can be reduced, thus reducing the pulls and improving the overall fit to the data (green bars). However, unless the signal spectrum dies off sufficiently fast above <img src="//media.springernature.com/lw93/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq620_HTML.gif" style="width:93px;max-width:none;" alt="">, the model will be penalized for causing larger pulls in the highest-<img src="//media.springernature.com/lw21/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq621_HTML.gif" style="width:21px;max-width:none;" alt=""> bins, as seen for instance for the unmodified signal spectrum (lightest green bars, corresponding to <span class="mathjax-tex">$a=0$</span>).</p><p>For the case where we impose a hard cut-off (left panel in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig8">8</a>), we find (at the <span class="mathjax-tex">$1\sigma $</span> level) separate parameter regions preferred by the CMS analysis (<span class="mathjax-tex">${\Lambda }\approx 700 \, \text {GeV}$</span>) and the ATLAS analysis (<span class="mathjax-tex">${\Lambda } > rsim 1 \, \text {TeV}$</span>), with the overall best-fit point corresponding to the latter and being preferred relative to the background-only hypothesis by <span class="mathjax-tex">$2 {\varDelta } \ln {\mathcal {L}} = 2.2$</span>. When allowing for a smooth cut-off, on the other hand, the best-fit solution produces a partially improved fit to both excesses simultaneously, by suppressing the signal distribution approximately proportional to <img src="//media.springernature.com/lw71/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq627_HTML.gif" style="width:71px;max-width:none;" alt="">. In this case, the best-fit point has <span class="mathjax-tex">$2 {\varDelta } \ln {\mathcal {L}} = 2.6$</span>.<sup><a href="#Fn18"><span class="u-visually-hidden">Footnote </span>18</a></sup> We refrain from translating these numbers into <i>p</i>-values, which would require extensive Monte Carlo simulations. For both choices of cut-off, the best-fit point predicts an annihilation cross-section that is slightly larger than the thermal cross-section, such that the DM particles in this case would only constitute a DM sub-component.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-10" data-title="Fig. 10"><figure><figcaption><b id="Fig10" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 10</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/10" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig10_HTML.png?as=webp"><img aria-describedby="Fig10" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig10_HTML.png" alt="figure 10" loading="lazy" width="685" height="263"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-10-desc"><p>Same as Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig8">8</a> but requiring the DM relic abundance to match the total observed DM abundance</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/10" data-track-dest="link:Figure10 Full size image" aria-label="Full size image figure 10" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>We emphasise that the preference for a non-zero signal contribution is to some degree an artefact of the way in which we have implemented the EFT validity requirement. Realistic UV completions typically do not introduce sharp features in the missing energy spectrum, making it harder to fit excesses observed in individual bins. Nevertheless, our findings emphasise the need to analyse missing energy searches at the LHC in terms of specific models in order to assess whether the signal preference found in the EFT approach can be recovered (at least partially) in a more complete setting.</p><h4 class="c-article__sub-heading c-article__sub-heading--small" id="Sec23"><span class="c-article-section__title-number">4.2.2 </span>Dimension-6 operators only (relic density saturated)</h4><p>We have also run scans with the full LHC likelihood and requiring the DM relic density to be saturated (see Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig10">10</a>). We find the expected changes with respect to Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig8">8</a>, namely that small DM masses are disfavoured. For the case of a hard cut-off, the position of the best-fit point is unaffected, while for a smooth cut-off, it is pushed to slightly larger values of <span class="mathjax-tex">$m_\chi $</span> and <span class="mathjax-tex">${\Lambda }$</span>. The respective preferences are reduced slightly to <span class="mathjax-tex">$2 {\varDelta } \ln {\mathcal {L}} = 1.9$</span> and 2.0. We also find that the best-fit point requires several Wilson coefficients to be non-zero. While the LHC signal can be fitted by either <img src="//media.springernature.com/lw28/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq632_HTML.gif" style="width:28px;max-width:none;" alt=""> or <img src="//media.springernature.com/lw28/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq633_HTML.gif" style="width:28px;max-width:none;" alt="">, the relic density can only be reproduced with a contribution from <img src="//media.springernature.com/lw28/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq634_HTML.gif" style="width:28px;max-width:none;" alt="">. This is because <img src="//media.springernature.com/lw30/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq635_HTML.gif" style="width:30px;max-width:none;" alt=""> lead to suppressed annihilation rates in the early universe, compared to <img src="//media.springernature.com/lw29/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq636_HTML.gif" style="width:29px;max-width:none;" alt="">, while <img src="//media.springernature.com/lw29/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq637_HTML.gif" style="width:29px;max-width:none;" alt=""> is strongly constrained by direct detection (see also Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Tab2">2</a>).</p><p>A summary of the various best-fit points from our scans with dimension-6 operators only is given in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Tab5">5</a>. We note that essentially all of our scans require a non-zero contribution from <img src="//media.springernature.com/lw28/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq638_HTML.gif" style="width:28px;max-width:none;" alt=""> at the best-fit point in order to satisfy the relic density requirement. This is an interesting finding given that this operator is present only for Dirac fermion DM but not for Majorana fermion DM. In other words, we expect our results to change considerably for the case of Majorana fermion DM. Satisfying the relic density constraint with dimension-6 operators only while evading experimental constraints will be very challenging in this case.</p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-5"><figure><figcaption class="c-article-table__figcaption"><b id="Tab5" data-test="table-caption">Table 5 Best-fit points from our various scans involving dimension-6 operators with restricted parameter ranges (<span class="mathjax-tex">$5 \, \mathrm {GeV} \le m_\chi \le 500 \, \text {GeV}$</span> and <span class="mathjax-tex">$20 \, \text {GeV} \le {\Lambda }\le 2 \, \text {TeV}$</span>). For most scans, there are degeneracies between different parameters around the best-fit point. In these cases, we only quote the combination that is well-constrained rather than each parameter individually. Parameters not stated explicitly are compatible with zero</b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-09712-6/tables/5" aria-label="Full size table 5"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><h4 class="c-article__sub-heading c-article__sub-heading--small" id="Sec24"><span class="c-article-section__title-number">4.2.3 </span>Operators up to dimension 7</h4><p>In Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig11">11</a>, we finally show the case where the full LHC likelihood is included when simultaneously considering all dimension-6 and dimension-7 operators, using either a hard cut-off (left) or profiling over possible smooth cut-offs (right). In the former case we find that the result looks very similar to the case of dimension-6 operators only (left panel of Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig8">8</a>) and also the likelihood at the best-fit point is very similar. In the latter case we find that it is now possible to simultaneously accommodate the upward fluctuations in the <i>Fermi</i>-LAT data (as in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig2">2</a>) and in the LHC data (as in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig8">8</a>). Doing so requires a small new-physics scale <span class="mathjax-tex">${\Lambda }\sim 80\,\text {GeV}$</span> together with a rather soft cut-off <span class="mathjax-tex">$a \approx 1.7$</span> of the <img src="//media.springernature.com/lw21/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq658_HTML.gif" style="width:21px;max-width:none;" alt=""> spectrum above <span class="mathjax-tex">${\Lambda }$</span>. The resulting best-fit point has <span class="mathjax-tex">$2 {\varDelta } \ln {\mathcal {L}} = 2.9$</span>, which is the highest likelihood found in any of our scans.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-11" data-title="Fig. 11"><figure><figcaption><b id="Fig11" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 11</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/11" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig11_HTML.png?as=webp"><img aria-describedby="Fig11" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fig11_HTML.png" alt="figure 11" loading="lazy" width="685" height="263"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-11-desc"><p>Profile likelihood in the <span class="mathjax-tex">$m_\chi $</span>–<span class="mathjax-tex">${\Lambda }$</span> parameter plane when considering dimension-6 and dimension-7 operators and including the full LHC likelihood. In the left (right) panel, we impose a hard (smooth) cut-off in the predicted missing energy spectrum for <img src="//media.springernature.com/lw57/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq663_HTML.gif" style="width:57px;max-width:none;" alt=""> (see text for more details)</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-09712-6/figures/11" data-track-dest="link:Figure11 Full size image" aria-label="Full size image figure 11" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>A closer analysis reveals that the contribution of the dimension-6 operators is in fact not necessary to accommodate the small LHC excesses, because sufficiently large contributions can also be obtained from the gluon operators. For example, the operator <img src="//media.springernature.com/lw29/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq664_HTML.gif" style="width:29px;max-width:none;" alt=""> is essentially unconstrained by direct detection and can induce sizeable LHC signals if <img src="//media.springernature.com/lw28/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq665_HTML.gif" style="width:28px;max-width:none;" alt=""> takes values close to the perturbativity bound. While it is challenging to satisfy the relic density requirement using only gluon operators, the allowed parameter space expands substantially when including a contribution from the dimension-7 DM-quark operators <img src="//media.springernature.com/lw43/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq666_HTML.gif" style="width:43px;max-width:none;" alt="">. As a result, the allowed regions in <span class="mathjax-tex">$m_\chi $</span>–<span class="mathjax-tex">${\Lambda }$</span> parameter space look very similar to the ones shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Fig11">11</a> even when the Wilson coefficients of all dimension-6 operators are set to zero. For the same reason we expect no significant difference between Dirac and Majorana DM particles in this case. This complex interplay between different operators only becomes apparent in a global analysis and would be missed when studying individual operators separately.</p></div></div></section><section data-title="Conclusions and outlook"><div class="c-article-section" id="Sec25-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec25"><span class="c-article-section__title-number">5 </span>Conclusions and outlook</h2><div class="c-article-section__content" id="Sec25-content"><p>In this work we have presented the first global analysis of the full set of effective operators up to dimension 7 involving a Dirac fermion DM particle and quarks or gluons. Key to enabling such an analysis were a number of technical developments:</p><ul class="u-list-style-dash"> <li> <p>We have fully automated the calculation of direct detection constraints, including mixing under RG evolution and matching onto non-relativistic effective operators at the hadronic scale, and indirect detection constraints, including cosmological constraints on energy injection;</p> </li> <li> <p>We have adopted a novel approach to address the issue of EFT validity at the LHC. Rather than performing a simple truncation procedure, we introduce a smooth cut-off for <img src="//media.springernature.com/lw57/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq669_HTML.gif" style="width:57px;max-width:none;" alt=""> and treat this parameter as a nuisance parameter to ensure that no artificially strong exclusions arise from the tails of the predicted distributions;</p> </li> <li> <p>We employ highly efficient likelihood calculations and sampling algorithms that make it possible to scan over up to 24 parameters (the DM mass <span class="mathjax-tex">$m_\chi $</span>, the new physics scale <span class="mathjax-tex">${\Lambda }$</span>, 14 Wilson coefficients and 8 nuisance parameters).</p> </li> </ul><p>In combination, these developments enable us, for the first time, to include interference effects between different operators in all parts of the analysis.</p><p>Our main result is that it is typically possible to suppress the scattering and annihilation cross-sections in the non-relativistic limit, and thereby evade direct and indirect detection constraints while satisfying the relic density requirement. Doing so does not require finely tuned cancellations or interference effects but is a direct consequence of the spin structure of the operators that we consider. The LHC, however, plays a special role, because the production of relativistic DM particles is less sensitive to the specific spin structure of the operator. As a result, we find generally strong constraints on small DM masses and large <span class="mathjax-tex">${\Lambda }$</span>, both for the case of dimension-6 operators only and also when including dimension-7 operators. Moreover, when allowing excesses in individual LHC bins to be fitted (rather than artificially capping the LHC likelihood), we find a slight preference for a DM signal with a relatively low new physics scale. Given that the magnitude of this excess is sensitive to the precise EFT validity prescription that we adopt, we have not attempted to quantify its significance within the EFT.</p><p>We find that it is typically not necessary to have simultaneous contributions from many different operators in order to find viable regions of parameter space. Indeed, large viable regions of parameter space are found both for the case when we consider only dimension-6 operators and only dimension-7 operators. These sets of operators can easily be generated by integrating out a heavy mediator with spin 1 or spin 0, respectively. However, we typically do require sizeable contributions from operators that violate parity and/or CP, reflecting the pressure on the simplest WIMP models from the non-observation of a DM signal in direct and indirect detection experiments (see Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 110" title="GAMBIT Collaboration: P. Athron et al., Global analyses of Higgs portal singlet dark matter models using GAMBIT. Eur. Phys. J. C 79, 38 (2019). 
 arXiv:1808.10465
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR110" id="ref-link-section-d52098281e24594">110</a>] for a similar discussion in the context of Higgs portal models).</p><p>A particularly interesting observation is that it is generally not possible to have a large hierarchy between the DM mass and the new physics scale without violating the relic density requirement. In particular, for <span class="mathjax-tex">$m_\chi \lesssim 100 \, \text {GeV}$</span>, constraints from the LHC require <span class="mathjax-tex">${\Lambda }\lesssim 200 \, \text {GeV}$</span>, meaning that the EFT is no longer valid at LHC energies and additional new degrees of freedom should be kinematically accessible. Moreover, the well-known unitarity bound on the DM mass implies a robust upper bound on the scale of new physics of the order of <span class="mathjax-tex">$300 \, \text {TeV}$</span>. We also note that for masses in the TeV range CTA will have a unique chance of probing part of the currently inaccessible parameter space that is spanned between the EFT validity and the relic density constraints.</p><p>We emphasise that it is generally possible for the DM particle under consideration to constitute only a DM sub-component (in which case, constraints from direct and indirect detection experiments are correspondingly suppressed), but large regions of viable parameter space also remain when requiring the relic density to be saturated. In future studies, it will be interesting to modify the way in which the relic density calculation is included. For example, one could consider an initial particle-antiparticle asymmetry in the dark sector, which would make it possible to saturate the relic density in parameter regions that would normally predict an underabundance, while at the same time suppressing constraints from indirect detection experiments. A more radical approach would be to not perform a relic density calculation at all and simply assume that the observed relic abundance (with <span class="mathjax-tex">$f_\chi =1$</span>) is achieved through some unspecified modification of standard cosmology. A detailed analysis of direct detection constraints on such a scenario is in preparation.</p><p>An exciting direction for future investigation is to embed the EFTs considered here into a more complete approach based on UV-complete (or simplified) models. Almost all of the machinery developed for the present work will also be directly applicable in this case. The main difference arises in the interpretation of the LHC signals. If the mediator of the DM interactions is kinematically accessible at LHC energies, it will be essential to not only consider the resulting changes in the missing energy spectra, but also additional signatures arising from visible decays of the mediator [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 177" title="M. Chala, F. Kahlhoefer, M. McCullough, G. Nardini, K. Schmidt-Hoberg, Constraining dark sectors with monojets and dijets. JHEP 07, 089 (2015). 
 arXiv:1503.05916
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR177" id="ref-link-section-d52098281e24722">177</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 178" title="M. Fairbairn, J. Heal, F. Kahlhoefer, P. Tunney, Constraints on Z’ models from LHC dijet searches and implications for dark matter. JHEP 09, 018 (2016). 
 arXiv:1605.07940
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR178" id="ref-link-section-d52098281e24725">178</a>] (see Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 179" title="I. Bischer, T. Plehn, W. Rodejohann, Dark matter EFT, the third-neutrino WIMPs. SciPost Phys. 10, 039 (2021). 
 arXiv:2008.04718
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR179" id="ref-link-section-d52098281e24728">179</a>] for a recent discussion of how to connect DM EFTs and UV-complete models). Furthermore, close to the EFT validity boundary the presence of the mediator will also modify the results of the relic density calculation, thus affecting the target couplings for these signals. It will also be interesting to see to what extent the slight LHC excesses can be accommodated in such a set-up.</p><p>Another important extension of the present work will be to also consider operators coupling DM to leptons as well as electroweak gauge and Higgs bosons in order to embed our approach into a framework that respects the unbroken electroweak symmetry. Given that the relevant RG evolution is known (and already implemented in <span class="u-sans-serif">DirectDM</span>) and that the relevant annihilation cross-sections and injection spectra can be calculated automatically, such an extension does not pose any conceptual difficulties regarding direct or indirect detection constraints and relic density calculations. Again, the most challenging part will be to include all relevant collider constraints (which in this case stem also from LEP). Given that these constraints are typically weaker than the corresponding ones for quarks, it will be interesting to see whether some of the conclusions found in the present work can be relaxed and additional viable parameter space opens up.</p><p>Finally, it will be very interesting to consider DM EFTs with non-trivial flavour structure, for example with couplings predominantly to the third generation. In such a set-up, one generally expects sizeable flavour-changing neutral currents and hence it will be essential to connect the EFTs used to study DM to the ones employed in flavour physics. Such a study would be particularly exciting given the recently observed anomalies in various flavour observables (see e.g. Refs. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="R. Barbieri, A view of flavour physics in 2021. Acta Phys. Polon. B 52, 789 (2021). 
 https://doi.org/10.5506/APhysPolB.52.789
 
 . 
 arXiv:2103.15635
 
 " href="#ref-CR180" id="ref-link-section-d52098281e24740">180</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="ATLAS, CMS, LHCb: E. Graverini, Flavour anomalies: a review. J. Phys. Conf. Ser. 1137, 012025 (2019). 
 arXiv:1807.11373
 
 " href="#ref-CR181" id="ref-link-section-d52098281e24740_1">181</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 182" title="LHCb: R. Aaij et al., Test of lepton universality in beauty-quark decays. 
 arXiv:2103.11769
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR182" id="ref-link-section-d52098281e24743">182</a>]). Moreover, the effects of electroweak operator mixing on the direct detection bounds are expected to be much more pronounced in such scenarios.</p><p>Of course, the most important outstanding task is to collect more data that may shed light on the nature of DM. Upcoming LHC analyses will improve the sensitivity to missing energy signatures of DM, the next generation of direct detection experiments [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 174" title="LUX-ZEPLIN: D.S. Akerib et al., Projected WIMP sensitivity of the LUX-ZEPLIN dark matter experiment. Phys. Rev. D 101, 052002 (2020). 
 arXiv:1802.06039
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR174" id="ref-link-section-d52098281e24749">174</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 183" title="PandaX: H. Zhang et al., Dark matter direct search sensitivity of the PandaX-4T experiment. Sci. China Phys. Mech. Astron. 62, 31011 (2019). 
 arXiv:1806.02229
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR183" id="ref-link-section-d52098281e24752">183</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 184" title="XENON: E. Aprile et al., Projected WIMP sensitivity of the XENONnT dark matter experiment. JCAP 11, 031 (2020). 
 arXiv:2007.08796
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR184" id="ref-link-section-d52098281e24755">184</a>] will be able to probe substantially smaller scattering cross-sections, and ongoing [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="MAGIC, Fermi-LAT: M.L. Ahnen et al., Limits to dark matter annihilation cross-section from a combined analysis of MAGIC and Fermi-LAT observations of dwarf satellite galaxies. JCAP 02, 039 (2016). 
 arXiv:1601.06590
 
 " href="#ref-CR185" id="ref-link-section-d52098281e24758">185</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="H.E.S.S.: H. Abdallah et al., Search for dark matter annihilations towards the inner Galactic halo from 10 years of observations with H.E.S.S. Phys. Rev. Lett. 117, 111301 (2016). 
 arXiv:1607.08142
 
 " href="#ref-CR186" id="ref-link-section-d52098281e24758_1">186</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 187" title="AMS: M. Aguilar et al., The Alpha Magnetic Spectrometer (AMS) on the international space station: part II—results from the first seven years. Phys. Rep. 894, 1–116 (2021)" href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR187" id="ref-link-section-d52098281e24761">187</a>] and planned [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 136" title="CTA: A. Acharyya et al., Sensitivity of the Cherenkov Telescope Array to a dark matter signal from the Galactic Centre. JCAP 01, 057 (2021). 
 arXiv:2007.16129
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR136" id="ref-link-section-d52098281e24765">136</a>] indirect detection experiments will probe the freeze-out paradigm with unprecedented precision. Our present work has shown that this effort is highly worthwhile given the wide regions of parameter space that cannot currently be excluded in a model-independent way. Reducing the vast number of viable possibilities to explain DM therefore remains a key challenge for years to come.</p></div></div></section> </div> <section data-title="Data Availability Statement"><div class="c-article-section" id="data-availability-statement-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="data-availability-statement">Data Availability Statement</h2><div class="c-article-section__content" id="data-availability-statement-content"> <p>This manuscript has associated data in a data repository. [Authors’ comment: see Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 66" title="GAMBIT Collaboration, Supplementary data: thermal WIMPs and the scale of new physics: global fits of dirac dark matter effective field theories (2021). 
 https://zenodo.org/record/4836397
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR66" id="ref-link-section-d52098281e24801">66</a>], the DOI being <a href="https://doi.org/10.5281/zenodo.4836397">https://doi.org/10.5281/zenodo.4836397</a>].</p> </div></div></section><section data-title="Notes"><div class="c-article-section" id="notes-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="notes">Notes</h2><div class="c-article-section__content" id="notes-content"><ol class="c-article-footnote c-article-footnote--listed"><li class="c-article-footnote--listed__item" id="Fn1" data-counter="1."><div class="c-article-footnote--listed__content"><p>Furthermore, there are two additional dimension-6 operators describing DM-photon interactions: the anapole moment and the charge radius [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 74" title="B.J. Kavanagh, P. Panci, R. Ziegler, Faint light from dark matter: classifying and constraining dark matter-photon effective operators. JHEP 04, 089 (2019). 
 arXiv:1810.00033
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR74" id="ref-link-section-d52098281e2453">74</a>]. For a recent discussion of LHC constraints on these operators we refer to Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 75" title="C. Arina, A. Cheek, K. Mimasu, L. Pagani, Light and darkness: consistently coupling dark matter to photons via effective operators. Eur. Phys. J. C 81, 223 (2021). 
 arXiv:2005.12789
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR75" id="ref-link-section-d52098281e2456">75</a>].</p></div></li><li class="c-article-footnote--listed__item" id="Fn2" data-counter="2."><div class="c-article-footnote--listed__content"><p>These constraints also ensure that the dimension-six operators do not explicitly break electroweak symmetry, which requires <img src="//media.springernature.com/lw186/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq55_HTML.gif" style="width:186px;max-width:none;" alt=""> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 76" title="U. Haisch, F. Kahlhoefer, T.M.P. Tait, On mono-W signatures in spin-1 simplified models. Phys. Lett. B 760, 207–213 (2016). 
 arXiv:1603.01267
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR76" id="ref-link-section-d52098281e2687">76</a>].</p></div></li><li class="c-article-footnote--listed__item" id="Fn3" data-counter="3."><div class="c-article-footnote--listed__content"><p>Note that as per our assumptions the Wilson coefficients <img src="//media.springernature.com/lw65/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq73_HTML.gif" style="width:65px;max-width:none;" alt=""> are taken to be zero at scale <span class="mathjax-tex">${\Lambda }$</span> and are only generated by the RG effects.</p></div></li><li class="c-article-footnote--listed__item" id="Fn4" data-counter="4."><div class="c-article-footnote--listed__content"><p>For historical reasons, in the numerical code <span class="mathjax-tex">$\log (m_t^2/{\Lambda }^2)$</span> instead of <span class="mathjax-tex">$\log (m_Z^2/{\Lambda }^2)$</span> was used. The effect on the numerical results is negligible.</p></div></li><li class="c-article-footnote--listed__item" id="Fn5" data-counter="5."><div class="c-article-footnote--listed__content"><p>Small remnant effects of the bottom and charm Yukawa coupling are taken into account below the EW scale via double weak insertions [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 79" title="J. Brod, B. Grinstein, E. Stamou, J. Zupan, Weak mixing below the weak scale in dark-matter direct detection. JHEP 02, 174 (2018). 
 arXiv:1801.04240
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR79" id="ref-link-section-d52098281e3512">79</a>] that are included in the <span class="u-sans-serif">DirectDM</span> code.</p></div></li><li class="c-article-footnote--listed__item" id="Fn6" data-counter="6."><div class="c-article-footnote--listed__content"><p>We emphasize that <span class="mathjax-tex">$m_{\chi \chi }$</span> and <img src="//media.springernature.com/lw21/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq133_HTML.gif" style="width:21px;max-width:none;" alt=""> are not strongly correlated in the sense that there are events with both <img src="//media.springernature.com/lw77/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq134_HTML.gif" style="width:77px;max-width:none;" alt=""> (if the DM pair is emitted approximately in the longitudinal direction) and <img src="//media.springernature.com/lw77/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq135_HTML.gif" style="width:77px;max-width:none;" alt=""> (if the two DM particles are light and approximately collinear). Since our approach does not modify the spectrum for <img src="//media.springernature.com/lw57/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq136_HTML.gif" style="width:57px;max-width:none;" alt="">, we risk overestimating the differential cross-section in this regime. However, the sensitivity of the LHC to DM EFTs typically stems from events with large <img src="//media.springernature.com/lw21/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq137_HTML.gif" style="width:21px;max-width:none;" alt="">, where our prescription is more appropriate.</p></div></li><li class="c-article-footnote--listed__item" id="Fn7" data-counter="7."><div class="c-article-footnote--listed__content"><p>We note that the explicit factor of <span class="mathjax-tex">$m_q$</span> in the definition of <img src="//media.springernature.com/lw50/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq161_HTML.gif" style="width:50px;max-width:none;" alt=""> not only affects the EFT validity but also directly the resulting phenomenology. Hence our results cannot be easily translated to operators with non-trivial flavour structure.</p></div></li><li class="c-article-footnote--listed__item" id="Fn8" data-counter="8."><div class="c-article-footnote--listed__content"><p>For a recent review on the effects of non-standard cosmological scenarios, see Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 129" title="A. Arbey, F. Mahmoudi, Dark matter and the early Universe: a review. Prog. Part. Nucl. Phys. 119, 103865 (2021). 
 arXiv:2104.11488
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR129" id="ref-link-section-d52098281e11557">129</a>].</p></div></li><li class="c-article-footnote--listed__item" id="Fn9" data-counter="9."><div class="c-article-footnote--listed__content"><p>Note that, since we include uncertainties in both the relic density calculation and the <i>Planck</i> measurement, <span class="mathjax-tex">${\varOmega }_\chi h^2$</span> can deviate slightly from 0.120 even when we require that the DM relic abundance is saturated. In this case we set <span class="mathjax-tex">$f_\chi = {\text {min}}({\varOmega }_\chi h^2 / 0.120, 1)$</span>, which can therefore slightly deviate from (but never exceed) unity.</p></div></li><li class="c-article-footnote--listed__item" id="Fn10" data-counter="10."><div class="c-article-footnote--listed__content"><p>It is noteworthy that <span class="u-sans-serif">DarkAges</span> calculates <span class="mathjax-tex">$ f_{\text {eff}} (z) $</span> as a redshift-dependent function instead of a single redshift-independent coefficient <span class="mathjax-tex">$ f_{\mathrm{eff}} $</span>, as it is implicitly assumed in Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Equ37">37</a>). In order to compress the function <span class="mathjax-tex">$ f_{\text {eff}} (z) $</span> into this coefficient, it is convolved with a weighting function <i>W</i>(<i>z</i>) that encodes the CMB sensitivity to energy injection through <i>s</i>–wave annihilation as a function of redshift [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 145" title="T.R. Slatyer, Indirect dark matter signatures in the cosmic dark ages. I. Generalizing the bound on s-wave dark matter annihilation from Planck results. Phys. Rev. D 93, 023527 (2016). 
 arXiv:1506.03811
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR145" id="ref-link-section-d52098281e14673">145</a>].</p></div></li><li class="c-article-footnote--listed__item" id="Fn11" data-counter="11."><div class="c-article-footnote--listed__content"><p>We note that this conclusion would be radically different for unsuppressed direct annihilation to leptons [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 153" title="L. Bergström, T. Bringmann, I. Cholis, D. Hooper, C. Weniger, New limits on dark matter annihilation from AMS cosmic ray positron data. Phys. Rev. Lett. 111, 171101 (2013). 
 arXiv:1306.3983
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR153" id="ref-link-section-d52098281e15092">153</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 154" title="A. Ibarra, A.S. Lamperstorfer, J. Silk, Dark matter annihilations and decays after the AMS-02 positron measurements. Phys. Rev. D 89, 063539 (2014). 
 arXiv:1309.2570
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR154" id="ref-link-section-d52098281e15095">154</a>], which would result from leptonic operators analogous to <img src="//media.springernature.com/lw30/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq368_HTML.gif" style="width:30px;max-width:none;" alt="">.</p></div></li><li class="c-article-footnote--listed__item" id="Fn12" data-counter="12."><div class="c-article-footnote--listed__content"><p>We note that this combination also reduces the impact of a local <span class="mathjax-tex">$\sim 2.5\sigma $</span> excess in the third-highest bin, which would otherwise strongly bias our analysis.</p></div></li><li class="c-article-footnote--listed__item" id="Fn13" data-counter="13."><div class="c-article-footnote--listed__content"><p>A practical benefit of having a continuous likelihood penalty rather than a hard cut is that it helps guide the parameter sampler towards the viable regions in the high-dimensional DM EFT parameter space.</p></div></li><li class="c-article-footnote--listed__item" id="Fn14" data-counter="14."><div class="c-article-footnote--listed__content"><p>This is based on taking an average of the asymmetric uncertainty <span class="mathjax-tex">$m_t (m_t) = 162.9^{+2.3}_{-1.6}$</span> GeV; see table 2 in Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 172" title="ATLAS: G. Aad et al., Measurement of the top-quark mass in 
 
 
 
 $$t{\bar{t}}+1$$
 
 
 t
 
 
 t
 
 
 ¯
 
 
 +
 1
 
 
 -jet events collected with the ATLAS detector in 
 
 
 
 $$pp$$
 
 
 pp
 
 
 collisions at 
 
 
 
 $$\sqrt{s}=8$$
 
 
 
 s
 
 =
 8
 
 
 TeV. JHEP 11, 150 (2019). 
 arXiv:1905.02302
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR172" id="ref-link-section-d52098281e18507">172</a>].</p></div></li><li class="c-article-footnote--listed__item" id="Fn15" data-counter="15."><div class="c-article-footnote--listed__content"><p>We note that for the largest values of <span class="mathjax-tex">$m_\chi $</span> and <span class="mathjax-tex">${\Lambda }$</span> that we consider in these scans our approach of specifying all operators in the broken phase of electroweak symmetry and ignoring the effects of running between <span class="mathjax-tex">$\mu = {\Lambda }$</span> and <span class="mathjax-tex">$\mu = m_Z$</span> becomes questionable. The constraints that we obtain above the TeV scale are therefore only approximate and should be interpreted with care.</p></div></li><li class="c-article-footnote--listed__item" id="Fn16" data-counter="16."><div class="c-article-footnote--listed__content"><p>We emphasize that, although the best-fit point lies close to the boundary of the parameter space, there is no preference for even smaller values of the DM mass and hence our findings would not change when extending the scan range.</p></div></li><li class="c-article-footnote--listed__item" id="Fn17" data-counter="17."><div class="c-article-footnote--listed__content"><p>We note that this mixing effect could in principle be cancelled by contributions from additional effective operators not included in our analysis, such that even smaller event rates may be achievable.</p></div></li><li class="c-article-footnote--listed__item" id="Fn18" data-counter="18."><div class="c-article-footnote--listed__content"><p>We note that in both cases, the likelihood is very flat around the maximum and hence the precise location of the best-fit point is somewhat arbitrary.</p></div></li><li class="c-article-footnote--listed__item" id="Fn19" data-counter="19."><div class="c-article-footnote--listed__content"><p>If <span class="u-sans-serif">MadGraph</span> and <span class="u-sans-serif">CalcHEP</span> output is generated from a fully functional <span class="u-sans-serif">FeynRules</span> model implementation with trivial colour structures, the only missing vertices should be four-fermion vertices.</p></div></li><li class="c-article-footnote--listed__item" id="Fn20" data-counter="20."><div class="c-article-footnote--listed__content"><p>Since <span class="u-sans-serif">GAMBIT</span> <span class="u-sans-serif">v2.0</span>, decaying DM is supported, such that the capability <img src="//media.springernature.com/lw87/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figad_HTML.gif" style="width:87px;max-width:none;" alt=""> was generalised and renamed.</p></div></li></ol></div></div></section><div id="MagazineFulltextArticleBodySuffix"><section aria-labelledby="Bib1" data-title="References"><div class="c-article-section" id="Bib1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Bib1">References</h2><div class="c-article-section__content" id="Bib1-content"><div data-container-section="references"><ol class="c-article-references" data-track-component="outbound reference" data-track-context="references section"><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="1."><p class="c-article-references__text" id="ref-CR1">B.W. Lee, S. Weinberg, Cosmological lower bound on heavy neutrino masses. Phys. Rev. Lett. <b>39</b>, 165–168 (1977)</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.39.165" data-track-item_id="10.1103/PhysRevLett.39.165" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.39.165" aria-label="Article reference 1" data-doi="10.1103/PhysRevLett.39.165">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=1977PhRvL..39..165L" aria-label="ADS reference 1">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 1" href="http://scholar.google.com/scholar_lookup?&title=Cosmological%20lower%20bound%20on%20heavy%20neutrino%20masses&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.39.165&volume=39&pages=165-168&publication_year=1977&author=Lee%2CBW&author=Weinberg%2CS"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="2."><p class="c-article-references__text" id="ref-CR2">G. Arcadi, M. Dutra et al., The waning of the WIMP? A review of models, searches, and constraints. Eur. Phys. J. C <b>78</b>, 203 (2018). [<a href="http://arxiv.org/abs/1703.07364" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1703.07364">arXiv:1703.07364</a>]</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1140/epjc/s10052-018-5662-y" data-track-item_id="10.1140/epjc/s10052-018-5662-y" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1140%2Fepjc%2Fs10052-018-5662-y" aria-label="Article reference 2" data-doi="10.1140/epjc/s10052-018-5662-y">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018EPJC...78..203A" aria-label="ADS reference 2">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 2" href="http://scholar.google.com/scholar_lookup?&title=The%20waning%20of%20the%20WIMP%3F%20A%20review%20of%20models%2C%20searches%2C%20and%20constraints&journal=Eur.%20Phys.%20J.%20C&doi=10.1140%2Fepjc%2Fs10052-018-5662-y&volume=78&publication_year=2018&author=Arcadi%2CG&author=Dutra%2CM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="3."><p class="c-article-references__text" id="ref-CR3">R.K. Leane, T.R. Slatyer, J.F. Beacom, K.C.Y. Ng, GeV-scale thermal WIMPs: not even slightly ruled out. Phys. Rev. D <b>98</b>, 023016 (2018). <a href="http://arxiv.org/abs/1805.10305" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1805.10305">arXiv:1805.10305</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.98.023016" data-track-item_id="10.1103/PhysRevD.98.023016" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.98.023016" aria-label="Article reference 3" data-doi="10.1103/PhysRevD.98.023016">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018PhRvD..98b3016L" aria-label="ADS reference 3">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 3" href="http://scholar.google.com/scholar_lookup?&title=GeV-scale%20thermal%20WIMPs%3A%20not%20even%20slightly%20ruled%20out&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.98.023016&volume=98&publication_year=2018&author=Leane%2CRK&author=Slatyer%2CTR&author=Beacom%2CJF&author=Ng%2CKCY"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="4."><p class="c-article-references__text" id="ref-CR4">J. Fan, M. Reece, L.-T. Wang, Non-relativistic effective theory of dark matter direct detection. JCAP <b>1011</b>, 042 (2010). <a href="http://arxiv.org/abs/1008.1591" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1008.1591">arXiv:1008.1591</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1475-7516/2010/11/042" data-track-item_id="10.1088/1475-7516/2010/11/042" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1475-7516%2F2010%2F11%2F042" aria-label="Article reference 4" data-doi="10.1088/1475-7516/2010/11/042">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2010JCAP...11..042F" aria-label="ADS reference 4">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 4" href="http://scholar.google.com/scholar_lookup?&title=Non-relativistic%20effective%20theory%20of%20dark%20matter%20direct%20detection&journal=JCAP&doi=10.1088%2F1475-7516%2F2010%2F11%2F042&volume=1011&publication_year=2010&author=Fan%2CJ&author=Reece%2CM&author=Wang%2CL-T"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="5."><p class="c-article-references__text" id="ref-CR5">P. Agrawal, Z. Chacko, C. Kilic, R.K. Mishra, A classification of dark matter candidates with primarily spin-dependent interactions with matter. <a href="http://arxiv.org/abs/1003.1912" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1003.1912">arXiv:1003.1912</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="6."><p class="c-article-references__text" id="ref-CR6">A. Fitzpatrick, K.M. Zurek, Dark moments and the DAMA-CoGeNT puzzle. Phys. Rev. D <b>82</b>, 075004 (2010). <a href="http://arxiv.org/abs/1007.5325" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1007.5325">arXiv:1007.5325</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.82.075004" data-track-item_id="10.1103/PhysRevD.82.075004" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.82.075004" aria-label="Article reference 6" data-doi="10.1103/PhysRevD.82.075004">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2010PhRvD..82g5004F" aria-label="ADS reference 6">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 6" href="http://scholar.google.com/scholar_lookup?&title=Dark%20moments%20and%20the%20DAMA-CoGeNT%20puzzle&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.82.075004&volume=82&publication_year=2010&author=Fitzpatrick%2CA&author=Zurek%2CKM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="7."><p class="c-article-references__text" id="ref-CR7">A. Crivellin, U. Haisch, Dark matter direct detection constraints from gauge bosons loops. Phys. Rev. D <b>90</b>, 115011 (2014). <a href="http://arxiv.org/abs/1408.5046" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1408.5046">arXiv:1408.5046</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.90.115011" data-track-item_id="10.1103/PhysRevD.90.115011" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.90.115011" aria-label="Article reference 7" data-doi="10.1103/PhysRevD.90.115011">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014PhRvD..90k5011C" aria-label="ADS reference 7">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 7" href="http://scholar.google.com/scholar_lookup?&title=Dark%20matter%20direct%20detection%20constraints%20from%20gauge%20bosons%20loops&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.90.115011&volume=90&publication_year=2014&author=Crivellin%2CA&author=Haisch%2CU"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="8."><p class="c-article-references__text" id="ref-CR8">F. D’Eramo, B.J. Kavanagh, P. Panci, You can hide but you have to run: direct detection with vector mediators. JHEP <b>08</b>, 111 (2016). <a href="http://arxiv.org/abs/1605.04917" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1605.04917">arXiv:1605.04917</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP08(2016)111" data-track-item_id="10.1007/JHEP08(2016)111" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP08(2016)111" aria-label="Article reference 8" data-doi="10.1007/JHEP08(2016)111">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016JHEP...08..111D" aria-label="ADS reference 8">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 8" href="http://scholar.google.com/scholar_lookup?&title=You%20can%20hide%20but%20you%20have%20to%20run%3A%20direct%20detection%20with%20vector%20mediators&journal=JHEP&doi=10.1007%2FJHEP08%282016%29111&volume=08&publication_year=2016&author=D%E2%80%99Eramo%2CF&author=Kavanagh%2CBJ&author=Panci%2CP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="9."><p class="c-article-references__text" id="ref-CR9">M. Hoferichter, P. Klos, J. Menéndez, A. Schwenk, Analysis strategies for general spin-independent WIMP-nucleus scattering. Phys. Rev. D <b>94</b>, 063505 (2016). <a href="http://arxiv.org/abs/1605.08043" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1605.08043">arXiv:1605.08043</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.94.063505" data-track-item_id="10.1103/PhysRevD.94.063505" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.94.063505" aria-label="Article reference 9" data-doi="10.1103/PhysRevD.94.063505">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016PhRvD..94f3505H" aria-label="ADS reference 9">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 9" href="http://scholar.google.com/scholar_lookup?&title=Analysis%20strategies%20for%20general%20spin-independent%20WIMP-nucleus%20scattering&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.94.063505&volume=94&publication_year=2016&author=Hoferichter%2CM&author=Klos%2CP&author=Men%C3%A9ndez%2CJ&author=Schwenk%2CA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="10."><p class="c-article-references__text" id="ref-CR10">F. Kahlhoefer, S. Wild, Studying generalised dark matter interactions with extended halo-independent methods. JCAP <b>10</b>, 032 (2016). <a href="http://arxiv.org/abs/1607.04418" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1607.04418">arXiv:1607.04418</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1475-7516/2016/10/032" data-track-item_id="10.1088/1475-7516/2016/10/032" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1475-7516%2F2016%2F10%2F032" aria-label="Article reference 10" data-doi="10.1088/1475-7516/2016/10/032">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016JCAP...10..032K" aria-label="ADS reference 10">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 10" href="http://scholar.google.com/scholar_lookup?&title=Studying%20generalised%20dark%20matter%20interactions%20with%20extended%20halo-independent%20methods&journal=JCAP&doi=10.1088%2F1475-7516%2F2016%2F10%2F032&volume=10&publication_year=2016&author=Kahlhoefer%2CF&author=Wild%2CS"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="11."><p class="c-article-references__text" id="ref-CR11">J. Goodman, M. Ibe et al., Gamma ray line constraints on effective theories of dark matter. Nucl. Phys. B <b>844</b>, 55–68 (2011). <a href="http://arxiv.org/abs/1009.0008" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1009.0008">arXiv:1009.0008</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.nuclphysb.2010.10.022" data-track-item_id="10.1016/j.nuclphysb.2010.10.022" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.nuclphysb.2010.10.022" aria-label="Article reference 11" data-doi="10.1016/j.nuclphysb.2010.10.022">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2011NuPhB.844...55G" aria-label="ADS reference 11">ADS</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="math reference" data-track-action="math reference" href="http://www.emis.de/MATH-item?1207.83078" aria-label="MATH reference 11">MATH</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 11" href="http://scholar.google.com/scholar_lookup?&title=Gamma%20ray%20line%20constraints%20on%20effective%20theories%20of%20dark%20matter&journal=Nucl.%20Phys.%20B&doi=10.1016%2Fj.nuclphysb.2010.10.022&volume=844&pages=55-68&publication_year=2011&author=Goodman%2CJ&author=Ibe%2CM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="12."><p class="c-article-references__text" id="ref-CR12">M. Beltran, D. Hooper, E.W. Kolb, Z.C. Krusberg, Deducing the nature of dark matter from direct and indirect detection experiments in the absence of collider signatures of new physics. Phys. Rev. D <b>80</b>, 043509 043509 (2009). <a href="http://arxiv.org/abs/0808.3384" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/0808.3384">arXiv:0808.3384</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.80.043509" data-track-item_id="10.1103/PhysRevD.80.043509" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.80.043509" aria-label="Article reference 12" data-doi="10.1103/PhysRevD.80.043509">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2009PhRvD..80d3509B" aria-label="ADS reference 12">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 12" href="http://scholar.google.com/scholar_lookup?&title=Deducing%20the%20nature%20of%20dark%20matter%20from%20direct%20and%20indirect%20detection%20experiments%20in%20the%20absence%20of%20collider%20signatures%20of%20new%20physics&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.80.043509&volume=80&publication_year=2009&author=Beltran%2CM&author=Hooper%2CD&author=Kolb%2CEW&author=Krusberg%2CZC"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="13."><p class="c-article-references__text" id="ref-CR13">K. Cheung, P.-Y. Tseng, T.-C. Yuan, Gamma-ray constraints on effective interactions of the dark matter. JCAP <b>06</b>, 023 (2011). <a href="http://arxiv.org/abs/1104.5329" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1104.5329">arXiv:1104.5329</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1475-7516/2011/06/023" data-track-item_id="10.1088/1475-7516/2011/06/023" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1475-7516%2F2011%2F06%2F023" aria-label="Article reference 13" data-doi="10.1088/1475-7516/2011/06/023">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2011JCAP...06..023C" aria-label="ADS reference 13">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 13" href="http://scholar.google.com/scholar_lookup?&title=Gamma-ray%20constraints%20on%20effective%20interactions%20of%20the%20dark%20matter&journal=JCAP&doi=10.1088%2F1475-7516%2F2011%2F06%2F023&volume=06&publication_year=2011&author=Cheung%2CK&author=Tseng%2CP-Y&author=Yuan%2CT-C"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="14."><p class="c-article-references__text" id="ref-CR14">R. Harnik, G.D. Kribs, An effective theory of Dirac dark matter. Phys. Rev. D <b>79</b>, 095007 (2009). <a href="http://arxiv.org/abs/0810.5557" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/0810.5557">arXiv:0810.5557</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.79.095007" data-track-item_id="10.1103/PhysRevD.79.095007" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.79.095007" aria-label="Article reference 14" data-doi="10.1103/PhysRevD.79.095007">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2009PhRvD..79i5007H" aria-label="ADS reference 14">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 14" href="http://scholar.google.com/scholar_lookup?&title=An%20effective%20theory%20of%20Dirac%20dark%20matter&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.79.095007&volume=79&publication_year=2009&author=Harnik%2CR&author=Kribs%2CGD"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="15."><p class="c-article-references__text" id="ref-CR15">A. De Simone, A. Monin, A. Thamm, A. Urbano, On the effective operators for Dark Matter annihilations. JCAP <b>02</b>, 039 (2013). <a href="http://arxiv.org/abs/1301.1486" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1301.1486">arXiv:1301.1486</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1475-7516/2013/02/039" data-track-item_id="10.1088/1475-7516/2013/02/039" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1475-7516%2F2013%2F02%2F039" aria-label="Article reference 15" data-doi="10.1088/1475-7516/2013/02/039">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=3038436" aria-label="MathSciNet reference 15">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 15" href="http://scholar.google.com/scholar_lookup?&title=On%20the%20effective%20operators%20for%20Dark%20Matter%20annihilations&journal=JCAP&doi=10.1088%2F1475-7516%2F2013%2F02%2F039&volume=02&publication_year=2013&author=Simone%2CA&author=Monin%2CA&author=Thamm%2CA&author=Urbano%2CA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="16."><p class="c-article-references__text" id="ref-CR16">C. Karwin, S. Murgia, T.M.P. Tait, T.A. Porter, P. Tanedo, Dark matter interpretation of the Fermi-LAT observation toward the Galactic Center. Phys. Rev. D <b>95</b>, 103005 (2017). <a href="http://arxiv.org/abs/1612.05687" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1612.05687">arXiv:1612.05687</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.95.103005" data-track-item_id="10.1103/PhysRevD.95.103005" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.95.103005" aria-label="Article reference 16" data-doi="10.1103/PhysRevD.95.103005">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2017PhRvD..95j3005K" aria-label="ADS reference 16">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 16" href="http://scholar.google.com/scholar_lookup?&title=Dark%20matter%20interpretation%20of%20the%20Fermi-LAT%20observation%20toward%20the%20Galactic%20Center&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.95.103005&volume=95&publication_year=2017&author=Karwin%2CC&author=Murgia%2CS&author=Tait%2CTMP&author=Porter%2CTA&author=Tanedo%2CP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="17."><p class="c-article-references__text" id="ref-CR17">L.M. Carpenter, R. Colburn, J. Goodman, T. Linden, Indirect detection constraints on s and t channel simplified models of dark matter. Phys. Rev. D <b>94</b>, 055027 (2016). <a href="http://arxiv.org/abs/1606.04138" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1606.04138">arXiv:1606.04138</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.94.055027" data-track-item_id="10.1103/PhysRevD.94.055027" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.94.055027" aria-label="Article reference 17" data-doi="10.1103/PhysRevD.94.055027">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016PhRvD..94e5027C" aria-label="ADS reference 17">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 17" href="http://scholar.google.com/scholar_lookup?&title=Indirect%20detection%20constraints%20on%20s%20and%20t%20channel%20simplified%20models%20of%20dark%20matter&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.94.055027&volume=94&publication_year=2016&author=Carpenter%2CLM&author=Colburn%2CR&author=Goodman%2CJ&author=Linden%2CT"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="18."><p class="c-article-references__text" id="ref-CR18">J. Abdallah et al., Simplified models for dark matter searches at the LHC. Phys. Dark Universe <b>9–10</b>, 8–23 (2015). <a href="http://arxiv.org/abs/1506.03116" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1506.03116">arXiv:1506.03116</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.dark.2015.08.001" data-track-item_id="10.1016/j.dark.2015.08.001" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.dark.2015.08.001" aria-label="Article reference 18" data-doi="10.1016/j.dark.2015.08.001">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2015PDU.....9....8A" aria-label="ADS reference 18">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 18" href="http://scholar.google.com/scholar_lookup?&title=Simplified%20models%20for%20dark%20matter%20searches%20at%20the%20LHC&journal=Phys.%20Dark%20Universe&doi=10.1016%2Fj.dark.2015.08.001&volume=9%E2%80%9310&pages=8-23&publication_year=2015&author=Abdallah%2CJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="19."><p class="c-article-references__text" id="ref-CR19">F. Kahlhoefer, Review of LHC dark matter searches. Int. J. Mod. Phys. A <b>32</b>, 1730006 (2017). <a href="http://arxiv.org/abs/1702.02430" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1702.02430">arXiv:1702.02430</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1142/S0217751X1730006X" data-track-item_id="10.1142/S0217751X1730006X" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1142%2FS0217751X1730006X" aria-label="Article reference 19" data-doi="10.1142/S0217751X1730006X">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2017IJMPA..3230006K" aria-label="ADS reference 19">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 19" href="http://scholar.google.com/scholar_lookup?&title=Review%20of%20LHC%20dark%20matter%20searches&journal=Int.%20J.%20Mod.%20Phys.%20A&doi=10.1142%2FS0217751X1730006X&volume=32&publication_year=2017&author=Kahlhoefer%2CF"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="20."><p class="c-article-references__text" id="ref-CR20">T. Alanne, F. Goertz, Extended dark matter EFT. Eur. Phys. J. C <b>80</b>, 446 (2020). <a href="http://arxiv.org/abs/1712.07626" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1712.07626">arXiv:1712.07626</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1140/epjc/s10052-020-7999-2" data-track-item_id="10.1140/epjc/s10052-020-7999-2" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1140%2Fepjc%2Fs10052-020-7999-2" aria-label="Article reference 20" data-doi="10.1140/epjc/s10052-020-7999-2">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2020EPJC...80..446A" aria-label="ADS reference 20">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 20" href="http://scholar.google.com/scholar_lookup?&title=Extended%20dark%20matter%20EFT&journal=Eur.%20Phys.%20J.%20C&doi=10.1140%2Fepjc%2Fs10052-020-7999-2&volume=80&publication_year=2020&author=Alanne%2CT&author=Goertz%2CF"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="21."><p class="c-article-references__text" id="ref-CR21">T. Alanne, G. Arcadi, F. Goertz, V. Tenorth, S. Vogl, Model-independent constraints with extended dark matter EFT. JHEP <b>10</b>, 172 (2020). <a href="http://arxiv.org/abs/2006.07174" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/2006.07174">arXiv:2006.07174</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP10(2020)172" data-track-item_id="10.1007/JHEP10(2020)172" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP10(2020)172" aria-label="Article reference 21" data-doi="10.1007/JHEP10(2020)172">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2020JHEP...10..172A" aria-label="ADS reference 21">ADS</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=4203933" aria-label="MathSciNet reference 21">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 21" href="http://scholar.google.com/scholar_lookup?&title=Model-independent%20constraints%20with%20extended%20dark%20matter%20EFT&journal=JHEP&doi=10.1007%2FJHEP10%282020%29172&volume=10&publication_year=2020&author=Alanne%2CT&author=Arcadi%2CG&author=Goertz%2CF&author=Tenorth%2CV&author=Vogl%2CS"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="22."><p class="c-article-references__text" id="ref-CR22">Y. Bai, P.J. Fox, R. Harnik, The Tevatron at the frontier of dark matter direct detection. JHEP <b>12</b>, 048 (2010). <a href="http://arxiv.org/abs/1005.3797" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1005.3797">arXiv:1005.3797</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP12(2010)048" data-track-item_id="10.1007/JHEP12(2010)048" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP12(2010)048" aria-label="Article reference 22" data-doi="10.1007/JHEP12(2010)048">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2010JHEP...12..048B" aria-label="ADS reference 22">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 22" href="http://scholar.google.com/scholar_lookup?&title=The%20Tevatron%20at%20the%20frontier%20of%20dark%20matter%20direct%20detection&journal=JHEP&doi=10.1007%2FJHEP12%282010%29048&volume=12&publication_year=2010&author=Bai%2CY&author=Fox%2CPJ&author=Harnik%2CR"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="23."><p class="c-article-references__text" id="ref-CR23">H. Dreiner, D. Schmeier, J. Tattersall, Contact interactions probe effective dark matter models at the LHC. EPL <b>102</b>, 51001 (2013). <a href="http://arxiv.org/abs/1303.3348" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1303.3348">arXiv:1303.3348</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1209/0295-5075/102/51001" data-track-item_id="10.1209/0295-5075/102/51001" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1209%2F0295-5075%2F102%2F51001" aria-label="Article reference 23" data-doi="10.1209/0295-5075/102/51001">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2013EL....10251001D" aria-label="ADS reference 23">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 23" href="http://scholar.google.com/scholar_lookup?&title=Contact%20interactions%20probe%20effective%20dark%20matter%20models%20at%20the%20LHC&journal=EPL&doi=10.1209%2F0295-5075%2F102%2F51001&volume=102&publication_year=2013&author=Dreiner%2CH&author=Schmeier%2CD&author=Tattersall%2CJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="24."><p class="c-article-references__text" id="ref-CR24">N. Zhou, D. Berge, D. Whiteson, Mono-everything: combined limits on dark matter production at colliders from multiple final states. Phys. Rev. D <b>87</b>, 095013 (2013). <a href="http://arxiv.org/abs/1302.3619" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1302.3619">arXiv:1302.3619</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.87.095013" data-track-item_id="10.1103/PhysRevD.87.095013" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.87.095013" aria-label="Article reference 24" data-doi="10.1103/PhysRevD.87.095013">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2013PhRvD..87i5013Z" aria-label="ADS reference 24">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 24" href="http://scholar.google.com/scholar_lookup?&title=Mono-everything%3A%20combined%20limits%20on%20dark%20matter%20production%20at%20colliders%20from%20multiple%20final%20states&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.87.095013&volume=87&publication_year=2013&author=Zhou%2CN&author=Berge%2CD&author=Whiteson%2CD"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="25."><p class="c-article-references__text" id="ref-CR25">P.J. Fox, R. Harnik, R. Primulando, C.-T. Yu, Taking a razor to dark matter parameter space at the LHC. Phys. Rev. D <b>86</b>, 015010 (2012). <a href="http://arxiv.org/abs/1203.1662" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1203.1662">arXiv:1203.1662</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.86.015010" data-track-item_id="10.1103/PhysRevD.86.015010" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.86.015010" aria-label="Article reference 25" data-doi="10.1103/PhysRevD.86.015010">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2012PhRvD..86a5010F" aria-label="ADS reference 25">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 25" href="http://scholar.google.com/scholar_lookup?&title=Taking%20a%20razor%20to%20dark%20matter%20parameter%20space%20at%20the%20LHC&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.86.015010&volume=86&publication_year=2012&author=Fox%2CPJ&author=Harnik%2CR&author=Primulando%2CR&author=Yu%2CC-T"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="26."><p class="c-article-references__text" id="ref-CR26">A. Rajaraman, W. Shepherd, T.M. Tait, A.M. Wijangco, LHC bounds on interactions of dark matter. Phys. Rev. D <b>84</b>, 095013 (2011). <a href="http://arxiv.org/abs/1108.1196" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1108.1196">arXiv:1108.1196</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.84.095013" data-track-item_id="10.1103/PhysRevD.84.095013" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.84.095013" aria-label="Article reference 26" data-doi="10.1103/PhysRevD.84.095013">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2011PhRvD..84i5013R" aria-label="ADS reference 26">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 26" href="http://scholar.google.com/scholar_lookup?&title=LHC%20bounds%20on%20interactions%20of%20dark%20matter&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.84.095013&volume=84&publication_year=2011&author=Rajaraman%2CA&author=Shepherd%2CW&author=Tait%2CTM&author=Wijangco%2CAM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="27."><p class="c-article-references__text" id="ref-CR27">J. Goodman, M. Ibe et al., Constraints on dark matter from colliders. Phys. Rev. D <b>82</b>, 116010 (2010). <a href="http://arxiv.org/abs/1008.1783" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1008.1783">arXiv:1008.1783</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.82.116010" data-track-item_id="10.1103/PhysRevD.82.116010" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.82.116010" aria-label="Article reference 27" data-doi="10.1103/PhysRevD.82.116010">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2010PhRvD..82k6010G" aria-label="ADS reference 27">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 27" href="http://scholar.google.com/scholar_lookup?&title=Constraints%20on%20dark%20matter%20from%20colliders&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.82.116010&volume=82&publication_year=2010&author=Goodman%2CJ&author=Ibe%2CM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="28."><p class="c-article-references__text" id="ref-CR28">P.J. Fox, R. Harnik, J. Kopp, Y. Tsai, Missing energy signatures of dark matter at the LHC. Phys. Rev. D <b>85</b>, 056011 (2012). <a href="http://arxiv.org/abs/1109.4398" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1109.4398">arXiv:1109.4398</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.85.056011" data-track-item_id="10.1103/PhysRevD.85.056011" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.85.056011" aria-label="Article reference 28" data-doi="10.1103/PhysRevD.85.056011">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2012PhRvD..85e6011F" aria-label="ADS reference 28">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 28" href="http://scholar.google.com/scholar_lookup?&title=Missing%20energy%20signatures%20of%20dark%20matter%20at%20the%20LHC&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.85.056011&volume=85&publication_year=2012&author=Fox%2CPJ&author=Harnik%2CR&author=Kopp%2CJ&author=Tsai%2CY"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="29."><p class="c-article-references__text" id="ref-CR29">M. Beltran, D. Hooper, E.W. Kolb, Z.A. Krusberg, T.M. Tait, Maverick dark matter at colliders. JHEP <b>09</b>, 037 (2010). <a href="http://arxiv.org/abs/1002.4137" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1002.4137">arXiv:1002.4137</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP09(2010)037" data-track-item_id="10.1007/JHEP09(2010)037" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP09(2010)037" aria-label="Article reference 29" data-doi="10.1007/JHEP09(2010)037">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2010JHEP...09..037B" aria-label="ADS reference 29">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 29" href="http://scholar.google.com/scholar_lookup?&title=Maverick%20dark%20matter%20at%20colliders&journal=JHEP&doi=10.1007%2FJHEP09%282010%29037&volume=09&publication_year=2010&author=Beltran%2CM&author=Hooper%2CD&author=Kolb%2CEW&author=Krusberg%2CZA&author=Tait%2CTM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="30."><p class="c-article-references__text" id="ref-CR30">O. Buchmueller, M.J. Dolan, C. McCabe, Beyond effective field theory for dark matter searches at the LHC. JHEP <b>01</b>, 025 (2014). <a href="http://arxiv.org/abs/1308.6799" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1308.6799">arXiv:1308.6799</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP01(2014)025" data-track-item_id="10.1007/JHEP01(2014)025" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP01(2014)025" aria-label="Article reference 30" data-doi="10.1007/JHEP01(2014)025">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014JHEP...01..025B" aria-label="ADS reference 30">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 30" href="http://scholar.google.com/scholar_lookup?&title=Beyond%20effective%20field%20theory%20for%20dark%20matter%20searches%20at%20the%20LHC&journal=JHEP&doi=10.1007%2FJHEP01%282014%29025&volume=01&publication_year=2014&author=Buchmueller%2CO&author=Dolan%2CMJ&author=McCabe%2CC"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="31."><p class="c-article-references__text" id="ref-CR31">A. Belyaev, L. Panizzi, A. Pukhov, M. Thomas, Dark matter characterization at the LHC in the effective field theory approach. JHEP <b>04</b>, 110 (2017). <a href="http://arxiv.org/abs/1610.07545" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1610.07545">arXiv:1610.07545</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP04(2017)110" data-track-item_id="10.1007/JHEP04(2017)110" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP04(2017)110" aria-label="Article reference 31" data-doi="10.1007/JHEP04(2017)110">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2017JHEP...04..110B" aria-label="ADS reference 31">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 31" href="http://scholar.google.com/scholar_lookup?&title=Dark%20matter%20characterization%20at%20the%20LHC%20in%20the%20effective%20field%20theory%20approach&journal=JHEP&doi=10.1007%2FJHEP04%282017%29110&volume=04&publication_year=2017&author=Belyaev%2CA&author=Panizzi%2CL&author=Pukhov%2CA&author=Thomas%2CM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="32."><p class="c-article-references__text" id="ref-CR32">F. Pobbe, A. Wulzer, M. Zanetti, Setting limits on effective field theories: the case of dark matter. JHEP <b>08</b>, 074 (2017). <a href="http://arxiv.org/abs/1704.00736" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1704.00736">arXiv:1704.00736</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP08(2017)074" data-track-item_id="10.1007/JHEP08(2017)074" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP08(2017)074" aria-label="Article reference 32" data-doi="10.1007/JHEP08(2017)074">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2017JHEP...08..074P" aria-label="ADS reference 32">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 32" href="http://scholar.google.com/scholar_lookup?&title=Setting%20limits%20on%20effective%20field%20theories%3A%20the%20case%20of%20dark%20matter&journal=JHEP&doi=10.1007%2FJHEP08%282017%29074&volume=08&publication_year=2017&author=Pobbe%2CF&author=Wulzer%2CA&author=Zanetti%2CM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="33."><p class="c-article-references__text" id="ref-CR33">ATLAS: G. Aad et al., Search for dark matter candidates and large extra dimensions in events with a jet and missing transverse momentum with the ATLAS detector. JHEP <b>04</b>, 075 (2013). <a href="http://arxiv.org/abs/1210.4491" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1210.4491">arXiv:1210.4491</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="34."><p class="c-article-references__text" id="ref-CR34">CMS: S. Chatrchyan et al., Search for dark matter and large extra dimensions in monojet events in <span class="mathjax-tex">$pp$</span> collisions at <span class="mathjax-tex">$\sqrt{s}=7$</span> TeV. JHEP <b>09</b>, 094 (2012). <a href="http://arxiv.org/abs/1206.5663" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1206.5663">arXiv:1206.5663</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="35."><p class="c-article-references__text" id="ref-CR35">M.R. Buckley, Asymmetric dark matter and effective operators. Phys. Rev. D <b>84</b>, 043510 (2011). <a href="http://arxiv.org/abs/1104.1429" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1104.1429">arXiv:1104.1429</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.84.043510" data-track-item_id="10.1103/PhysRevD.84.043510" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.84.043510" aria-label="Article reference 35" data-doi="10.1103/PhysRevD.84.043510">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2011PhRvD..84d3510B" aria-label="ADS reference 35">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 35" href="http://scholar.google.com/scholar_lookup?&title=Asymmetric%20dark%20matter%20and%20effective%20operators&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.84.043510&volume=84&publication_year=2011&author=Buckley%2CMR"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="36."><p class="c-article-references__text" id="ref-CR36">K. Cheung, P.-Y. Tseng, Y.-L.S. Tsai, T.-C. Yuan, Global constraints on effective dark matter interactions: relic density, direct detection, indirect detection, and collider. JCAP <b>1205</b>, 001 (2012). <a href="http://arxiv.org/abs/1201.3402" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1201.3402">arXiv:1201.3402</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2012JCAP...05..001C" aria-label="ADS reference 36">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 36" href="http://scholar.google.com/scholar_lookup?&title=Global%20constraints%20on%20effective%20dark%20matter%20interactions%3A%20relic%20density%2C%20direct%20detection%2C%20indirect%20detection%2C%20and%20collider&journal=JCAP&volume=1205&publication_year=2012&author=Cheung%2CK&author=Tseng%2CP-Y&author=Tsai%2CY-LS&author=Yuan%2CT-C"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="37."><p class="c-article-references__text" id="ref-CR37">J. March-Russell, J. Unwin, S.M. West, Closing in on asymmetric dark matter I: model independent limits for interactions with quarks. JHEP <b>08</b>, 029 (2012). <a href="http://arxiv.org/abs/1203.4854" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1203.4854">arXiv:1203.4854</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP08(2012)029" data-track-item_id="10.1007/JHEP08(2012)029" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP08(2012)029" aria-label="Article reference 37" data-doi="10.1007/JHEP08(2012)029">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2012JHEP...08..029M" aria-label="ADS reference 37">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 37" href="http://scholar.google.com/scholar_lookup?&title=Closing%20in%20on%20asymmetric%20dark%20matter%20I%3A%20model%20independent%20limits%20for%20interactions%20with%20quarks&journal=JHEP&doi=10.1007%2FJHEP08%282012%29029&volume=08&publication_year=2012&author=March-Russell%2CJ&author=Unwin%2CJ&author=West%2CSM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="38."><p class="c-article-references__text" id="ref-CR38">J.-M. Zheng, Z.-H. Yu et al., Constraining the interaction strength between dark matter and visible matter: I.Fermionic dark matter. Nucl. Phys. B <b>854</b>, 350–374 (2012). <a href="http://arxiv.org/abs/1012.2022" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1012.2022">arXiv:1012.2022</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.nuclphysb.2011.09.009" data-track-item_id="10.1016/j.nuclphysb.2011.09.009" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.nuclphysb.2011.09.009" aria-label="Article reference 38" data-doi="10.1016/j.nuclphysb.2011.09.009">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2012NuPhB.854..350Z" aria-label="ADS reference 38">ADS</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="math reference" data-track-action="math reference" href="http://www.emis.de/MATH-item?1229.83090" aria-label="MATH reference 38">MATH</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 38" href="http://scholar.google.com/scholar_lookup?&title=Constraining%20the%20interaction%20strength%20between%20dark%20matter%20and%20visible%20matter%3A%20I.Fermionic%20dark%20matter&journal=Nucl.%20Phys.%20B&doi=10.1016%2Fj.nuclphysb.2011.09.009&volume=854&pages=350-374&publication_year=2012&author=Zheng%2CJ-M&author=Yu%2CZ-H"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="39."><p class="c-article-references__text" id="ref-CR39">A. Belyaev, E. Bertuzzo et al., Interplay of the LHC and non-LHC dark matter searches in the effective field theory approach. Phys. Rev. D <b>99</b>, 015006 (2019). <a href="http://arxiv.org/abs/1807.03817" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1807.03817">arXiv:1807.03817</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.99.015006" data-track-item_id="10.1103/PhysRevD.99.015006" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.99.015006" aria-label="Article reference 39" data-doi="10.1103/PhysRevD.99.015006">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2019PhRvD..99a5006B" aria-label="ADS reference 39">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 39" href="http://scholar.google.com/scholar_lookup?&title=Interplay%20of%20the%20LHC%20and%20non-LHC%20dark%20matter%20searches%20in%20the%20effective%20field%20theory%20approach&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.99.015006&volume=99&publication_year=2019&author=Belyaev%2CA&author=Bertuzzo%2CE"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="40."><p class="c-article-references__text" id="ref-CR40">E. Bertuzzo, C.J. Caniu Barros, G. Grilli di Cortona, MeV dark matter: model independent bounds. JHEP <b>09</b>, 116 (2017). <a href="http://arxiv.org/abs/1707.00725" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1707.00725">arXiv:1707.00725</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP09(2017)116" data-track-item_id="10.1007/JHEP09(2017)116" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP09(2017)116" aria-label="Article reference 40" data-doi="10.1007/JHEP09(2017)116">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2017JHEP...09..116B" aria-label="ADS reference 40">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 40" href="http://scholar.google.com/scholar_lookup?&title=MeV%20dark%20matter%3A%20model%20independent%20bounds&journal=JHEP&doi=10.1007%2FJHEP09%282017%29116&volume=09&publication_year=2017&author=Bertuzzo%2CE&author=Caniu%20Barros%2CCJ&author=Grilli%20di%20Cortona%2CG"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="41."><p class="c-article-references__text" id="ref-CR41">M. Cirelli, E. Del Nobile, P. Panci, Tools for model-independent bounds in direct dark matter searches. JCAP <b>10</b>, 019 (2013). <a href="http://arxiv.org/abs/1307.5955" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1307.5955">arXiv:1307.5955</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1475-7516/2013/10/019" data-track-item_id="10.1088/1475-7516/2013/10/019" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1475-7516%2F2013%2F10%2F019" aria-label="Article reference 41" data-doi="10.1088/1475-7516/2013/10/019">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2013JCAP...10..019C" aria-label="ADS reference 41">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 41" href="http://scholar.google.com/scholar_lookup?&title=Tools%20for%20model-independent%20bounds%20in%20direct%20dark%20matter%20searches&journal=JCAP&doi=10.1088%2F1475-7516%2F2013%2F10%2F019&volume=10&publication_year=2013&author=Cirelli%2CM&author=Nobile%2CE&author=Panci%2CP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="42."><p class="c-article-references__text" id="ref-CR42">J. Kumar, D. Marfatia, Matrix element analyses of dark matter scattering and annihilation. Phys. Rev. D <b>88</b>, 014035 (2013). <a href="http://arxiv.org/abs/1305.1611" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1305.1611">arXiv:1305.1611</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.88.014035" data-track-item_id="10.1103/PhysRevD.88.014035" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.88.014035" aria-label="Article reference 42" data-doi="10.1103/PhysRevD.88.014035">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2013PhRvD..88a4035K" aria-label="ADS reference 42">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 42" href="http://scholar.google.com/scholar_lookup?&title=Matrix%20element%20analyses%20of%20dark%20matter%20scattering%20and%20annihilation&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.88.014035&volume=88&publication_year=2013&author=Kumar%2CJ&author=Marfatia%2CD"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="43."><p class="c-article-references__text" id="ref-CR43">C. Balázs, T. Li, J.L. Newstead, Thermal dark matter implies new physics not far above the weak scale. JHEP <b>08</b>, 061 (2014). <a href="http://arxiv.org/abs/1403.5829" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1403.5829">arXiv:1403.5829</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP08(2014)061" data-track-item_id="10.1007/JHEP08(2014)061" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP08(2014)061" aria-label="Article reference 43" data-doi="10.1007/JHEP08(2014)061">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014JHEP...08..061B" aria-label="ADS reference 43">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 43" href="http://scholar.google.com/scholar_lookup?&title=Thermal%20dark%20matter%20implies%20new%20physics%20not%20far%20above%20the%20weak%20scale&journal=JHEP&doi=10.1007%2FJHEP08%282014%29061&volume=08&publication_year=2014&author=Bal%C3%A1zs%2CC&author=Li%2CT&author=Newstead%2CJL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="44."><p class="c-article-references__text" id="ref-CR44">S. Liem, G. Bertone et al., Effective field theory of dark matter: a global analysis. JHEP <b>9</b>, 77 (2016). <a href="http://arxiv.org/abs/1603.05994" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1603.05994">arXiv:1603.05994</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP09(2016)077" data-track-item_id="10.1007/JHEP09(2016)077" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP09(2016)077" aria-label="Article reference 44" data-doi="10.1007/JHEP09(2016)077">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016JHEP...09..077L" aria-label="ADS reference 44">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 44" href="http://scholar.google.com/scholar_lookup?&title=Effective%20field%20theory%20of%20dark%20matter%3A%20a%20global%20analysis&journal=JHEP&doi=10.1007%2FJHEP09%282016%29077&volume=9&publication_year=2016&author=Liem%2CS&author=Bertone%2CG"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="45."><p class="c-article-references__text" id="ref-CR45">S. Matsumoto, S. Mukhopadhyay, Y.-L.S. Tsai, Singlet Majorana fermion dark matter: a comprehensive analysis in effective field theory. JHEP <b>10</b>, 155 (2014). <a href="http://arxiv.org/abs/1407.1859" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1407.1859">arXiv:1407.1859</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP10(2014)155" data-track-item_id="10.1007/JHEP10(2014)155" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP10(2014)155" aria-label="Article reference 45" data-doi="10.1007/JHEP10(2014)155">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014JHEP...10..155M" aria-label="ADS reference 45">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 45" href="http://scholar.google.com/scholar_lookup?&title=Singlet%20Majorana%20fermion%20dark%20matter%3A%20a%20comprehensive%20analysis%20in%20effective%20field%20theory&journal=JHEP&doi=10.1007%2FJHEP10%282014%29155&volume=10&publication_year=2014&author=Matsumoto%2CS&author=Mukhopadhyay%2CS&author=Tsai%2CY-LS"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="46."><p class="c-article-references__text" id="ref-CR46">M. Blennow, P. Coloma, E. Fernandez-Martinez, P.A.N. Machado, B. Zaldivar, Global constraints on vector-like WIMP effective interactions. JCAP <b>04</b>, 015 (2016). <a href="http://arxiv.org/abs/1509.01587" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1509.01587">arXiv:1509.01587</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1475-7516/2016/04/015" data-track-item_id="10.1088/1475-7516/2016/04/015" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1475-7516%2F2016%2F04%2F015" aria-label="Article reference 46" data-doi="10.1088/1475-7516/2016/04/015">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016JCAP...04..015B" aria-label="ADS reference 46">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 46" href="http://scholar.google.com/scholar_lookup?&title=Global%20constraints%20on%20vector-like%20WIMP%20effective%20interactions&journal=JCAP&doi=10.1088%2F1475-7516%2F2016%2F04%2F015&volume=04&publication_year=2016&author=Blennow%2CM&author=Coloma%2CP&author=Fernandez-Martinez%2CE&author=Machado%2CPAN&author=Zaldivar%2CB"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="47."><p class="c-article-references__text" id="ref-CR47">S. Matsumoto, S. Mukhopadhyay, Y.-L.S. Tsai, Effective theory of WIMP dark matter supplemented by simplified models: singlet-like Majorana fermion case. Phys. Rev. D <b>94</b>, 065034 (2016). <a href="http://arxiv.org/abs/1604.02230" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1604.02230">arXiv:1604.02230</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.94.065034" data-track-item_id="10.1103/PhysRevD.94.065034" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.94.065034" aria-label="Article reference 47" data-doi="10.1103/PhysRevD.94.065034">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016PhRvD..94f5034M" aria-label="ADS reference 47">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 47" href="http://scholar.google.com/scholar_lookup?&title=Effective%20theory%20of%20WIMP%20dark%20matter%20supplemented%20by%20simplified%20models%3A%20singlet-like%20Majorana%20fermion%20case&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.94.065034&volume=94&publication_year=2016&author=Matsumoto%2CS&author=Mukhopadhyay%2CS&author=Tsai%2CY-LS"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="48."><p class="c-article-references__text" id="ref-CR48"><span class="u-sans-serif">GAMBIT</span> Collaboration: P. Athron, C. Balázs et al., GAMBIT: the global and modular beyond-the-standard-model inference tool. Eur. Phys. J. C <b>77</b>, 784 (2017). <a href="http://arxiv.org/abs/1705.07908" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1705.07908">arXiv:1705.07908</a>. Addendum in [190]</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="49."><p class="c-article-references__text" id="ref-CR49">M. Duerr, P. Fileviez Perez, Theory for baryon number and dark matter at the LHC. Phys. Rev. D <b>91</b>, 095001 (2015). <a href="http://arxiv.org/abs/1409.8165" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1409.8165">arXiv:1409.8165</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.91.095001" data-track-item_id="10.1103/PhysRevD.91.095001" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.91.095001" aria-label="Article reference 49" data-doi="10.1103/PhysRevD.91.095001">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2015PhRvD..91i5001D" aria-label="ADS reference 49">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 49" href="http://scholar.google.com/scholar_lookup?&title=Theory%20for%20baryon%20number%20and%20dark%20matter%20at%20the%20LHC&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.91.095001&volume=91&publication_year=2015&author=Duerr%2CM&author=Fileviez%20Perez%2CP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="50."><p class="c-article-references__text" id="ref-CR50">E. Dudas, L. Heurtier, Y. Mambrini, B. Zaldivar, Extra U(1), effective operators, anomalies and dark matter. JHEP <b>11</b>, 083 (2013). <a href="http://arxiv.org/abs/1307.0005" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1307.0005">arXiv:1307.0005</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP11(2013)083" data-track-item_id="10.1007/JHEP11(2013)083" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP11(2013)083" aria-label="Article reference 50" data-doi="10.1007/JHEP11(2013)083">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2013JHEP...11..083D" aria-label="ADS reference 50">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 50" href="http://scholar.google.com/scholar_lookup?&title=Extra%20U%281%29%2C%20effective%20operators%2C%20anomalies%20and%20dark%20matter&journal=JHEP&doi=10.1007%2FJHEP11%282013%29083&volume=11&publication_year=2013&author=Dudas%2CE&author=Heurtier%2CL&author=Mambrini%2CY&author=Zaldivar%2CB"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="51."><p class="c-article-references__text" id="ref-CR51">M. Bauer, S. Diefenbacher, T. Plehn, M. Russell, D.A. Camargo, Dark matter in anomaly-free gauge extensions. SciPost Phys. <b>5</b>, 036 (2018). <a href="http://arxiv.org/abs/1805.01904" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1805.01904">arXiv:1805.01904</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.21468/SciPostPhys.5.4.036" data-track-item_id="10.21468/SciPostPhys.5.4.036" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.21468%2FSciPostPhys.5.4.036" aria-label="Article reference 51" data-doi="10.21468/SciPostPhys.5.4.036">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018ScPP....5...36B" aria-label="ADS reference 51">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 51" href="http://scholar.google.com/scholar_lookup?&title=Dark%20matter%20in%20anomaly-free%20gauge%20extensions&journal=SciPost%20Phys.&doi=10.21468%2FSciPostPhys.5.4.036&volume=5&publication_year=2018&author=Bauer%2CM&author=Diefenbacher%2CS&author=Plehn%2CT&author=Russell%2CM&author=Camargo%2CDA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="52."><p class="c-article-references__text" id="ref-CR52"><span class="u-sans-serif">GAMBIT</span> Dark Matter Workgroup: T. Bringmann, J. Conrad et al., DarkBit: a GAMBIT module for computing dark matter observables and likelihoods. Eur. Phys. J. C <b>77</b>, 831 (2017). <a href="http://arxiv.org/abs/1705.07920" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1705.07920">arXiv:1705.07920</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="53."><p class="c-article-references__text" id="ref-CR53">A.L. Fitzpatrick, W. Haxton, E. Katz, N. Lubbers, Y. Xu, The effective field theory of dark matter direct detection. JCAP <b>1302</b>, 004 (2013). <a href="http://arxiv.org/abs/1203.3542" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1203.3542">arXiv:1203.3542</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1475-7516/2013/02/004" data-track-item_id="10.1088/1475-7516/2013/02/004" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1475-7516%2F2013%2F02%2F004" aria-label="Article reference 53" data-doi="10.1088/1475-7516/2013/02/004">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2013JCAP...02..004F" aria-label="ADS reference 53">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 53" href="http://scholar.google.com/scholar_lookup?&title=The%20effective%20field%20theory%20of%20dark%20matter%20direct%20detection&journal=JCAP&doi=10.1088%2F1475-7516%2F2013%2F02%2F004&volume=1302&publication_year=2013&author=Fitzpatrick%2CAL&author=Haxton%2CW&author=Katz%2CE&author=Lubbers%2CN&author=Xu%2CY"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="54."><p class="c-article-references__text" id="ref-CR54"><span class="u-sans-serif">GAMBIT</span> Cosmology Workgroup: J.J. Renk, P. Stöcker et al., CosmoBit: a GAMBIT module for computing cosmological observables and likelihoods. JCAP <b>02</b>, 022 (2021). <a href="http://arxiv.org/abs/2009.03286" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/2009.03286">arXiv:2009.03286</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="55."><p class="c-article-references__text" id="ref-CR55">T.E. Gonzalo, GAMBIT: the global and modular BSM inference tool, in <i>Tools for High Energy Physics and Cosmology</i> (2021). <a href="http://arxiv.org/abs/2105.03165" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/2105.03165">arXiv:2105.03165</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="56."><p class="c-article-references__text" id="ref-CR56">S. Bloor, T.E. Gonzalo et al., The GAMBIT universal model machine: from Lagrangians to likelihoods. <a href="http://arxiv.org/abs/2107.00030" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/2107.00030">arXiv:2107.00030</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="57."><p class="c-article-references__text" id="ref-CR57">I.M. Shoemaker, L. Vecchi, Unitarity and monojet bounds on models for DAMA, CoGeNT, and CRESST-II. Phys. Rev. D <b>86</b>, 015023 (2012). <a href="http://arxiv.org/abs/1112.5457" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1112.5457">arXiv:1112.5457</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.86.015023" data-track-item_id="10.1103/PhysRevD.86.015023" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.86.015023" aria-label="Article reference 57" data-doi="10.1103/PhysRevD.86.015023">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2012PhRvD..86a5023S" aria-label="ADS reference 57">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 57" href="http://scholar.google.com/scholar_lookup?&title=Unitarity%20and%20monojet%20bounds%20on%20models%20for%20DAMA%2C%20CoGeNT%2C%20and%20CRESST-II&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.86.015023&volume=86&publication_year=2012&author=Shoemaker%2CIM&author=Vecchi%2CL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="58."><p class="c-article-references__text" id="ref-CR58">G. Busoni, A. De Simone, E. Morgante, A. Riotto, On the validity of the effective field theory for dark matter searches at the LHC. Phys. Lett. B <b>728</b>, 412–421 (2014). <a href="http://arxiv.org/abs/1307.2253" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1307.2253">arXiv:1307.2253</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.physletb.2013.11.069" data-track-item_id="10.1016/j.physletb.2013.11.069" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.physletb.2013.11.069" aria-label="Article reference 58" data-doi="10.1016/j.physletb.2013.11.069">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014PhLB..728..412B" aria-label="ADS reference 58">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 58" href="http://scholar.google.com/scholar_lookup?&title=On%20the%20validity%20of%20the%20effective%20field%20theory%20for%20dark%20matter%20searches%20at%20the%20LHC&journal=Phys.%20Lett.%20B&doi=10.1016%2Fj.physletb.2013.11.069&volume=728&pages=412-421&publication_year=2014&author=Busoni%2CG&author=Simone%2CA&author=Morgante%2CE&author=Riotto%2CA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="59."><p class="c-article-references__text" id="ref-CR59">G. Busoni, A. De Simone, J. Gramling, E. Morgante, A. Riotto, On the validity of the effective field theory for dark matter searches at the LHC, part II: complete analysis for the <span class="mathjax-tex">$s$</span>-channel. JCAP <b>06</b>, 060 (2014). <a href="http://arxiv.org/abs/1402.1275" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1402.1275">arXiv:1402.1275</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1475-7516/2014/06/060" data-track-item_id="10.1088/1475-7516/2014/06/060" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1475-7516%2F2014%2F06%2F060" aria-label="Article reference 59" data-doi="10.1088/1475-7516/2014/06/060">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014JCAP...06..060B" aria-label="ADS reference 59">ADS</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=3230358" aria-label="MathSciNet reference 59">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 59" href="http://scholar.google.com/scholar_lookup?&title=On%20the%20validity%20of%20the%20effective%20field%20theory%20for%20dark%20matter%20searches%20at%20the%20LHC%2C%20part%20II%3A%20complete%20analysis%20for%20the%20%24%24s%24%24%20s%20-channel&journal=JCAP&doi=10.1088%2F1475-7516%2F2014%2F06%2F060&volume=06&publication_year=2014&author=Busoni%2CG&author=Simone%2CA&author=Gramling%2CJ&author=Morgante%2CE&author=Riotto%2CA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="60."><p class="c-article-references__text" id="ref-CR60">G. Busoni, A. De Simone, T. Jacques, E. Morgante, A. Riotto, On the validity of the effective field theory for dark matter searches at the LHC part III: analysis for the <span class="mathjax-tex">$t$</span>-channel. JCAP <b>09</b>, 022 (2014). <a href="http://arxiv.org/abs/1405.3101" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1405.3101">arXiv:1405.3101</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1475-7516/2014/09/022" data-track-item_id="10.1088/1475-7516/2014/09/022" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1475-7516%2F2014%2F09%2F022" aria-label="Article reference 60" data-doi="10.1088/1475-7516/2014/09/022">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014JCAP...09..022B" aria-label="ADS reference 60">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 60" href="http://scholar.google.com/scholar_lookup?&title=On%20the%20validity%20of%20the%20effective%20field%20theory%20for%20dark%20matter%20searches%20at%20the%20LHC%20part%20III%3A%20analysis%20for%20the%20%24%24t%24%24%20t%20-channel&journal=JCAP&doi=10.1088%2F1475-7516%2F2014%2F09%2F022&volume=09&publication_year=2014&author=Busoni%2CG&author=Simone%2CA&author=Jacques%2CT&author=Morgante%2CE&author=Riotto%2CA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="61."><p class="c-article-references__text" id="ref-CR61">M. Endo, Y. Yamamoto, Unitarity bounds on dark matter effective interactions at LHC. JHEP <b>06</b>, 126 (2014). <a href="http://arxiv.org/abs/1403.6610" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1403.6610">arXiv:1403.6610</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP06(2014)126" data-track-item_id="10.1007/JHEP06(2014)126" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP06(2014)126" aria-label="Article reference 61" data-doi="10.1007/JHEP06(2014)126">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014JHEP...06..126E" aria-label="ADS reference 61">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 61" href="http://scholar.google.com/scholar_lookup?&title=Unitarity%20bounds%20on%20dark%20matter%20effective%20interactions%20at%20LHC&journal=JHEP&doi=10.1007%2FJHEP06%282014%29126&volume=06&publication_year=2014&author=Endo%2CM&author=Yamamoto%2CY"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="62."><p class="c-article-references__text" id="ref-CR62">N. Bell, G. Busoni, A. Kobakhidze, D.M. Long, M.A. Schmidt, Unitarisation of EFT amplitudes for dark matter searches at the LHC. JHEP <b>08</b>, 125 (2016). <a href="http://arxiv.org/abs/1606.02722" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1606.02722">arXiv:1606.02722</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP08(2016)125" data-track-item_id="10.1007/JHEP08(2016)125" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP08(2016)125" aria-label="Article reference 62" data-doi="10.1007/JHEP08(2016)125">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016JHEP...08..125B" aria-label="ADS reference 62">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 62" href="http://scholar.google.com/scholar_lookup?&title=Unitarisation%20of%20EFT%20amplitudes%20for%20dark%20matter%20searches%20at%20the%20LHC&journal=JHEP&doi=10.1007%2FJHEP08%282016%29125&volume=08&publication_year=2016&author=Bell%2CN&author=Busoni%2CG&author=Kobakhidze%2CA&author=Long%2CDM&author=Schmidt%2CMA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="63."><p class="c-article-references__text" id="ref-CR63">D. Racco, A. Wulzer, F. Zwirner, Robust collider limits on heavy-mediator Dark Matter. JHEP <b>05</b>, 009 (2015). <a href="http://arxiv.org/abs/1502.04701" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1502.04701">arXiv:1502.04701</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP05(2015)009" data-track-item_id="10.1007/JHEP05(2015)009" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP05(2015)009" aria-label="Article reference 63" data-doi="10.1007/JHEP05(2015)009">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2015JHEP...05..009R" aria-label="ADS reference 63">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 63" href="http://scholar.google.com/scholar_lookup?&title=Robust%20collider%20limits%20on%20heavy-mediator%20Dark%20Matter&journal=JHEP&doi=10.1007%2FJHEP05%282015%29009&volume=05&publication_year=2015&author=Racco%2CD&author=Wulzer%2CA&author=Zwirner%2CF"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="64."><p class="c-article-references__text" id="ref-CR64">S. Bruggisser, F. Riva, A. Urbano, The last gasp of dark matter effective theory. JHEP <b>11</b>, 069 (2016). <a href="http://arxiv.org/abs/1607.02475" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1607.02475">arXiv:1607.02475</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP11(2016)069" data-track-item_id="10.1007/JHEP11(2016)069" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP11(2016)069" aria-label="Article reference 64" data-doi="10.1007/JHEP11(2016)069">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016JHEP...11..069B" aria-label="ADS reference 64">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 64" href="http://scholar.google.com/scholar_lookup?&title=The%20last%20gasp%20of%20dark%20matter%20effective%20theory&journal=JHEP&doi=10.1007%2FJHEP11%282016%29069&volume=11&publication_year=2016&author=Bruggisser%2CS&author=Riva%2CF&author=Urbano%2CA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="65."><p class="c-article-references__text" id="ref-CR65">K. Griest, M. Kamionkowski, Unitarity limits on the mass and radius of dark matter particles. Phys. Rev. Lett. <b>64</b>, 615 (1990)</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.64.615" data-track-item_id="10.1103/PhysRevLett.64.615" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.64.615" aria-label="Article reference 65" data-doi="10.1103/PhysRevLett.64.615">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=1990PhRvL..64..615G" aria-label="ADS reference 65">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 65" href="http://scholar.google.com/scholar_lookup?&title=Unitarity%20limits%20on%20the%20mass%20and%20radius%20of%20dark%20matter%20particles&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.64.615&volume=64&publication_year=1990&author=Griest%2CK&author=Kamionkowski%2CM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="66."><p class="c-article-references__text" id="ref-CR66"><span class="u-sans-serif">GAMBIT</span> Collaboration, Supplementary data: thermal WIMPs and the scale of new physics: global fits of dirac dark matter effective field theories (2021). <a href="https://zenodo.org/record/4836397" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="https://zenodo.org/record/4836397">https://zenodo.org/record/4836397</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="67."><p class="c-article-references__text" id="ref-CR67">F. Bishara, J. Brod, B. Grinstein, J. Zupan, DirectDM: a tool for dark matter direct detection. <a href="http://arxiv.org/abs/1708.02678" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1708.02678">arXiv:1708.02678</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="68."><p class="c-article-references__text" id="ref-CR68">J. Brod, A. Gootjes-Dreesbach, M. Tammaro, J. Zupan, Effective field theory for dark matter direct detection up to dimension seven. JHEP <b>10</b>, 065 (2018). <a href="http://arxiv.org/abs/1710.10218" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1710.10218">arXiv:1710.10218</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP10(2018)065" data-track-item_id="10.1007/JHEP10(2018)065" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP10(2018)065" aria-label="Article reference 68" data-doi="10.1007/JHEP10(2018)065">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018JHEP...10..065B" aria-label="ADS reference 68">ADS</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=3891031" aria-label="MathSciNet reference 68">MathSciNet</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="math reference" data-track-action="math reference" href="http://www.emis.de/MATH-item?1402.83064" aria-label="MATH reference 68">MATH</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 68" href="http://scholar.google.com/scholar_lookup?&title=Effective%20field%20theory%20for%20dark%20matter%20direct%20detection%20up%20to%20dimension%20seven&journal=JHEP&doi=10.1007%2FJHEP10%282018%29065&volume=10&publication_year=2018&author=Brod%2CJ&author=Gootjes-Dreesbach%2CA&author=Tammaro%2CM&author=Zupan%2CJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="69."><p class="c-article-references__text" id="ref-CR69">J. Kopp, V. Niro, T. Schwetz, J. Zupan, DAMA/LIBRA and leptonically interacting Dark Matter. Phys. Rev. D <b>80</b>, 083502 (2009). <a href="http://arxiv.org/abs/0907.3159" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/0907.3159">arXiv:0907.3159</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.80.083502" data-track-item_id="10.1103/PhysRevD.80.083502" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.80.083502" aria-label="Article reference 69" data-doi="10.1103/PhysRevD.80.083502">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2009PhRvD..80h3502K" aria-label="ADS reference 69">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 69" href="http://scholar.google.com/scholar_lookup?&title=DAMA%2FLIBRA%20and%20leptonically%20interacting%20Dark%20Matter&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.80.083502&volume=80&publication_year=2009&author=Kopp%2CJ&author=Niro%2CV&author=Schwetz%2CT&author=Zupan%2CJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="70."><p class="c-article-references__text" id="ref-CR70">P.J. Fox, R. Harnik, J. Kopp, Y. Tsai, LEP shines light on dark matter. Phys. Rev. D <b>84</b>, 014028 (2011). <a href="http://arxiv.org/abs/1103.0240" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1103.0240">arXiv:1103.0240</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.84.014028" data-track-item_id="10.1103/PhysRevD.84.014028" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.84.014028" aria-label="Article reference 70" data-doi="10.1103/PhysRevD.84.014028">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2011PhRvD..84a4028F" aria-label="ADS reference 70">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 70" href="http://scholar.google.com/scholar_lookup?&title=LEP%20shines%20light%20on%20dark%20matter&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.84.014028&volume=84&publication_year=2011&author=Fox%2CPJ&author=Harnik%2CR&author=Kopp%2CJ&author=Tsai%2CY"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="71."><p class="c-article-references__text" id="ref-CR71">N. Weiner, I. Yavin, UV completions of magnetic inelastic and Rayleigh dark matter for the Fermi line(s). Phys. Rev. D <b>87</b>, 023523 (2013). <a href="http://arxiv.org/abs/1209.1093" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1209.1093">arXiv:1209.1093</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.87.023523" data-track-item_id="10.1103/PhysRevD.87.023523" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.87.023523" aria-label="Article reference 71" data-doi="10.1103/PhysRevD.87.023523">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2013PhRvD..87b3523W" aria-label="ADS reference 71">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 71" href="http://scholar.google.com/scholar_lookup?&title=UV%20completions%20of%20magnetic%20inelastic%20and%20Rayleigh%20dark%20matter%20for%20the%20Fermi%20line%28s%29&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.87.023523&volume=87&publication_year=2013&author=Weiner%2CN&author=Yavin%2CI"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="72."><p class="c-article-references__text" id="ref-CR72">M.T. Frandsen, U. Haisch, F. Kahlhoefer, P. Mertsch, K. Schmidt-Hoberg, Loop-induced dark matter direct detection signals from gamma-ray lines. JCAP <b>10</b>, 033 (2012). <a href="http://arxiv.org/abs/1207.3971" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1207.3971">arXiv:1207.3971</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1475-7516/2012/10/033" data-track-item_id="10.1088/1475-7516/2012/10/033" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1475-7516%2F2012%2F10%2F033" aria-label="Article reference 72" data-doi="10.1088/1475-7516/2012/10/033">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2012JCAP...10..033F" aria-label="ADS reference 72">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 72" href="http://scholar.google.com/scholar_lookup?&title=Loop-induced%20dark%20matter%20direct%20detection%20signals%20from%20gamma-ray%20lines&journal=JCAP&doi=10.1088%2F1475-7516%2F2012%2F10%2F033&volume=10&publication_year=2012&author=Frandsen%2CMT&author=Haisch%2CU&author=Kahlhoefer%2CF&author=Mertsch%2CP&author=Schmidt-Hoberg%2CK"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="73."><p class="c-article-references__text" id="ref-CR73">G. Paz, A.A. Petrov, M. Tammaro, J. Zupan, Shining dark matter in Xenon1T. Phys. Rev. D <b>103</b>, L051703 (2021). <a href="https://doi.org/10.1103/PhysRevD.103.L051703" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1103/PhysRevD.103.L051703">https://doi.org/10.1103/PhysRevD.103.L051703</a>. <a href="http://arxiv.org/abs/2006.12462" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/2006.12462">arXiv:2006.12462</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="74."><p class="c-article-references__text" id="ref-CR74">B.J. Kavanagh, P. Panci, R. Ziegler, Faint light from dark matter: classifying and constraining dark matter-photon effective operators. JHEP <b>04</b>, 089 (2019). <a href="http://arxiv.org/abs/1810.00033" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1810.00033">arXiv:1810.00033</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP04(2019)089" data-track-item_id="10.1007/JHEP04(2019)089" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP04(2019)089" aria-label="Article reference 74" data-doi="10.1007/JHEP04(2019)089">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2019JHEP...04..089K" aria-label="ADS reference 74">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 74" href="http://scholar.google.com/scholar_lookup?&title=Faint%20light%20from%20dark%20matter%3A%20classifying%20and%20constraining%20dark%20matter-photon%20effective%20operators&journal=JHEP&doi=10.1007%2FJHEP04%282019%29089&volume=04&publication_year=2019&author=Kavanagh%2CBJ&author=Panci%2CP&author=Ziegler%2CR"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="75."><p class="c-article-references__text" id="ref-CR75">C. Arina, A. Cheek, K. Mimasu, L. Pagani, Light and darkness: consistently coupling dark matter to photons via effective operators. Eur. Phys. J. C <b>81</b>, 223 (2021). <a href="http://arxiv.org/abs/2005.12789" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/2005.12789">arXiv:2005.12789</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1140/epjc/s10052-021-09010-1" data-track-item_id="10.1140/epjc/s10052-021-09010-1" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1140%2Fepjc%2Fs10052-021-09010-1" aria-label="Article reference 75" data-doi="10.1140/epjc/s10052-021-09010-1">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2021EPJC...81..223A" aria-label="ADS reference 75">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 75" href="http://scholar.google.com/scholar_lookup?&title=Light%20and%20darkness%3A%20consistently%20coupling%20dark%20matter%20to%20photons%20via%20effective%20operators&journal=Eur.%20Phys.%20J.%20C&doi=10.1140%2Fepjc%2Fs10052-021-09010-1&volume=81&publication_year=2021&author=Arina%2CC&author=Cheek%2CA&author=Mimasu%2CK&author=Pagani%2CL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="76."><p class="c-article-references__text" id="ref-CR76">U. Haisch, F. Kahlhoefer, T.M.P. Tait, On mono-W signatures in spin-1 simplified models. Phys. Lett. B <b>760</b>, 207–213 (2016). <a href="http://arxiv.org/abs/1603.01267" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1603.01267">arXiv:1603.01267</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.physletb.2016.06.063" data-track-item_id="10.1016/j.physletb.2016.06.063" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.physletb.2016.06.063" aria-label="Article reference 76" data-doi="10.1016/j.physletb.2016.06.063">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016PhLB..760..207H" aria-label="ADS reference 76">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 76" href="http://scholar.google.com/scholar_lookup?&title=On%20mono-W%20signatures%20in%20spin-1%20simplified%20models&journal=Phys.%20Lett.%20B&doi=10.1016%2Fj.physletb.2016.06.063&volume=760&pages=207-213&publication_year=2016&author=Haisch%2CU&author=Kahlhoefer%2CF&author=Tait%2CTMP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="77."><p class="c-article-references__text" id="ref-CR77">R.J. Hill, M.P. Solon, Standard model anatomy of WIMP dark matter direct detection II: QCD analysis and hadronic matrix elements. Phys. Rev. D <b>91</b>, 043505 (2015). <a href="http://arxiv.org/abs/1409.8290" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1409.8290">arXiv:1409.8290</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.91.043505" data-track-item_id="10.1103/PhysRevD.91.043505" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.91.043505" aria-label="Article reference 77" data-doi="10.1103/PhysRevD.91.043505">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2015PhRvD..91d3505H" aria-label="ADS reference 77">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 77" href="http://scholar.google.com/scholar_lookup?&title=Standard%20model%20anatomy%20of%20WIMP%20dark%20matter%20direct%20detection%20II%3A%20QCD%20analysis%20and%20hadronic%20matrix%20elements&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.91.043505&volume=91&publication_year=2015&author=Hill%2CRJ&author=Solon%2CMP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="78."><p class="c-article-references__text" id="ref-CR78">F. Bishara, J. Brod, B. Grinstein, J. Zupan, Renormalization group effects in dark matter interactions. JHEP <b>03</b>, 089 (2020). <a href="http://arxiv.org/abs/1809.03506" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1809.03506">arXiv:1809.03506</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP03(2020)089" data-track-item_id="10.1007/JHEP03(2020)089" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP03(2020)089" aria-label="Article reference 78" data-doi="10.1007/JHEP03(2020)089">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2020JHEP...03..089B" aria-label="ADS reference 78">ADS</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=4090048" aria-label="MathSciNet reference 78">MathSciNet</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="math reference" data-track-action="math reference" href="http://www.emis.de/MATH-item?1435.85007" aria-label="MATH reference 78">MATH</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 78" href="http://scholar.google.com/scholar_lookup?&title=Renormalization%20group%20effects%20in%20dark%20matter%20interactions&journal=JHEP&doi=10.1007%2FJHEP03%282020%29089&volume=03&publication_year=2020&author=Bishara%2CF&author=Brod%2CJ&author=Grinstein%2CB&author=Zupan%2CJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="79."><p class="c-article-references__text" id="ref-CR79">J. Brod, B. Grinstein, E. Stamou, J. Zupan, Weak mixing below the weak scale in dark-matter direct detection. JHEP <b>02</b>, 174 (2018). <a href="http://arxiv.org/abs/1801.04240" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1801.04240">arXiv:1801.04240</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP02(2018)174" data-track-item_id="10.1007/JHEP02(2018)174" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP02(2018)174" aria-label="Article reference 79" data-doi="10.1007/JHEP02(2018)174">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018JHEP...02..174B" aria-label="ADS reference 79">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 79" href="http://scholar.google.com/scholar_lookup?&title=Weak%20mixing%20below%20the%20weak%20scale%20in%20dark-matter%20direct%20detection&journal=JHEP&doi=10.1007%2FJHEP02%282018%29174&volume=02&publication_year=2018&author=Brod%2CJ&author=Grinstein%2CB&author=Stamou%2CE&author=Zupan%2CJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="80."><p class="c-article-references__text" id="ref-CR80">U. Haisch, F. Kahlhoefer, On the importance of loop-induced spin-independent interactions for dark matter direct detection. JCAP <b>1304</b>, 050 (2013). <a href="http://arxiv.org/abs/1302.4454" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1302.4454">arXiv:1302.4454</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1475-7516/2013/04/050" data-track-item_id="10.1088/1475-7516/2013/04/050" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1475-7516%2F2013%2F04%2F050" aria-label="Article reference 80" data-doi="10.1088/1475-7516/2013/04/050">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2013JCAP...04..050H" aria-label="ADS reference 80">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 80" href="http://scholar.google.com/scholar_lookup?&title=On%20the%20importance%20of%20loop-induced%20spin-independent%20interactions%20for%20dark%20matter%20direct%20detection&journal=JCAP&doi=10.1088%2F1475-7516%2F2013%2F04%2F050&volume=1304&publication_year=2013&author=Haisch%2CU&author=Kahlhoefer%2CF"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="81."><p class="c-article-references__text" id="ref-CR81">A. Crivellin, F. D’Eramo, M. Procura, New constraints on dark matter effective theories from standard model loops. Phys. Rev. Lett. <b>112</b>, 191304 (2014). <a href="http://arxiv.org/abs/1402.1173" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1402.1173">arXiv:1402.1173</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.112.191304" data-track-item_id="10.1103/PhysRevLett.112.191304" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.112.191304" aria-label="Article reference 81" data-doi="10.1103/PhysRevLett.112.191304">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014PhRvL.112s1304C" aria-label="ADS reference 81">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 81" href="http://scholar.google.com/scholar_lookup?&title=New%20constraints%20on%20dark%20matter%20effective%20theories%20from%20standard%20model%20loops&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.112.191304&volume=112&publication_year=2014&author=Crivellin%2CA&author=D%E2%80%99Eramo%2CF&author=Procura%2CM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="82."><p class="c-article-references__text" id="ref-CR82">U. Haisch, F. Kahlhoefer, J. Unwin, The impact of heavy-quark loops on LHC dark matter searches. JHEP <b>07</b>, 125 (2013). <a href="http://arxiv.org/abs/1208.4605" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1208.4605">arXiv:1208.4605</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP07(2013)125" data-track-item_id="10.1007/JHEP07(2013)125" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP07(2013)125" aria-label="Article reference 82" data-doi="10.1007/JHEP07(2013)125">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2013JHEP...07..125H" aria-label="ADS reference 82">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 82" href="http://scholar.google.com/scholar_lookup?&title=The%20impact%20of%20heavy-quark%20loops%20on%20LHC%20dark%20matter%20searches&journal=JHEP&doi=10.1007%2FJHEP07%282013%29125&volume=07&publication_year=2013&author=Haisch%2CU&author=Kahlhoefer%2CF&author=Unwin%2CJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="83."><p class="c-article-references__text" id="ref-CR83">A. Berlin, T. Lin, L.-T. Wang, Mono-Higgs detection of dark matter at the LHC. JHEP <b>06</b>, 078 (2014). <a href="http://arxiv.org/abs/1402.7074" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1402.7074">arXiv:1402.7074</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP06(2014)078" data-track-item_id="10.1007/JHEP06(2014)078" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP06(2014)078" aria-label="Article reference 83" data-doi="10.1007/JHEP06(2014)078">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014JHEP...06..078B" aria-label="ADS reference 83">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 83" href="http://scholar.google.com/scholar_lookup?&title=Mono-Higgs%20detection%20of%20dark%20matter%20at%20the%20LHC&journal=JHEP&doi=10.1007%2FJHEP06%282014%29078&volume=06&publication_year=2014&author=Berlin%2CA&author=Lin%2CT&author=Wang%2CL-T"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="84."><p class="c-article-references__text" id="ref-CR84">SuperCDMS: R. Agnese et al., New results from the search for low-mass weakly interacting massive particles with the CDMS low ionization threshold experiment. Phys. Rev. Lett. <b>116</b>, 071301 (2016). <a href="http://arxiv.org/abs/1509.02448" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1509.02448">arXiv:1509.02448</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="85."><p class="c-article-references__text" id="ref-CR85">CRESST: G. Angloher et al., Results on light dark matter particles with a low-threshold CRESST-II detector. Eur. Phys. J. C <b>76</b>, 25 (2016). <a href="http://arxiv.org/abs/1509.01515" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1509.01515">arXiv:1509.01515</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="86."><p class="c-article-references__text" id="ref-CR86">CRESST: A.H. Abdelhameed et al., First results from the CRESST-III low-mass dark matter program. Phys. Rev. D <b>100</b>, 102002 (2019). <a href="http://arxiv.org/abs/1904.00498" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1904.00498">arXiv:1904.00498</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="87."><p class="c-article-references__text" id="ref-CR87">P. Agnes et al., DarkSide-50 532-day dark matter search with low-radioactivity argon. Phys. Rev. D <b>98</b>, 102006 (2018). <a href="https://doi.org/10.1103/PhysRevD.98.102006" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1103/PhysRevD.98.102006">https://doi.org/10.1103/PhysRevD.98.102006</a>. <a href="http://arxiv.org/abs/1802.07198" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1802.07198">arXiv:1802.07198</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="88."><p class="c-article-references__text" id="ref-CR88">LUX: D.S. Akerib et al., Results from a search for dark matter in the complete LUX exposure. Phys. Rev. Lett. <b>118</b>, 021303 (2017). <a href="http://arxiv.org/abs/1608.07648" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1608.07648">arXiv:1608.07648</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="89."><p class="c-article-references__text" id="ref-CR89">PICO: C. Amole et al., Dark matter search results from the PICO-60 C<span class="mathjax-tex">$_3$</span>F<span class="mathjax-tex">$_8$</span> bubble chamber. Phys. Rev. Lett. <b>118</b>, 251301 (2017). <a href="http://arxiv.org/abs/1702.07666" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1702.07666">arXiv:1702.07666</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="90."><p class="c-article-references__text" id="ref-CR90">PICO: C. Amole et al., Dark matter search results from the complete exposure of the PICO-60 C<span class="mathjax-tex">$_3$</span>F<span class="mathjax-tex">$_8$</span> bubble chamber. Phys. Rev. D <b>100</b>, 022001 (2019). <a href="http://arxiv.org/abs/1902.04031" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1902.04031">arXiv:1902.04031</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="91."><p class="c-article-references__text" id="ref-CR91">PandaX-II: A. Tan et al., Dark matter results from first 98.7 days of data from the PandaX-II experiment. Phys. Rev. Lett. <b>117</b>, 121303 (2016). <a href="http://arxiv.org/abs/1607.07400" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1607.07400">arXiv:1607.07400</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="92."><p class="c-article-references__text" id="ref-CR92">PandaX-II: X. Cui et al., Dark matter results from 54-ton-day exposure of PandaX-II experiment. Phys. Rev. Lett. <b>119</b>, 181302 (2017). <a href="http://arxiv.org/abs/1708.06917" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1708.06917">arXiv:1708.06917</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="93."><p class="c-article-references__text" id="ref-CR93">XENON: E. Aprile et al., Dark matter search results from a one ton-year exposure of XENON1T. Phys. Rev. Lett. <b>121</b>, 111302 (2018). <a href="http://arxiv.org/abs/1805.12562" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1805.12562">arXiv:1805.12562</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="94."><p class="c-article-references__text" id="ref-CR94">ATLAS: G. Aad et al., Search for new phenomena in events with an energetic jet and missing transverse momentum in <span class="mathjax-tex">$pp$</span> collisions at <span class="mathjax-tex">$\sqrt{s} = 13$</span> TeV with the ATLAS detector. <a href="http://arxiv.org/abs/2102.10874" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/2102.10874">arXiv:2102.10874</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="95."><p class="c-article-references__text" id="ref-CR95">CMS: A.M. Sirunyan et al., Search for new physics in final states with an energetic jet or a hadronically decaying <span class="mathjax-tex">$W$</span> or <span class="mathjax-tex">$Z$</span> boson and transverse momentum imbalance at <span class="mathjax-tex">$\sqrt{s}=13\,\text{TeV}$</span>. Phys. Rev. D <b>97</b>, 092005 (2018). <a href="http://arxiv.org/abs/1712.02345" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1712.02345">arXiv:1712.02345</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="96."><p class="c-article-references__text" id="ref-CR96">Fermi-LAT: M. Ackermann et al., Searching for dark matter annihilation from Milky Way dwarf spheroidal galaxies with six years of Fermi large area telescope data. Phys. Rev. Lett. <b>115</b>, 231301 (2015). <a href="http://arxiv.org/abs/1503.02641" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1503.02641">arXiv:1503.02641</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="97."><p class="c-article-references__text" id="ref-CR97">IceCube Collaboration: M.G. Aartsen et al., Improved limits on dark matter annihilation in the Sun with the 79-string IceCube detector and implications for supersymmetry. JCAP <b>04</b>, 022 (2016). <a href="http://arxiv.org/abs/1601.00653" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1601.00653">arXiv:1601.00653</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="98."><p class="c-article-references__text" id="ref-CR98">Planck: N. Aghanim et al., Planck 2018 results. VI. Cosmological parameters. Astron. Astrophys. <b>641</b>, A6 (2020). <a href="http://arxiv.org/abs/1807.06209" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1807.06209">arXiv:1807.06209</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="99."><p class="c-article-references__text" id="ref-CR99">N. Anand, A.L. Fitzpatrick, W.C. Haxton, Weakly interacting massive particle-nucleus elastic scattering response. Phys. Rev. C <b>89</b>, 065501 (2014). <a href="http://arxiv.org/abs/1308.6288" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1308.6288">arXiv:1308.6288</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevC.89.065501" data-track-item_id="10.1103/PhysRevC.89.065501" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevC.89.065501" aria-label="Article reference 99" data-doi="10.1103/PhysRevC.89.065501">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014PhRvC..89f5501A" aria-label="ADS reference 99">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 99" href="http://scholar.google.com/scholar_lookup?&title=Weakly%20interacting%20massive%20particle-nucleus%20elastic%20scattering%20response&journal=Phys.%20Rev.%20C&doi=10.1103%2FPhysRevC.89.065501&volume=89&publication_year=2014&author=Anand%2CN&author=Fitzpatrick%2CAL&author=Haxton%2CWC"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="100."><p class="c-article-references__text" id="ref-CR100">F. Bishara, J. Brod, B. Grinstein, J. Zupan, Chiral effective theory of dark matter direct detection. JCAP <b>1702</b>, 009 (2017). <a href="http://arxiv.org/abs/1611.00368" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1611.00368">arXiv:1611.00368</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1475-7516/2017/02/009" data-track-item_id="10.1088/1475-7516/2017/02/009" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1475-7516%2F2017%2F02%2F009" aria-label="Article reference 100" data-doi="10.1088/1475-7516/2017/02/009">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2017JCAP...02..009B" aria-label="ADS reference 100">ADS</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="math reference" data-track-action="math reference" href="http://www.emis.de/MATH-item?1383.81144" aria-label="MATH reference 100">MATH</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 100" href="http://scholar.google.com/scholar_lookup?&title=Chiral%20effective%20theory%20of%20dark%20matter%20direct%20detection&journal=JCAP&doi=10.1088%2F1475-7516%2F2017%2F02%2F009&volume=1702&publication_year=2017&author=Bishara%2CF&author=Brod%2CJ&author=Grinstein%2CB&author=Zupan%2CJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="101."><p class="c-article-references__text" id="ref-CR101">F. Bishara, J. Brod, B. Grinstein, J. Zupan, From quarks to nucleons in dark matter direct detection. JHEP <b>11</b>, 059 (2017). <a href="http://arxiv.org/abs/1707.06998" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1707.06998">arXiv:1707.06998</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP11(2017)059" data-track-item_id="10.1007/JHEP11(2017)059" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP11(2017)059" aria-label="Article reference 101" data-doi="10.1007/JHEP11(2017)059">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2017JHEP...11..059B" aria-label="ADS reference 101">ADS</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="math reference" data-track-action="math reference" href="http://www.emis.de/MATH-item?1383.81144" aria-label="MATH reference 101">MATH</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 101" href="http://scholar.google.com/scholar_lookup?&title=From%20quarks%20to%20nucleons%20in%20dark%20matter%20direct%20detection&journal=JHEP&doi=10.1007%2FJHEP11%282017%29059&volume=11&publication_year=2017&author=Bishara%2CF&author=Brod%2CJ&author=Grinstein%2CB&author=Zupan%2CJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="102."><p class="c-article-references__text" id="ref-CR102">Particle Data Group: P.A. Zyla et al., Review of particle physics. Prog. Theor. Exp. Phys. <b>083</b>, C01 (2020)</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="103."><p class="c-article-references__text" id="ref-CR103">A. Crivellin, M. Hoferichter, M. Procura, Accurate evaluation of hadronic uncertainties in spin-independent WIMP-nucleon scattering: disentangling two- and three-flavor effects. Phys. Rev. D <b>89</b>, 054021 (2014). <a href="http://arxiv.org/abs/1312.4951" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1312.4951">arXiv:1312.4951</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.89.054021" data-track-item_id="10.1103/PhysRevD.89.054021" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.89.054021" aria-label="Article reference 103" data-doi="10.1103/PhysRevD.89.054021">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014PhRvD..89e4021C" aria-label="ADS reference 103">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 103" href="http://scholar.google.com/scholar_lookup?&title=Accurate%20evaluation%20of%20hadronic%20uncertainties%20in%20spin-independent%20WIMP-nucleon%20scattering%3A%20disentangling%20two-%20and%20three-flavor%20effects&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.89.054021&volume=89&publication_year=2014&author=Crivellin%2CA&author=Hoferichter%2CM&author=Procura%2CM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="104."><p class="c-article-references__text" id="ref-CR104">D. Djukanovic, K. Ottnad, J. Wilhelm, H. Wittig, Strange electromagnetic form factors of the nucleon with <span class="mathjax-tex">$N_f = 2 + 1{\cal{O}}(a)$</span>-improved Wilson fermions. Phys. Rev. Lett. <b>123</b>, 212001 (2019). <a href="http://arxiv.org/abs/1903.12566" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1903.12566">arXiv:1903.12566</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.123.212001" data-track-item_id="10.1103/PhysRevLett.123.212001" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.123.212001" aria-label="Article reference 104" data-doi="10.1103/PhysRevLett.123.212001">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2019PhRvL.123u2001D" aria-label="ADS reference 104">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 104" href="http://scholar.google.com/scholar_lookup?&title=Strange%20electromagnetic%20form%20factors%20of%20the%20nucleon%20with%20%24%24N_f%20%3D%202%20%2B%201%7B%5Ccal%7BO%7D%7D%28a%29%24%24%20N%20f%20%3D%202%20%2B%201%20O%20%28%20a%20%29%20-improved%20Wilson%20fermions&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.123.212001&volume=123&publication_year=2019&author=Djukanovic%2CD&author=Ottnad%2CK&author=Wilhelm%2CJ&author=Wittig%2CH"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="105."><p class="c-article-references__text" id="ref-CR105">R.S. Sufian, Y.-B. Yang et al., Strange quark magnetic moment of the nucleon at the physical point. Phys. Rev. Lett. <b>118</b>, 042001 (2017). <a href="http://arxiv.org/abs/1606.07075" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1606.07075">arXiv:1606.07075</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.118.042001" data-track-item_id="10.1103/PhysRevLett.118.042001" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.118.042001" aria-label="Article reference 105" data-doi="10.1103/PhysRevLett.118.042001">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2017PhRvL.118d2001S" aria-label="ADS reference 105">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 105" href="http://scholar.google.com/scholar_lookup?&title=Strange%20quark%20magnetic%20moment%20of%20the%20nucleon%20at%20the%20physical%20point&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.118.042001&volume=118&publication_year=2017&author=Sufian%2CRS&author=Yang%2CY-B"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="106."><p class="c-article-references__text" id="ref-CR106">R. Gupta, B. Yoon et al., Flavor diagonal tensor charges of the nucleon from (2 + 1 + 1)-flavor lattice QCD. Phys. Rev. D <b>98</b>, 091501 (2018). <a href="http://arxiv.org/abs/1808.07597" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1808.07597">arXiv:1808.07597</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.98.091501" data-track-item_id="10.1103/PhysRevD.98.091501" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.98.091501" aria-label="Article reference 106" data-doi="10.1103/PhysRevD.98.091501">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018PhRvD..98i1501G" aria-label="ADS reference 106">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 106" href="http://scholar.google.com/scholar_lookup?&title=Flavor%20diagonal%20tensor%20charges%20of%20the%20nucleon%20from%20%282%C2%A0%2B%C2%A01%C2%A0%2B%C2%A01%29-flavor%20lattice%20QCD&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.98.091501&volume=98&publication_year=2018&author=Gupta%2CR&author=Yoon%2CB"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="107."><p class="c-article-references__text" id="ref-CR107">Flavour Lattice Averaging Group: S. Aoki et al., FLAG review 2019: Flavour Lattice Averaging Group (FLAG). Eur. Phys. J. C <b>80</b>, 113 (2020). <a href="http://arxiv.org/abs/1902.08191" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1902.08191">arXiv:1902.08191</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="108."><p class="c-article-references__text" id="ref-CR108">J. Liang, Y.-B. Yang, T. Draper, M. Gong, K.-F. Liu, Quark spins and anomalous ward identity. Phys. Rev. D <b>98</b>, 074505 (2018). <a href="http://arxiv.org/abs/1806.08366" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1806.08366">arXiv:1806.08366</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.98.074505" data-track-item_id="10.1103/PhysRevD.98.074505" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.98.074505" aria-label="Article reference 108" data-doi="10.1103/PhysRevD.98.074505">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018PhRvD..98g4505L" aria-label="ADS reference 108">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 108" href="http://scholar.google.com/scholar_lookup?&title=Quark%20spins%20and%20anomalous%20ward%20identity&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.98.074505&volume=98&publication_year=2018&author=Liang%2CJ&author=Yang%2CY-B&author=Draper%2CT&author=Gong%2CM&author=Liu%2CK-F"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="109."><p class="c-article-references__text" id="ref-CR109">B. Pasquini, M. Pincetti, S. Boffi, Chiral-odd generalized parton distributions in constituent quark models. Phys. Rev. D <b>72</b>, 094029 (2005). <a href="http://arxiv.org/abs/hep-ph/0510376" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/hep-ph/0510376">arXiv:hep-ph/0510376</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.72.094029" data-track-item_id="10.1103/PhysRevD.72.094029" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.72.094029" aria-label="Article reference 109" data-doi="10.1103/PhysRevD.72.094029">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2005PhRvD..72i4029P" aria-label="ADS reference 109">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 109" href="http://scholar.google.com/scholar_lookup?&title=Chiral-odd%20generalized%20parton%20distributions%20in%20constituent%20quark%20models&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.72.094029&volume=72&publication_year=2005&author=Pasquini%2CB&author=Pincetti%2CM&author=Boffi%2CS"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="110."><p class="c-article-references__text" id="ref-CR110">GAMBIT Collaboration: P. Athron et al., Global analyses of Higgs portal singlet dark matter models using GAMBIT. Eur. Phys. J. C <b>79</b>, 38 (2019). <a href="http://arxiv.org/abs/1808.10465" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1808.10465">arXiv:1808.10465</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="111."><p class="c-article-references__text" id="ref-CR111">QCDSF-UKQCD: R. Horsley, Y. Nakamura et al., Hyperon sigma terms for 2 + 1 quark flavours. Phys. Rev. D <b>85</b>, 034506 (2012). <a href="http://arxiv.org/abs/1110.4971" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1110.4971">arXiv:1110.4971</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="112."><p class="c-article-references__text" id="ref-CR112">S. Durr et al., Lattice computation of the nucleon scalar quark contents at the physical point. Phys. Rev. Lett. <b>116</b>, 172001 (2016). <a href="http://arxiv.org/abs/1510.08013" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1510.08013">arXiv:1510.08013</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.116.172001" data-track-item_id="10.1103/PhysRevLett.116.172001" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.116.172001" aria-label="Article reference 112" data-doi="10.1103/PhysRevLett.116.172001">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016PhRvL.116q2001D" aria-label="ADS reference 112">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 112" href="http://scholar.google.com/scholar_lookup?&title=Lattice%20computation%20of%20the%20nucleon%20scalar%20quark%20contents%20at%20the%20physical%20point&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.116.172001&volume=116&publication_year=2016&author=Durr%2CS"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="113."><p class="c-article-references__text" id="ref-CR113">xQCD: Y.-B. Yang, A. Alexandru, T. Draper, J. Liang, K.-F. Liu, <span class="mathjax-tex">$\pi $</span>N and strangeness sigma terms at the physical point with chiral fermions. Phys. Rev. D <b>94</b>, 054503 (2016). <a href="http://arxiv.org/abs/1511.09089" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1511.09089">arXiv:1511.09089</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="114."><p class="c-article-references__text" id="ref-CR114">ETM: A. Abdel-Rehim, C. Alexandrou et al., Direct evaluation of the quark content of nucleons from lattice QCD at the physical point. Phys. Rev. Lett. <b>116</b>, 252001 (2016). <a href="http://arxiv.org/abs/1601.01624" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1601.01624">arXiv:1601.01624</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="115."><p class="c-article-references__text" id="ref-CR115">RQCD: G.S. Bali, S. Collins et al., Direct determinations of the nucleon and pion terms at nearly physical quark masses. Phys. Rev. D <b>93</b>, 094504 (2016). <a href="http://arxiv.org/abs/1603.00827" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1603.00827">arXiv:1603.00827</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="116."><p class="c-article-references__text" id="ref-CR116">C. Alexandrou, S. Bacchio et al., Nucleon axial, tensor, and scalar charges and -terms in lattice QCD. Phys. Rev. D <b>102</b>, 054517 (2020). <a href="http://arxiv.org/abs/1909.00485" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1909.00485">arXiv:1909.00485</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.102.054517" data-track-item_id="10.1103/PhysRevD.102.054517" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.102.054517" aria-label="Article reference 116" data-doi="10.1103/PhysRevD.102.054517">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2020PhRvD.102e4517A" aria-label="ADS reference 116">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 116" href="http://scholar.google.com/scholar_lookup?&title=Nucleon%20axial%2C%20tensor%2C%20and%20scalar%20charges%20and%20-terms%20in%20lattice%20QCD&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.102.054517&volume=102&publication_year=2020&author=Alexandrou%2CC&author=Bacchio%2CS"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="117."><p class="c-article-references__text" id="ref-CR117">JLQCD: N. Yamanaka, S. Hashimoto, T. Kaneko, H. Ohki, Nucleon charges with dynamical overlap fermions. Phys. Rev. D <b>98</b>, 054516 (2018). <a href="http://arxiv.org/abs/1805.10507" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1805.10507">arXiv:1805.10507</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="118."><p class="c-article-references__text" id="ref-CR118">S. Borsanyi, Z. Fodor et al., Ab-initio calculation of the proton and the neutron’s scalar couplings for new physics searches. <a href="http://arxiv.org/abs/2007.03319" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/2007.03319">arXiv:2007.03319</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="119."><p class="c-article-references__text" id="ref-CR119">J.M. Alarcon, J. Martin Camalich, J.A. Oller, The chiral representation of the <span class="mathjax-tex">$\pi N$</span> scattering amplitude and the pion-nucleon sigma term. Phys. Rev. D <b>85</b>, 051503 (2012). <a href="http://arxiv.org/abs/1110.3797" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1110.3797">arXiv:1110.3797</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2012PhRvD..85e1503A" aria-label="ADS reference 119">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 119" href="http://scholar.google.com/scholar_lookup?&title=The%20chiral%20representation%20of%20the%20%24%24%5Cpi%20N%24%24%20%CF%80%20N%20scattering%20amplitude%20and%20the%20pion-nucleon%20sigma%20term&journal=Phys.%20Rev.%20D&volume=85&publication_year=2012&author=Alarcon%2CJM&author=Martin%20Camalich%2CJ&author=Oller%2CJA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="120."><p class="c-article-references__text" id="ref-CR120">M. Hoferichter, J. Ruiz de Elvira, B. Kubis, U.-G. Meissner, High-precision determination of the pion-nucleon term from Roy–Steiner equations. Phys. Rev. Lett. <b>115</b>, 092301 (2015). <a href="http://arxiv.org/abs/1506.04142" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1506.04142">arXiv:1506.04142</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.115.092301" data-track-item_id="10.1103/PhysRevLett.115.092301" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.115.092301" aria-label="Article reference 120" data-doi="10.1103/PhysRevLett.115.092301">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2015PhRvL.115i2301H" aria-label="ADS reference 120">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 120" href="http://scholar.google.com/scholar_lookup?&title=High-precision%20determination%20of%20the%20pion-nucleon%20term%20from%20Roy%E2%80%93Steiner%20equations&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.115.092301&volume=115&publication_year=2015&author=Hoferichter%2CM&author=Ruiz%20de%20Elvira%2CJ&author=Kubis%2CB&author=Meissner%2CU-G"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="121."><p class="c-article-references__text" id="ref-CR121">V. Dmitrašinović, H.-X. Chen, A. Hosaka, Baryon fields with <span class="mathjax-tex">$U_L(3)$</span> Ö <span class="mathjax-tex">$U_R(3)$</span> chiral symmetry. V. Pion-nucleon and kaon-nucleon <span class="mathjax-tex">${{\varSigma }}$</span> terms. Phys. Rev. C <b>93</b>, 065208 (2016). <a href="http://arxiv.org/abs/1812.03414" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1812.03414">arXiv:1812.03414</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="122."><p class="c-article-references__text" id="ref-CR122">J. Ruiz de Elvira, M. Hoferichter, B. Kubis, U.-G. Meissner, Extracting the -term from low-energy pion-nucleon scattering. J. Phys. G <b>45</b>, 024001 (2018). <a href="http://arxiv.org/abs/1706.01465" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1706.01465">arXiv:1706.01465</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1361-6471/aa9422" data-track-item_id="10.1088/1361-6471/aa9422" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1361-6471%2Faa9422" aria-label="Article reference 122" data-doi="10.1088/1361-6471/aa9422">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018JPhG...45b4001R" aria-label="ADS reference 122">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 122" href="http://scholar.google.com/scholar_lookup?&title=Extracting%20the%20-term%20from%20low-energy%20pion-nucleon%20scattering&journal=J.%20Phys.%20G&doi=10.1088%2F1361-6471%2Faa9422&volume=45&publication_year=2018&author=Ruiz%20de%20Elvira%2CJ&author=Hoferichter%2CM&author=Kubis%2CB&author=Meissner%2CU-G"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="123."><p class="c-article-references__text" id="ref-CR123">E. Friedman, A. Gal, The pion-nucleon <span class="mathjax-tex">${\sigma }$</span> term from pionic atoms. Phys. Lett. B <b>792</b>, 340–344 (2019). <a href="http://arxiv.org/abs/1901.03130" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1901.03130">arXiv:1901.03130</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="124."><p class="c-article-references__text" id="ref-CR124">P. Gondolo, G. Gelmini, Cosmic abundances of stable particles: improved analysis. Nucl. Phys. A <b>360</b>, 145–179 (1991)</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/0550-3213(91)90438-4" data-track-item_id="10.1016/0550-3213(91)90438-4" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2F0550-3213%2891%2990438-4" aria-label="Article reference 124" data-doi="10.1016/0550-3213(91)90438-4">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 124" href="http://scholar.google.com/scholar_lookup?&title=Cosmic%20abundances%20of%20stable%20particles%3A%20improved%20analysis&journal=Nucl.%20Phys.%20A&doi=10.1016%2F0550-3213%2891%2990438-4&volume=360&pages=145-179&publication_year=1991&author=Gondolo%2CP&author=Gelmini%2CG"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="125."><p class="c-article-references__text" id="ref-CR125">T. Binder, T. Bringmann, M. Gustafsson, A. Hryczuk, Early kinetic decoupling of dark matter: when the standard way of calculating the thermal relic density fails. Phys. Rev. D <b>96</b>, 115010 (2017). <a href="http://arxiv.org/abs/1706.07433" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1706.07433">arXiv:1706.07433</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.96.115010" data-track-item_id="10.1103/PhysRevD.96.115010" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.96.115010" aria-label="Article reference 125" data-doi="10.1103/PhysRevD.96.115010">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2017PhRvD..96k5010B" aria-label="ADS reference 125">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 125" href="http://scholar.google.com/scholar_lookup?&title=Early%20kinetic%20decoupling%20of%20dark%20matter%3A%20when%20the%20standard%20way%20of%20calculating%20the%20thermal%20relic%20density%20fails&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.96.115010&volume=96&publication_year=2017&author=Binder%2CT&author=Bringmann%2CT&author=Gustafsson%2CM&author=Hryczuk%2CA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="126."><p class="c-article-references__text" id="ref-CR126">D.E. Kaplan, M.A. Luty, K.M. Zurek, Asymmetric dark matter. Phys. Rev. D <b>79</b>, 115016 (2009). <a href="http://arxiv.org/abs/0901.4117" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/0901.4117">arXiv:0901.4117</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.79.115016" data-track-item_id="10.1103/PhysRevD.79.115016" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.79.115016" aria-label="Article reference 126" data-doi="10.1103/PhysRevD.79.115016">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2009PhRvD..79k5016K" aria-label="ADS reference 126">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 126" href="http://scholar.google.com/scholar_lookup?&title=Asymmetric%20dark%20matter&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.79.115016&volume=79&publication_year=2009&author=Kaplan%2CDE&author=Luty%2CMA&author=Zurek%2CKM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="127."><p class="c-article-references__text" id="ref-CR127">A. Pukhov, CalcHEP 2.3: MSSM, structure functions, event generation, batchs, and generation of matrix elements for other packages. <a href="http://arxiv.org/abs/hep-ph/0412191" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/hep-ph/0412191">arXiv:hep-ph/0412191</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="128."><p class="c-article-references__text" id="ref-CR128">A. Belyaev, N.D. Christensen, A. Pukhov, CalcHEP 3.4 for collider physics within and beyond the Standard Model. Comput. Phys. Commun. <b>184</b>, 1729–1769 (2013). <a href="http://arxiv.org/abs/1207.6082" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1207.6082">arXiv:1207.6082</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.cpc.2013.01.014" data-track-item_id="10.1016/j.cpc.2013.01.014" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.cpc.2013.01.014" aria-label="Article reference 128" data-doi="10.1016/j.cpc.2013.01.014">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2013CoPhC.184.1729B" aria-label="ADS reference 128">ADS</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="math reference" data-track-action="math reference" href="http://www.emis.de/MATH-item?1286.81009" aria-label="MATH reference 128">MATH</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 128" href="http://scholar.google.com/scholar_lookup?&title=CalcHEP%203.4%20for%20collider%20physics%20within%20and%20beyond%20the%20Standard%20Model&journal=Comput.%20Phys.%20Commun.&doi=10.1016%2Fj.cpc.2013.01.014&volume=184&pages=1729-1769&publication_year=2013&author=Belyaev%2CA&author=Christensen%2CND&author=Pukhov%2CA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="129."><p class="c-article-references__text" id="ref-CR129">A. Arbey, F. Mahmoudi, Dark matter and the early Universe: a review. Prog. Part. Nucl. Phys. <b>119</b>, 103865 (2021). <a href="http://arxiv.org/abs/2104.11488" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/2104.11488">arXiv:2104.11488</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.ppnp.2021.103865" data-track-item_id="10.1016/j.ppnp.2021.103865" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.ppnp.2021.103865" aria-label="Article reference 129" data-doi="10.1016/j.ppnp.2021.103865">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 129" href="http://scholar.google.com/scholar_lookup?&title=Dark%20matter%20and%20the%20early%20Universe%3A%20a%20review&journal=Prog.%20Part.%20Nucl.%20Phys.&doi=10.1016%2Fj.ppnp.2021.103865&volume=119&publication_year=2021&author=Arbey%2CA&author=Mahmoudi%2CF"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="130."><p class="c-article-references__text" id="ref-CR130">T. Bringmann, J. Edsjö, P. Gondolo, P. Ullio, L. Bergström, DarkSUSY 6: an advanced tool to compute dark matter properties numerically. JCAP <b>1807</b>, 033 (2018). <a href="http://arxiv.org/abs/1802.03399" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1802.03399">arXiv:1802.03399</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1475-7516/2018/07/033" data-track-item_id="10.1088/1475-7516/2018/07/033" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1475-7516%2F2018%2F07%2F033" aria-label="Article reference 130" data-doi="10.1088/1475-7516/2018/07/033">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018JCAP...07..033B" aria-label="ADS reference 130">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 130" href="http://scholar.google.com/scholar_lookup?&title=DarkSUSY%206%3A%20an%20advanced%20tool%20to%20compute%20dark%20matter%20properties%20numerically&journal=JCAP&doi=10.1088%2F1475-7516%2F2018%2F07%2F033&volume=1807&publication_year=2018&author=Bringmann%2CT&author=Edsj%C3%B6%2CJ&author=Gondolo%2CP&author=Ullio%2CP&author=Bergstr%C3%B6m%2CL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="131."><p class="c-article-references__text" id="ref-CR131">P. Gondolo, J. Edsjo et al., DarkSUSY: computing supersymmetric dark matter properties numerically. JCAP <b>0407</b>, 008 (2004). <a href="http://arxiv.org/abs/astro-ph/0406204" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/astro-ph/0406204">arXiv:astro-ph/0406204</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1475-7516/2004/07/008" data-track-item_id="10.1088/1475-7516/2004/07/008" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1475-7516%2F2004%2F07%2F008" aria-label="Article reference 131" data-doi="10.1088/1475-7516/2004/07/008">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2004JCAP...07..008G" aria-label="ADS reference 131">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 131" href="http://scholar.google.com/scholar_lookup?&title=DarkSUSY%3A%20computing%20supersymmetric%20dark%20matter%20properties%20numerically&journal=JCAP&doi=10.1088%2F1475-7516%2F2004%2F07%2F008&volume=0407&publication_year=2004&author=Gondolo%2CP&author=Edsjo%2CJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="132."><p class="c-article-references__text" id="ref-CR132">N.F. Bell, Y. Cai, A.D. Medina, Co-annihilating dark matter: effective operator analysis and collider phenomenology. Phys. Rev. D <b>89</b>, 115001 (2014). <a href="http://arxiv.org/abs/1311.6169" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1311.6169">arXiv:1311.6169</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.89.115001" data-track-item_id="10.1103/PhysRevD.89.115001" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.89.115001" aria-label="Article reference 132" data-doi="10.1103/PhysRevD.89.115001">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014PhRvD..89k5001B" aria-label="ADS reference 132">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 132" href="http://scholar.google.com/scholar_lookup?&title=Co-annihilating%20dark%20matter%3A%20effective%20operator%20analysis%20and%20collider%20phenomenology&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.89.115001&volume=89&publication_year=2014&author=Bell%2CNF&author=Cai%2CY&author=Medina%2CAD"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="133."><p class="c-article-references__text" id="ref-CR133">M.J. Baker et al., The coannihilation codex. JHEP <b>12</b>, 120 (2015). <a href="http://arxiv.org/abs/1510.03434" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1510.03434">arXiv:1510.03434</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2015JHEP...12..120B" aria-label="ADS reference 133">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 133" href="http://scholar.google.com/scholar_lookup?&title=The%20coannihilation%20codex&journal=JHEP&volume=12&publication_year=2015&author=Baker%2CMJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="134."><p class="c-article-references__text" id="ref-CR134">T. Bringmann, C. Weniger, Gamma ray signals from dark matter: concepts, status and prospects. Phys. Dark Universe <b>1</b>, 194–217 (2012). <a href="http://arxiv.org/abs/1208.5481" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1208.5481">arXiv:1208.5481</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.dark.2012.10.005" data-track-item_id="10.1016/j.dark.2012.10.005" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.dark.2012.10.005" aria-label="Article reference 134" data-doi="10.1016/j.dark.2012.10.005">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2012PDU.....1..194B" aria-label="ADS reference 134">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 134" href="http://scholar.google.com/scholar_lookup?&title=Gamma%20ray%20signals%20from%20dark%20matter%3A%20concepts%2C%20status%20and%20prospects&journal=Phys.%20Dark%20Universe&doi=10.1016%2Fj.dark.2012.10.005&volume=1&pages=194-217&publication_year=2012&author=Bringmann%2CT&author=Weniger%2CC"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="135."><p class="c-article-references__text" id="ref-CR135">Fermi-LAT: M. Ackermann et al., The Fermi Galactic Center GeV excess and implications for dark matter. Astrophys. J. <b>840</b>, 43 (2017). <a href="http://arxiv.org/abs/1704.03910" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1704.03910">arXiv:1704.03910</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="136."><p class="c-article-references__text" id="ref-CR136">CTA: A. Acharyya et al., Sensitivity of the Cherenkov Telescope Array to a dark matter signal from the Galactic Centre. JCAP <b>01</b>, 057 (2021). <a href="http://arxiv.org/abs/2007.16129" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/2007.16129">arXiv:2007.16129</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="137."><p class="c-article-references__text" id="ref-CR137">Super-Kamiokande: K. Choi et al., Search for neutrinos from annihilation of captured low-mass dark matter particles in the Sun by Super-Kamiokande. Phys. Rev. Lett. <b>114</b>, 141301 (2015). <a href="http://arxiv.org/abs/1503.04858" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1503.04858">arXiv:1503.04858</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="138."><p class="c-article-references__text" id="ref-CR138">IceCube: M.G. Aartsen et al., Search for annihilating dark matter in the Sun with 3 years of IceCube data. Eur. Phys. J. C <b>77</b>, 146 (2017). <a href="http://arxiv.org/abs/1612.05949" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1612.05949">arXiv:1612.05949</a> [Erratum: Eur. Phys. J. C <b>79</b>, 214 (2019)]</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="139."><p class="c-article-references__text" id="ref-CR139">N. Avis Kozar, A. Caddell, L. Fraser-Leach, P. Scott, A.C. Vincent, Capt’n General: a generalized stellar dark matter capture and heat transport code (2021). <a href="http://arxiv.org/abs/2105.06810" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/2105.06810">arXiv:2105.06810</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="140."><p class="c-article-references__text" id="ref-CR140">R. Catena, B. Schwabe, Form factors for dark matter capture by the Sun in effective theories. JCAP <b>04</b>, 042 (2015). <a href="http://arxiv.org/abs/1501.03729" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1501.03729">arXiv:1501.03729</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1475-7516/2015/04/042" data-track-item_id="10.1088/1475-7516/2015/04/042" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1475-7516%2F2015%2F04%2F042" aria-label="Article reference 140" data-doi="10.1088/1475-7516/2015/04/042">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2015JCAP...04..042C" aria-label="ADS reference 140">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 140" href="http://scholar.google.com/scholar_lookup?&title=Form%20factors%20for%20dark%20matter%20capture%20by%20the%20Sun%20in%20effective%20theories&journal=JCAP&doi=10.1088%2F1475-7516%2F2015%2F04%2F042&volume=04&publication_year=2015&author=Catena%2CR&author=Schwabe%2CB"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="141."><p class="c-article-references__text" id="ref-CR141">N. Vinyoles, A.M. Serenelli et al., A new generation of standard solar models. Astrophys. J. <b>835</b>, 202 (2017). <a href="http://arxiv.org/abs/1611.09867" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1611.09867">arXiv:1611.09867</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.3847/1538-4357/835/2/202" data-track-item_id="10.3847/1538-4357/835/2/202" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.3847%2F1538-4357%2F835%2F2%2F202" aria-label="Article reference 141" data-doi="10.3847/1538-4357/835/2/202">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2017ApJ...835..202V" aria-label="ADS reference 141">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 141" href="http://scholar.google.com/scholar_lookup?&title=A%20new%20generation%20of%20standard%20solar%20models&journal=Astrophys.%20J.&doi=10.3847%2F1538-4357%2F835%2F2%2F202&volume=835&publication_year=2017&author=Vinyoles%2CN&author=Serenelli%2CAM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="142."><p class="c-article-references__text" id="ref-CR142">M. Asplund, N. Grevesse, A.J. Sauval, P. Scott, The chemical composition of the Sun. ARA&A <b>47</b>, 481–522 (2009). <a href="http://arxiv.org/abs/0909.0948" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/0909.0948">arXiv:0909.0948</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1146/annurev.astro.46.060407.145222" data-track-item_id="10.1146/annurev.astro.46.060407.145222" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1146%2Fannurev.astro.46.060407.145222" aria-label="Article reference 142" data-doi="10.1146/annurev.astro.46.060407.145222">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2009ARA%26A..47..481A" aria-label="ADS reference 142">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 142" href="http://scholar.google.com/scholar_lookup?&title=The%20chemical%20composition%20of%20the%20Sun&journal=ARA%26A&doi=10.1146%2Fannurev.astro.46.060407.145222&volume=47&pages=481-522&publication_year=2009&author=Asplund%2CM&author=Grevesse%2CN&author=Sauval%2CAJ&author=Scott%2CP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="143."><p class="c-article-references__text" id="ref-CR143">IceCube Collaboration: M.G. Aartsen, R. Abbasi et al., Search for dark matter annihilations in the Sun with the 79-String IceCube detector. Phys. Rev. Lett. <b>110</b>, 131302 (2013). <a href="http://arxiv.org/abs/1212.4097" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1212.4097">arXiv:1212.4097</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="144."><p class="c-article-references__text" id="ref-CR144">P. Scott, C. Savage, J. Edsjö, The IceCube Collaboration: R. Abbasi et al., Use of event-level neutrino telescope data in global fits for theories of new physics. JCAP <b>11</b>, 57 (2012). <a href="http://arxiv.org/abs/1207.0810" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1207.0810">arXiv:1207.0810</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="145."><p class="c-article-references__text" id="ref-CR145">T.R. Slatyer, Indirect dark matter signatures in the cosmic dark ages. I. Generalizing the bound on s-wave dark matter annihilation from Planck results. Phys. Rev. D <b>93</b>, 023527 (2016). <a href="http://arxiv.org/abs/1506.03811" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1506.03811">arXiv:1506.03811</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.93.023527" data-track-item_id="10.1103/PhysRevD.93.023527" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.93.023527" aria-label="Article reference 145" data-doi="10.1103/PhysRevD.93.023527">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016PhRvD..93b3527S" aria-label="ADS reference 145">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 145" href="http://scholar.google.com/scholar_lookup?&title=Indirect%20dark%20matter%20signatures%20in%20the%20cosmic%20dark%20ages.%20I.%20Generalizing%20the%20bound%20on%20s-wave%20dark%20matter%20annihilation%20from%20Planck%20results&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.93.023527&volume=93&publication_year=2016&author=Slatyer%2CTR"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="146."><p class="c-article-references__text" id="ref-CR146">T.R. Slatyer, Indirect dark matter signatures in the cosmic dark ages II. Ionization, heating and photon production from arbitrary energy injections. Phys. Rev. D <b>93</b>, 023521 (2016). <a href="http://arxiv.org/abs/1506.03812" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1506.03812">arXiv:1506.03812</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.93.023521" data-track-item_id="10.1103/PhysRevD.93.023521" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.93.023521" aria-label="Article reference 146" data-doi="10.1103/PhysRevD.93.023521">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016PhRvD..93b3521S" aria-label="ADS reference 146">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 146" href="http://scholar.google.com/scholar_lookup?&title=Indirect%20dark%20matter%20signatures%20in%20the%20cosmic%20dark%20ages%20II.%20Ionization%2C%20heating%20and%20photon%20production%20from%20arbitrary%20energy%20injections&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.93.023521&volume=93&publication_year=2016&author=Slatyer%2CTR"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="147."><p class="c-article-references__text" id="ref-CR147">P. Stöcker, M. Krämer, J. Lesgourgues, V. Poulin, Exotic energy injection with ExoCLASS: application to the Higgs portal model and evaporating black holes. JCAP <b>1803</b>, 018 (2018). <a href="http://arxiv.org/abs/1801.01871" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1801.01871">arXiv:1801.01871</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1475-7516/2018/03/018" data-track-item_id="10.1088/1475-7516/2018/03/018" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1475-7516%2F2018%2F03%2F018" aria-label="Article reference 147" data-doi="10.1088/1475-7516/2018/03/018">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018JCAP...03..018S" aria-label="ADS reference 147">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 147" href="http://scholar.google.com/scholar_lookup?&title=Exotic%20energy%20injection%20with%20ExoCLASS%3A%20application%20to%20the%20Higgs%20portal%20model%20and%20evaporating%20black%20holes&journal=JCAP&doi=10.1088%2F1475-7516%2F2018%2F03%2F018&volume=1803&publication_year=2018&author=St%C3%B6cker%2CP&author=Kr%C3%A4mer%2CM&author=Lesgourgues%2CJ&author=Poulin%2CV"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="148."><p class="c-article-references__text" id="ref-CR148">Planck: N. Aghanim et al., Planck 2018 results. V. CMB power spectra and likelihoods. Astron. Astrophys. <b>641</b>, A5 (2020). <a href="http://arxiv.org/abs/1907.12875" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1907.12875">arXiv:1907.12875</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="149."><p class="c-article-references__text" id="ref-CR149">F. Beutler, C. Blake et al., The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant. MNRAS <b>416</b>, 3017–3032 (2011). <a href="http://arxiv.org/abs/1106.3366" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1106.3366">arXiv:1106.3366</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1111/j.1365-2966.2011.19250.x" data-track-item_id="10.1111/j.1365-2966.2011.19250.x" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1111%2Fj.1365-2966.2011.19250.x" aria-label="Article reference 149" data-doi="10.1111/j.1365-2966.2011.19250.x">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2011MNRAS.416.3017B" aria-label="ADS reference 149">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 149" href="http://scholar.google.com/scholar_lookup?&title=The%206dF%20Galaxy%20Survey%3A%20baryon%20acoustic%20oscillations%20and%20the%20local%20Hubble%20constant&journal=MNRAS&doi=10.1111%2Fj.1365-2966.2011.19250.x&volume=416&pages=3017-3032&publication_year=2011&author=Beutler%2CF&author=Blake%2CC"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="150."><p class="c-article-references__text" id="ref-CR150">A.J. Ross, L. Samushia et al., The clustering of the SDSS DR7 main Galaxy sample—I. A 4 per cent distance measure at z = 0.15. MNRAS <b>449</b>, 835–847 (2015). <a href="http://arxiv.org/abs/1409.3242" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1409.3242">arXiv:1409.3242</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="151."><p class="c-article-references__text" id="ref-CR151">BOSS: S. Alam et al., The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample. MNRAS <b>470</b>, 2617–2652 (2017). <a href="http://arxiv.org/abs/1607.03155" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1607.03155">arXiv:1607.03155</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="152."><p class="c-article-references__text" id="ref-CR152">J. Kopp, Constraints on dark matter annihilation from AMS-02 results. Phys. Rev. D <b>88</b>, 076013 (2013). <a href="http://arxiv.org/abs/1304.1184" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1304.1184">arXiv:1304.1184</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.88.076013" data-track-item_id="10.1103/PhysRevD.88.076013" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.88.076013" aria-label="Article reference 152" data-doi="10.1103/PhysRevD.88.076013">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2013PhRvD..88g6013K" aria-label="ADS reference 152">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 152" href="http://scholar.google.com/scholar_lookup?&title=Constraints%20on%20dark%20matter%20annihilation%20from%20AMS-02%20results&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.88.076013&volume=88&publication_year=2013&author=Kopp%2CJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="153."><p class="c-article-references__text" id="ref-CR153">L. Bergström, T. Bringmann, I. Cholis, D. Hooper, C. Weniger, New limits on dark matter annihilation from AMS cosmic ray positron data. Phys. Rev. Lett. <b>111</b>, 171101 (2013). <a href="http://arxiv.org/abs/1306.3983" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1306.3983">arXiv:1306.3983</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.111.171101" data-track-item_id="10.1103/PhysRevLett.111.171101" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.111.171101" aria-label="Article reference 153" data-doi="10.1103/PhysRevLett.111.171101">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2013PhRvL.111q1101B" aria-label="ADS reference 153">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 153" href="http://scholar.google.com/scholar_lookup?&title=New%20limits%20on%20dark%20matter%20annihilation%20from%20AMS%20cosmic%20ray%20positron%20data&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.111.171101&volume=111&publication_year=2013&author=Bergstr%C3%B6m%2CL&author=Bringmann%2CT&author=Cholis%2CI&author=Hooper%2CD&author=Weniger%2CC"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="154."><p class="c-article-references__text" id="ref-CR154">A. Ibarra, A.S. Lamperstorfer, J. Silk, Dark matter annihilations and decays after the AMS-02 positron measurements. Phys. Rev. D <b>89</b>, 063539 (2014). <a href="http://arxiv.org/abs/1309.2570" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1309.2570">arXiv:1309.2570</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.89.063539" data-track-item_id="10.1103/PhysRevD.89.063539" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.89.063539" aria-label="Article reference 154" data-doi="10.1103/PhysRevD.89.063539">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014PhRvD..89f3539I" aria-label="ADS reference 154">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 154" href="http://scholar.google.com/scholar_lookup?&title=Dark%20matter%20annihilations%20and%20decays%20after%20the%20AMS-02%20positron%20measurements&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.89.063539&volume=89&publication_year=2014&author=Ibarra%2CA&author=Lamperstorfer%2CAS&author=Silk%2CJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="155."><p class="c-article-references__text" id="ref-CR155">L. Bergstrom, J. Edsjo, P. Ullio, Cosmic anti-protons as a probe for supersymmetric dark matter? Astrophys. J. <b>526</b>, 215–235 (1999). <a href="http://arxiv.org/abs/astro-ph/9902012" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/astro-ph/9902012">arXiv:astro-ph/9902012</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1086/307975" data-track-item_id="10.1086/307975" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1086%2F307975" aria-label="Article reference 155" data-doi="10.1086/307975">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=1999ApJ...526..215B" aria-label="ADS reference 155">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 155" href="http://scholar.google.com/scholar_lookup?&title=Cosmic%20anti-protons%20as%20a%20probe%20for%20supersymmetric%20dark%20matter%3F&journal=Astrophys.%20J.&doi=10.1086%2F307975&volume=526&pages=215-235&publication_year=1999&author=Bergstrom%2CL&author=Edsjo%2CJ&author=Ullio%2CP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="156."><p class="c-article-references__text" id="ref-CR156">T. Bringmann, P. Salati, The galactic antiproton spectrum at high energies: background expectation vs. exotic contributions. Phys. Rev. D <b>75</b>, 083006 (2007). <a href="http://arxiv.org/abs/astro-ph/0612514" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/astro-ph/0612514">arXiv:astro-ph/0612514</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevD.75.083006" data-track-item_id="10.1103/PhysRevD.75.083006" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevD.75.083006" aria-label="Article reference 156" data-doi="10.1103/PhysRevD.75.083006">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2007PhRvD..75h3006B" aria-label="ADS reference 156">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 156" href="http://scholar.google.com/scholar_lookup?&title=The%20galactic%20antiproton%20spectrum%20at%20high%20energies%3A%20background%20expectation%20vs.%20exotic%20contributions&journal=Phys.%20Rev.%20D&doi=10.1103%2FPhysRevD.75.083006&volume=75&publication_year=2007&author=Bringmann%2CT&author=Salati%2CP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="157."><p class="c-article-references__text" id="ref-CR157">A. Cuoco, M. Krämer, M. Korsmeier, Novel dark matter constraints from antiprotons in light of AMS-02. Phys. Rev. Lett. <b>118</b>, 191102 191102 (2017). <a href="http://arxiv.org/abs/1610.03071" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1610.03071">arXiv:1610.03071</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevLett.118.191102" data-track-item_id="10.1103/PhysRevLett.118.191102" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevLett.118.191102" aria-label="Article reference 157" data-doi="10.1103/PhysRevLett.118.191102">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2017PhRvL.118s1102C" aria-label="ADS reference 157">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 157" href="http://scholar.google.com/scholar_lookup?&title=Novel%20dark%20matter%20constraints%20from%20antiprotons%20in%20light%20of%20AMS-02&journal=Phys.%20Rev.%20Lett.&doi=10.1103%2FPhysRevLett.118.191102&volume=118&publication_year=2017&author=Cuoco%2CA&author=Kr%C3%A4mer%2CM&author=Korsmeier%2CM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="158."><p class="c-article-references__text" id="ref-CR158">J. Heisig, M. Korsmeier, M.W. Winkler, Dark matter or correlated errors: systematics of the AMS-02 antiproton excess. Phys. Rev. Res. <b>2</b>, 043017 (2020). <a href="http://arxiv.org/abs/2005.04237" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/2005.04237">arXiv:2005.04237</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevResearch.2.043017" data-track-item_id="10.1103/PhysRevResearch.2.043017" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevResearch.2.043017" aria-label="Article reference 158" data-doi="10.1103/PhysRevResearch.2.043017">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 158" href="http://scholar.google.com/scholar_lookup?&title=Dark%20matter%20or%20correlated%20errors%3A%20systematics%20of%20the%20AMS-02%20antiproton%20excess&journal=Phys.%20Rev.%20Res.&doi=10.1103%2FPhysRevResearch.2.043017&volume=2&publication_year=2020&author=Heisig%2CJ&author=Korsmeier%2CM&author=Winkler%2CMW"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="159."><p class="c-article-references__text" id="ref-CR159">M. Boudaud, Y. Génolini et al., AMS-02 antiprotons’ consistency with a secondary astrophysical origin. Phys. Rev. Res. <b>2</b>, 023022 (2020). <a href="http://arxiv.org/abs/1906.07119" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1906.07119">arXiv:1906.07119</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1103/PhysRevResearch.2.023022" data-track-item_id="10.1103/PhysRevResearch.2.023022" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1103%2FPhysRevResearch.2.023022" aria-label="Article reference 159" data-doi="10.1103/PhysRevResearch.2.023022">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 159" href="http://scholar.google.com/scholar_lookup?&title=AMS-02%20antiprotons%E2%80%99%20consistency%20with%20a%20secondary%20astrophysical%20origin&journal=Phys.%20Rev.%20Res.&doi=10.1103%2FPhysRevResearch.2.023022&volume=2&publication_year=2020&author=Boudaud%2CM&author=G%C3%A9nolini%2CY"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="160."><p class="c-article-references__text" id="ref-CR160">G. Jóhannesson et al., Bayesian analysis of cosmic-ray propagation: evidence against homogeneous diffusion. Astrophys. J. <b>824</b>, 16 (2016). <a href="http://arxiv.org/abs/1602.02243" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1602.02243">arXiv:1602.02243</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.3847/0004-637X/824/1/16" data-track-item_id="10.3847/0004-637X/824/1/16" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.3847%2F0004-637X%2F824%2F1%2F16" aria-label="Article reference 160" data-doi="10.3847/0004-637X/824/1/16">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016ApJ...824...16J" aria-label="ADS reference 160">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 160" href="http://scholar.google.com/scholar_lookup?&title=Bayesian%20analysis%20of%20cosmic-ray%20propagation%3A%20evidence%20against%20homogeneous%20diffusion&journal=Astrophys.%20J.&doi=10.3847%2F0004-637X%2F824%2F1%2F16&volume=824&publication_year=2016&author=J%C3%B3hannesson%2CG"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="161."><p class="c-article-references__text" id="ref-CR161">M. Bauer, M. Klassen, V. Tenorth, Universal properties of pseudoscalar mediators in dark matter extensions of 2HDMs. JHEP <b>07</b>, 107 (2018). <a href="http://arxiv.org/abs/1712.06597" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1712.06597">arXiv:1712.06597</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP07(2018)107" data-track-item_id="10.1007/JHEP07(2018)107" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP07(2018)107" aria-label="Article reference 161" data-doi="10.1007/JHEP07(2018)107">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2018JHEP...07..107B" aria-label="ADS reference 161">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 161" href="http://scholar.google.com/scholar_lookup?&title=Universal%20properties%20of%20pseudoscalar%20mediators%20in%20dark%20matter%20extensions%20of%202HDMs&journal=JHEP&doi=10.1007%2FJHEP07%282018%29107&volume=07&publication_year=2018&author=Bauer%2CM&author=Klassen%2CM&author=Tenorth%2CV"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="162."><p class="c-article-references__text" id="ref-CR162">A.J. Brennan, M.F. McDonald, J. Gramling, T.D. Jacques, Collide and conquer: constraints on simplified dark matter models using mono-X collider searches. JHEP <b>05</b>, 112 (2016). <a href="http://arxiv.org/abs/1603.01366" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1603.01366">arXiv:1603.01366</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP05(2016)112" data-track-item_id="10.1007/JHEP05(2016)112" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP05(2016)112" aria-label="Article reference 162" data-doi="10.1007/JHEP05(2016)112">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016JHEP...05..112B" aria-label="ADS reference 162">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 162" href="http://scholar.google.com/scholar_lookup?&title=Collide%20and%20conquer%3A%20constraints%20on%20simplified%20dark%20matter%20models%20using%20mono-X%20collider%20searches&journal=JHEP&doi=10.1007%2FJHEP05%282016%29112&volume=05&publication_year=2016&author=Brennan%2CAJ&author=McDonald%2CMF&author=Gramling%2CJ&author=Jacques%2CTD"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="163."><p class="c-article-references__text" id="ref-CR163">A. Alloul, N.D. Christensen, C. Degrande, C. Duhr, B. Fuks, FeynRules 2.0—a complete toolbox for tree-level phenomenology. Comput. Phys. Commun. <b>185</b>, 2250–2300 (2014). <a href="http://arxiv.org/abs/1310.1921" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1310.1921">arXiv:1310.1921</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="164."><p class="c-article-references__text" id="ref-CR164">J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, T. Stelzer, MadGraph 5: going beyond. JHEP <b>06</b>, 128 (2011). <a href="http://arxiv.org/abs/1106.0522" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1106.0522">arXiv:1106.0522</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP06(2011)128" data-track-item_id="10.1007/JHEP06(2011)128" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP06(2011)128" aria-label="Article reference 164" data-doi="10.1007/JHEP06(2011)128">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2011JHEP...06..128A" aria-label="ADS reference 164">ADS</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="math reference" data-track-action="math reference" href="http://www.emis.de/MATH-item?1298.81362" aria-label="MATH reference 164">MATH</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 164" href="http://scholar.google.com/scholar_lookup?&title=MadGraph%205%3A%20going%20beyond&journal=JHEP&doi=10.1007%2FJHEP06%282011%29128&volume=06&publication_year=2011&author=Alwall%2CJ&author=Herquet%2CM&author=Maltoni%2CF&author=Mattelaer%2CO&author=Stelzer%2CT"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="165."><p class="c-article-references__text" id="ref-CR165">T. Sjostrand, S. Mrenna, P.Z. Skands, A brief introduction to PYTHIA 8.1. Comput. Phys. Commun. <b>178</b>, 852–867 (2008). <a href="http://arxiv.org/abs/0710.3820" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/0710.3820">arXiv:0710.3820</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.cpc.2008.01.036" data-track-item_id="10.1016/j.cpc.2008.01.036" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.cpc.2008.01.036" aria-label="Article reference 165" data-doi="10.1016/j.cpc.2008.01.036">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2008CoPhC.178..852S" aria-label="ADS reference 165">ADS</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="math reference" data-track-action="math reference" href="http://www.emis.de/MATH-item?1196.81038" aria-label="MATH reference 165">MATH</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 165" href="http://scholar.google.com/scholar_lookup?&title=A%20brief%20introduction%20to%20PYTHIA%208.1&journal=Comput.%20Phys.%20Commun.&doi=10.1016%2Fj.cpc.2008.01.036&volume=178&pages=852-867&publication_year=2008&author=Sjostrand%2CT&author=Mrenna%2CS&author=Skands%2CPZ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="166."><p class="c-article-references__text" id="ref-CR166">DELPHES 3: J. de Favereau, C. Delaere et al., DELPHES 3, a modular framework for fast simulation of a generic collider experiment. JHEP <b>02</b>, 057 (2014). <a href="http://arxiv.org/abs/1307.6346" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1307.6346">arXiv:1307.6346</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="167."><p class="c-article-references__text" id="ref-CR167">CMS Collaboration, Simplified likelihood for the re-interpretation of public CMS results. CMS-NOTE-2017-001 (2017)</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="168."><p class="c-article-references__text" id="ref-CR168"><span class="u-sans-serif">GAMBIT</span> Collider Workgroup: C. Balázs, A. Buckley et al., ColliderBit: a GAMBIT module for the calculation of high-energy collider observables and likelihoods. Eur. Phys. J. C <b>77</b>, 795 (2017). <a href="http://arxiv.org/abs/1705.07919" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1705.07919">arXiv:1705.07919</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="169."><p class="c-article-references__text" id="ref-CR169">GAMBIT Collaboration: P. Athron et al., Combined collider constraints on neutralinos and charginos. Eur. Phys. J. C <b>79</b>, 395 (2019). <a href="http://arxiv.org/abs/1809.02097" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1809.02097">arXiv:1809.02097</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="170."><p class="c-article-references__text" id="ref-CR170">M.J. Reid et al., Trigonometric parallaxes of high mass star forming regions: the structure and kinematics of the Milky Way. Astrophys. J. <b>783</b>, 130 (2014). <a href="http://arxiv.org/abs/1401.5377" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1401.5377">arXiv:1401.5377</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/0004-637X/783/2/130" data-track-item_id="10.1088/0004-637X/783/2/130" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F0004-637X%2F783%2F2%2F130" aria-label="Article reference 170" data-doi="10.1088/0004-637X/783/2/130">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2014ApJ...783..130R" aria-label="ADS reference 170">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 170" href="http://scholar.google.com/scholar_lookup?&title=Trigonometric%20parallaxes%20of%20high%20mass%20star%20forming%20regions%3A%20the%20structure%20and%20kinematics%20of%20the%20Milky%20Way&journal=Astrophys.%20J.&doi=10.1088%2F0004-637X%2F783%2F2%2F130&volume=783&publication_year=2014&author=Reid%2CMJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="171."><p class="c-article-references__text" id="ref-CR171">A.J. Deason, A. Fattahi et al., The local high-velocity tail and the galactic escape speed. MNRAS <b>485</b>, 3514–3526 (2019). <a href="http://arxiv.org/abs/1901.02016" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1901.02016">arXiv:1901.02016</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1093/mnras/stz623" data-track-item_id="10.1093/mnras/stz623" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1093%2Fmnras%2Fstz623" aria-label="Article reference 171" data-doi="10.1093/mnras/stz623">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2019MNRAS.485.3514D" aria-label="ADS reference 171">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 171" href="http://scholar.google.com/scholar_lookup?&title=The%20local%20high-velocity%20tail%20and%20the%20galactic%20escape%20speed&journal=MNRAS&doi=10.1093%2Fmnras%2Fstz623&volume=485&pages=3514-3526&publication_year=2019&author=Deason%2CAJ&author=Fattahi%2CA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="172."><p class="c-article-references__text" id="ref-CR172">ATLAS: G. Aad et al., Measurement of the top-quark mass in <span class="mathjax-tex">$t{\bar{t}}+1$</span>-jet events collected with the ATLAS detector in <span class="mathjax-tex">$pp$</span> collisions at <span class="mathjax-tex">$\sqrt{s}=8$</span> TeV. JHEP <b>11</b>, 150 (2019). <a href="http://arxiv.org/abs/1905.02302" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1905.02302">arXiv:1905.02302</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="173."><p class="c-article-references__text" id="ref-CR173"><span class="u-sans-serif">GAMBIT</span> Scanner Workgroup: G.D. Martinez, J. McKay et al., Comparison of statistical sampling methods with ScannerBit, the GAMBIT scanning module. Eur. Phys. J. C <b>77</b>, 761 (2017). <a href="http://arxiv.org/abs/1705.07959" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1705.07959">arXiv:1705.07959</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="174."><p class="c-article-references__text" id="ref-CR174">LUX-ZEPLIN: D.S. Akerib et al., Projected WIMP sensitivity of the LUX-ZEPLIN dark matter experiment. Phys. Rev. D <b>101</b>, 052002 (2020). <a href="http://arxiv.org/abs/1802.06039" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1802.06039">arXiv:1802.06039</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="175."><p class="c-article-references__text" id="ref-CR175">DARWIN: J. Aalbers et al., DARWIN: towards the ultimate dark matter detector. JCAP <b>11</b>, 017 (2016). <a href="http://arxiv.org/abs/1606.07001" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1606.07001">arXiv:1606.07001</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="176."><p class="c-article-references__text" id="ref-CR176">C.E. Aalseth et al., DarkSide-20k: a 20 tonne two-phase LAr TPC for direct dark matter detection at LNGS. Eur. Phys. J. Plus <b>133</b>, 131 (2018). <a href="http://arxiv.org/abs/1707.08145" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1707.08145">arXiv:1707.08145</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1140/epjp/i2018-11973-4" data-track-item_id="10.1140/epjp/i2018-11973-4" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1140%2Fepjp%2Fi2018-11973-4" aria-label="Article reference 176" data-doi="10.1140/epjp/i2018-11973-4">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 176" href="http://scholar.google.com/scholar_lookup?&title=DarkSide-20k%3A%20a%2020%C2%A0tonne%20two-phase%20LAr%20TPC%20for%20direct%20dark%20matter%20detection%20at%20LNGS&journal=Eur.%20Phys.%20J.%20Plus&doi=10.1140%2Fepjp%2Fi2018-11973-4&volume=133&publication_year=2018&author=Aalseth%2CCE"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="177."><p class="c-article-references__text" id="ref-CR177">M. Chala, F. Kahlhoefer, M. McCullough, G. Nardini, K. Schmidt-Hoberg, Constraining dark sectors with monojets and dijets. JHEP <b>07</b>, 089 (2015). <a href="http://arxiv.org/abs/1503.05916" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1503.05916">arXiv:1503.05916</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP07(2015)089" data-track-item_id="10.1007/JHEP07(2015)089" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP07(2015)089" aria-label="Article reference 177" data-doi="10.1007/JHEP07(2015)089">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2015JHEP...07..089C" aria-label="ADS reference 177">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 177" href="http://scholar.google.com/scholar_lookup?&title=Constraining%20dark%20sectors%20with%20monojets%20and%20dijets&journal=JHEP&doi=10.1007%2FJHEP07%282015%29089&volume=07&publication_year=2015&author=Chala%2CM&author=Kahlhoefer%2CF&author=McCullough%2CM&author=Nardini%2CG&author=Schmidt-Hoberg%2CK"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="178."><p class="c-article-references__text" id="ref-CR178">M. Fairbairn, J. Heal, F. Kahlhoefer, P. Tunney, Constraints on Z’ models from LHC dijet searches and implications for dark matter. JHEP <b>09</b>, 018 (2016). <a href="http://arxiv.org/abs/1605.07940" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1605.07940">arXiv:1605.07940</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/JHEP09(2016)018" data-track-item_id="10.1007/JHEP09(2016)018" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/JHEP09(2016)018" aria-label="Article reference 178" data-doi="10.1007/JHEP09(2016)018">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2016JHEP...09..018F" aria-label="ADS reference 178">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 178" href="http://scholar.google.com/scholar_lookup?&title=Constraints%20on%20Z%E2%80%99%20models%20from%20LHC%20dijet%20searches%20and%20implications%20for%20dark%20matter&journal=JHEP&doi=10.1007%2FJHEP09%282016%29018&volume=09&publication_year=2016&author=Fairbairn%2CM&author=Heal%2CJ&author=Kahlhoefer%2CF&author=Tunney%2CP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="179."><p class="c-article-references__text" id="ref-CR179">I. Bischer, T. Plehn, W. Rodejohann, Dark matter EFT, the third-neutrino WIMPs. SciPost Phys. <b>10</b>, 039 (2021). <a href="http://arxiv.org/abs/2008.04718" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/2008.04718">arXiv:2008.04718</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.21468/SciPostPhys.10.2.039" data-track-item_id="10.21468/SciPostPhys.10.2.039" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.21468%2FSciPostPhys.10.2.039" aria-label="Article reference 179" data-doi="10.21468/SciPostPhys.10.2.039">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="ads reference" data-track-action="ads reference" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2021ScPP...10...39B" aria-label="ADS reference 179">ADS</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 179" href="http://scholar.google.com/scholar_lookup?&title=Dark%20matter%20EFT%2C%20the%20third-neutrino%20WIMPs&journal=SciPost%20Phys.&doi=10.21468%2FSciPostPhys.10.2.039&volume=10&publication_year=2021&author=Bischer%2CI&author=Plehn%2CT&author=Rodejohann%2CW"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="180."><p class="c-article-references__text" id="ref-CR180">R. Barbieri, A view of flavour physics in 2021. Acta Phys. Polon. B <b>52</b>, 789 (2021). <a href="https://doi.org/10.5506/APhysPolB.52.789" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.5506/APhysPolB.52.789">https://doi.org/10.5506/APhysPolB.52.789</a>. <a href="http://arxiv.org/abs/2103.15635" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/2103.15635">arXiv:2103.15635</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="181."><p class="c-article-references__text" id="ref-CR181">ATLAS, CMS, LHCb: E. Graverini, Flavour anomalies: a review. J. Phys. Conf. Ser. <b>1137</b>, 012025 (2019). <a href="http://arxiv.org/abs/1807.11373" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1807.11373">arXiv:1807.11373</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="182."><p class="c-article-references__text" id="ref-CR182">LHCb: R. Aaij et al., Test of lepton universality in beauty-quark decays. <a href="http://arxiv.org/abs/2103.11769" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/2103.11769">arXiv:2103.11769</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="183."><p class="c-article-references__text" id="ref-CR183">PandaX: H. Zhang et al., Dark matter direct search sensitivity of the PandaX-4T experiment. Sci. China Phys. Mech. Astron. <b>62</b>, 31011 (2019). <a href="http://arxiv.org/abs/1806.02229" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1806.02229">arXiv:1806.02229</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="184."><p class="c-article-references__text" id="ref-CR184">XENON: E. Aprile et al., Projected WIMP sensitivity of the XENONnT dark matter experiment. JCAP <b>11</b>, 031 (2020). <a href="http://arxiv.org/abs/2007.08796" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/2007.08796">arXiv:2007.08796</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="185."><p class="c-article-references__text" id="ref-CR185">MAGIC, Fermi-LAT: M.L. Ahnen et al., Limits to dark matter annihilation cross-section from a combined analysis of MAGIC and Fermi-LAT observations of dwarf satellite galaxies. JCAP <b>02</b>, 039 (2016). <a href="http://arxiv.org/abs/1601.06590" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1601.06590">arXiv:1601.06590</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="186."><p class="c-article-references__text" id="ref-CR186">H.E.S.S.: H. Abdallah et al., Search for dark matter annihilations towards the inner Galactic halo from 10 years of observations with H.E.S.S. Phys. Rev. Lett. <b>117</b>, 111301 (2016). <a href="http://arxiv.org/abs/1607.08142" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1607.08142">arXiv:1607.08142</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="187."><p class="c-article-references__text" id="ref-CR187">AMS: M. Aguilar et al., The Alpha Magnetic Spectrometer (AMS) on the international space station: part II—results from the first seven years. Phys. Rep. <b>894</b>, 1–116 (2021)</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="188."><p class="c-article-references__text" id="ref-CR188">P. Scott, Pippi—painless parsing, post-processing and plotting of posterior and likelihood samples. Eur. Phys. J. Plus <b>127</b>, 138 (2012). <a href="http://arxiv.org/abs/1206.2245" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1206.2245">arXiv:1206.2245</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1140/epjp/i2012-12138-3" data-track-item_id="10.1140/epjp/i2012-12138-3" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1140%2Fepjp%2Fi2012-12138-3" aria-label="Article reference 188" data-doi="10.1140/epjp/i2012-12138-3">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 188" href="http://scholar.google.com/scholar_lookup?&title=Pippi%E2%80%94painless%20parsing%2C%20post-processing%20and%20plotting%20of%20posterior%20and%20likelihood%20samples&journal=Eur.%20Phys.%20J.%20Plus&doi=10.1140%2Fepjp%2Fi2012-12138-3&volume=127&publication_year=2012&author=Scott%2CP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="189."><p class="c-article-references__text" id="ref-CR189">A. Semenov, LanHEP: a package for the automatic generation of Feynman rules in field theory. Version 3.0. Comput. Phys. Commun. <b>180</b>, 431–454 (2009). <a href="http://arxiv.org/abs/0805.0555" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/0805.0555">arXiv:0805.0555</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="190."><p class="c-article-references__text" id="ref-CR190"><span class="u-sans-serif">GAMBIT</span> Collaboration: P. Athron, C. Balázs et al., GAMBIT: the global and modular beyond-the-standard-model inference tool. Addendum for GAMBIT 1.1: Mathematica backends, SUSYHD interface and updated likelihoods. Eur. Phys. J. C <b>78</b>, 98 (2018). <a href="http://arxiv.org/abs/1705.07908" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="http://arxiv.org/abs/1705.07908">arXiv:1705.07908</a>. Addendum to [48]</p></li></ol><p class="c-article-references__download u-hide-print"><a data-track="click" data-track-action="download citation references" data-track-label="link" rel="nofollow" href="https://citation-needed.springer.com/v2/references/10.1140/epjc/s10052-021-09712-6?format=refman&flavour=references">Download references<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-download-medium"></use></svg></a></p></div></div></div></section></div><section data-title="Acknowledgements"><div class="c-article-section" id="Ack1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Ack1">Acknowledgements</h2><div class="c-article-section__content" id="Ack1-content"><p>We thank all members of the <span class="u-sans-serif">GAMBIT</span> community as well as Fady Bishara for discussions and checks. For computing, we thank PRACE for awarding us access to Marconi at CINECA and Joliot-Curie at CEA. This project was also undertaken with the assistance of resources and services from the National Computational Infrastructure, which is supported by the Australian Government. We thank Astronomy Australia Limited for financial support of computing resources, and the Astronomy Supercomputer Time Allocation Committee for its generous grant of computing time. We thank Juan Fuster, Adrián Irles, Davide Melini and Marcel Vos for clarifications regarding Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 172" title="ATLAS: G. Aad et al., Measurement of the top-quark mass in 
 
 
 
 $$t{\bar{t}}+1$$
 
 
 t
 
 
 t
 
 
 ¯
 
 
 +
 1
 
 
 -jet events collected with the ATLAS detector in 
 
 
 
 $$pp$$
 
 
 pp
 
 
 collisions at 
 
 
 
 $$\sqrt{s}=8$$
 
 
 
 s
 
 =
 8
 
 
 TeV. JHEP 11, 150 (2019). 
 arXiv:1905.02302
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR172" id="ref-link-section-d52098281e24784">172</a>]. PA is supported by the Australian Research Council Future Fellowship grant FT160100274, and PA, CB, TEG and MW also acknowledge support from ARC Discovery Project DP180102209. NAK and ACV are supported by the Arthur B. McDonald Canadian Astroparticle Physics Research Institute and NSERC, with equipment funded by the Canada Foundation for Innovation and the Province of Ontario, and supported by the Queen’s Centre for Advanced Computing. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science, and Economic Development, and by the Province of Ontario. AB acknowledges support by F.N.R.S. through the F.6001.19 convention, JB and JZ by DOE grant DE-SC0011784, BF by the Horizon 2020 Marie Skłodowska-Curie actions (EU; H2020-MSCA-IF-2016-752162), WH by a Royal Society University Research Fellowship, FK, TEG and PSt from the DFG Emmy Noether Grant No. KA 4662/1-1 and Grant 396021762 – TRR 257, JJR by Katherine Freese through a grant from the Swedish Research Council (Contract No. 638-2013-8993). MTP is supported by the Argelander Starter-Kit Grant of the University of Bonn and BMBF Grant No. 05H19PDKB1. AF is supported by an NSFC Research Fund for International Young Scientists grant 11950410509. PS acknowledges funding support from the Australian Research Council under Future Fellowship FT190100814. MW and AS are further supported by the Australian Research Council under Centre of Excellence CE200100008. This article made use of <span class="u-sans-serif">pippi v2.1</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 188" title="P. Scott, Pippi—painless parsing, post-processing and plotting of posterior and likelihood samples. Eur. Phys. J. Plus 127, 138 (2012). 
 arXiv:1206.2245
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR188" id="ref-link-section-d52098281e24790">188</a>].</p></div></div></section><section aria-labelledby="author-information" data-title="Author information"><div class="c-article-section" id="author-information-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="author-information">Author information</h2><div class="c-article-section__content" id="author-information-content"><h3 class="c-article__sub-heading" id="affiliations">Authors and Affiliations</h3><ol class="c-article-author-affiliation__list"><li id="Aff1"><p class="c-article-author-affiliation__address">School of Physics and Astronomy, Monash University, Melbourne, VIC, 3800, Australia</p><p class="c-article-author-affiliation__authors-list">Peter Athron, Csaba Balázs & Tomás E. Gonzalo</p></li><li id="Aff2"><p class="c-article-author-affiliation__address">Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, 210023, Jiangsu, China</p><p class="c-article-author-affiliation__authors-list">Peter Athron & Andrew Fowlie</p></li><li id="Aff3"><p class="c-article-author-affiliation__address">Arthur B. McDonald Canadian Astroparticle Physics Research Institute, Kingston, ON, K7L 3N6, Canada</p><p class="c-article-author-affiliation__authors-list">Neal Avis Kozar & Aaron C. Vincent</p></li><li id="Aff4"><p class="c-article-author-affiliation__address">Department of Physics, Engineering Physics and Astronomy, Queen’s University, Kingston, ON, K7L 3N6, Canada</p><p class="c-article-author-affiliation__authors-list">Neal Avis Kozar & Aaron C. Vincent</p></li><li id="Aff5"><p class="c-article-author-affiliation__address">Center for Cosmology, Particle Physics and Phenomenology, Université catholique de Louvain, 1348, Louvain-la-Neuve, Belgium</p><p class="c-article-author-affiliation__authors-list">Ankit Beniwal</p></li><li id="Aff6"><p class="c-article-author-affiliation__address">Department of Physics, Blackett Laboratory, Imperial College London, Prince Consort Road, London, SW7 2AZ, UK</p><p class="c-article-author-affiliation__authors-list">Sanjay Bloor, Janina J. Renk & Pat Scott</p></li><li id="Aff7"><p class="c-article-author-affiliation__address">School of Mathematics and Physics, The University of Queensland, St. Lucia, Brisbane, QLD, 4072, Australia</p><p class="c-article-author-affiliation__authors-list">Sanjay Bloor, Christopher Chang & Pat Scott</p></li><li id="Aff8"><p class="c-article-author-affiliation__address">Department of Physics, University of Oslo, 0316, Oslo, Norway</p><p class="c-article-author-affiliation__authors-list">Torsten Bringmann, Anders Kvellestad & Are Raklev</p></li><li id="Aff9"><p class="c-article-author-affiliation__address">Department of Physics, University of Cincinnati, Cincinnati, OH, 45221, USA</p><p class="c-article-author-affiliation__authors-list">Joachim Brod & Jure Zupan</p></li><li id="Aff10"><p class="c-article-author-affiliation__address">Department of Physics, Weber State University, 1415 Edvalson St., Dept. 2508, Ogden, UT, 84408, USA</p><p class="c-article-author-affiliation__authors-list">Jonathan M. Cornell</p></li><li id="Aff11"><p class="c-article-author-affiliation__address">Bureau of Meteorology, Melbourne, VIC, 3001, Australia</p><p class="c-article-author-affiliation__authors-list">Ben Farmer</p></li><li id="Aff12"><p class="c-article-author-affiliation__address">Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056, Aachen, Germany</p><p class="c-article-author-affiliation__authors-list">Tomás E. Gonzalo, Felix Kahlhoefer & Patrick Stöcker</p></li><li id="Aff13"><p class="c-article-author-affiliation__address">Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK</p><p class="c-article-author-affiliation__authors-list">Will Handley</p></li><li id="Aff14"><p class="c-article-author-affiliation__address">Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, UK</p><p class="c-article-author-affiliation__authors-list">Will Handley</p></li><li id="Aff15"><p class="c-article-author-affiliation__address">Univ Lyon, Univ Lyon 1, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon, UMR 5822, 69622, Villeurbanne, France</p><p class="c-article-author-affiliation__authors-list">Farvah Mahmoudi</p></li><li id="Aff16"><p class="c-article-author-affiliation__address">Theoretical Physics Department, CERN, 1211, Geneva 23, Switzerland</p><p class="c-article-author-affiliation__authors-list">Farvah Mahmoudi</p></li><li id="Aff17"><p class="c-article-author-affiliation__address">Physikalisches Institut der Rheinischen Friedrich-Wilhelms-Universität Bonn, 53115, Bonn, Germany</p><p class="c-article-author-affiliation__authors-list">Markus T. Prim</p></li><li id="Aff18"><p class="c-article-author-affiliation__address">Oskar Klein Centre for Cosmoparticle Physics, AlbaNova University Centre, 10691, Stockholm, Sweden</p><p class="c-article-author-affiliation__authors-list">Janina J. Renk</p></li><li id="Aff19"><p class="c-article-author-affiliation__address">ARC Centre of Excellence for Dark Matter Particle Physics and CSSM, Department of Physics, University of Adelaide, Adelaide, SA, 5005, Australia</p><p class="c-article-author-affiliation__authors-list">Andre Scaffidi & Martin White</p></li><li id="Aff20"><p class="c-article-author-affiliation__address">Istituto Nazionale di Fisica Nucleare, Sezione di Torino, via P. 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scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li></ol></div><h3 class="c-article__sub-heading" id="groups">Consortia</h3><div class="c-article-author-institutional-author" id="group-1"><h3 class="c-article-author-institutional-author__name u-h3">GAMBIT Collaboration</h3></div><h3 class="c-article__sub-heading" id="corresponding-author">Corresponding author</h3><p id="corresponding-author-list">Correspondence to <a id="corresp-c1" href="mailto:ankit.beniwal@uclouvain.be">Ankit Beniwal</a>.</p></div></div></section><section aria-labelledby="appendices"><div class="c-article-section" id="appendices-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="appendices">Appendices</h2><div class="c-article-section__content" id="appendices-content"><h3 class="c-article__sub-heading" id="App1">Appendix A: DirectDM interface</h3><p>We briefly describe the <span class="u-sans-serif">GAMBIT</span> interface to the new backend <span class="u-sans-serif">DirectDM</span>, its interface to <span class="u-sans-serif">DDCalc</span>, and how to interface a new model to <span class="u-sans-serif">DirectDM</span>. For more background on the technical aspects of the <span class="u-sans-serif">GAMBIT</span> framework, please refer to the original <span class="u-sans-serif">GAMBIT</span> manual [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 48" title="GAMBIT Collaboration: P. Athron, C. Balázs et al., GAMBIT: the global and modular beyond-the-standard-model inference tool. Eur. Phys. J. C 77, 784 (2017). 
 arXiv:1705.07908
 
 . Addendum in [190]" href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR48" id="ref-link-section-d52098281e24840">48</a>], and the <span class="u-sans-serif">GUM</span> paper [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 55" title="T.E. Gonzalo, GAMBIT: the global and modular BSM inference tool, in Tools for High Energy Physics and Cosmology (2021). 
 arXiv:2105.03165
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR55" id="ref-link-section-d52098281e24846">55</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 56" title="S. Bloor, T.E. Gonzalo et al., The GAMBIT universal model machine: from Lagrangians to likelihoods. 
 arXiv:2107.00030
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR56" id="ref-link-section-d52098281e24849">56</a>].</p><p><span class="u-sans-serif">DirectDM</span> matches Wilson coefficients of a relativistic EFT onto a non-relativistic EFT valid at the nuclear scale. The <span class="u-sans-serif">GAMBIT</span> implementation interfaces with the <span class="u-sans-serif">Python</span> version of this package.</p><p>Relativistic Wilson coefficients can be defined at the 3-, 4- or 5-quark scale, with the capability <img src="//media.springernature.com/lw86/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figa_HTML.gif" style="width:86px;max-width:none;" alt=""><img src="//media.springernature.com/lw75/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figb_HTML.gif" style="width:75px;max-width:none;" alt="">. For a given model, a new module function providing this capability should be written, returning the type <img src="//media.springernature.com/lw87/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figc_HTML.gif" style="width:87px;max-width:none;" alt=""> (<img src="//media.springernature.com/lw210/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figd_HTML.gif" style="width:210px;max-width:none;" alt="">). Once this capability has been fulfilled, <span class="u-sans-serif">GAMBIT</span> uses the module function <img src="//media.springernature.com/lw186/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fige_HTML.gif" style="width:186px;max-width:none;" alt=""> to call the <span class="u-sans-serif">DirectDM</span> backend via the convenience function <img src="//media.springernature.com/lw118/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figf_HTML.gif" style="width:118px;max-width:none;" alt="">. This provides the capability <img src="//media.springernature.com/lw100/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figg_HTML.gif" style="width:100px;max-width:none;" alt=""> which can be connected to the <span class="u-sans-serif">DDCalc</span> backend.</p><p>This module function providing the capability <img src="//media.springernature.com/lw80/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figh_HTML.gif" style="width:80px;max-width:none;" alt=""><img src="//media.springernature.com/lw26/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figi_HTML.gif" style="width:26px;max-width:none;" alt=""> depends on the capability <img src="//media.springernature.com/lw117/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figj_HTML.gif" style="width:117px;max-width:none;" alt="">, of native <span class="u-sans-serif">GAMBIT</span> type <img src="//media.springernature.com/lw70/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figk_HTML.gif" style="width:70px;max-width:none;" alt="">. <img src="//media.springernature.com/lw117/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figl_HTML.gif" style="width:117px;max-width:none;" alt=""> supplies the particle information about the WIMP candidate, such as its spin, mass, and whether or not it is self-conjugate, extracted from the particle database and either the spectrum or model parameters.</p><p>As an example, consider a simplified model where a vector mediator governs the interaction between <i>d</i>-type quarks and a fermionic DM candidate <span class="mathjax-tex">$\chi $</span>, with the following interaction Lagrangian,</p><div id="Equ45" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} {\mathcal {L}}_{\mathrm{int}} \supset g_\chi {\overline{\chi }} \gamma _\mu \chi V^\mu + g_b \sum _{q = d,s,b} {\overline{q}} \gamma _\mu q V^\mu . \end{aligned}$$</span></div><div class="c-article-equation__number"> (45) </div></div><p>The model implementation within <span class="u-sans-serif">GAMBIT</span> will contain four free parameters: the couplings <span class="mathjax-tex">$g_\chi $</span> and <span class="mathjax-tex">$g_b$</span>, the DM mass <span class="mathjax-tex">$m_\chi $</span>, and the mediator mass <span class="mathjax-tex">$m_V$</span>. The model definition for the above simplified model looks like:</p><div class="c-article-section__figure c-article-section__figure--no-border" data-test="figure" data-container-section="figure" id="figure-m"><figure><div class="c-article-section__figure-content" id="Figm"><div class="c-article-section__figure-item"><div class="c-article-section__figure-content"><picture><img aria-describedby="Figm" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figm_HTML.png" alt="figure m" loading="lazy" width="685" height="101"></picture></div></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-m-desc"></div></div></figure></div><p>The information about the WIMP properties should be added to the particle database, if it does not exist already, in the following format</p><div class="c-article-section__figure c-article-section__figure--no-border" data-test="figure" data-container-section="figure" id="figure-n"><figure><div class="c-article-section__figure-content" id="Fign"><div class="c-article-section__figure-item"><div class="c-article-section__figure-content"><picture><img aria-describedby="Fign" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Fign_HTML.png" alt="figure n" loading="lazy" width="685" height="105"></picture></div></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-n-desc"></div></div></figure></div><p>and the <img src="//media.springernature.com/lw117/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figo_HTML.gif" style="width:117px;max-width:none;" alt=""> module function should be modified accordingly, adding the current model as allowed</p><div class="c-article-section__figure c-article-section__figure--no-border" data-test="figure" data-container-section="figure" id="figure-p"><figure><div class="c-article-section__figure-content" id="Figp"><div class="c-article-section__figure-item"><div class="c-article-section__figure-content"><picture><img aria-describedby="Figp" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figp_HTML.png" alt="figure p" loading="lazy" width="685" height="114"></picture></div></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-p-desc"></div></div></figure></div><p>and providing a source for the mass of the DM candidate, in this case from the model parameters, as</p><div class="c-article-section__figure c-article-section__figure--no-border" data-test="figure" data-container-section="figure" id="figure-q"><figure><div class="c-article-section__figure-content" id="Figq"><div class="c-article-section__figure-item"><div class="c-article-section__figure-content"><picture><img aria-describedby="Figq" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figq_HTML.png" alt="figure q" loading="lazy" width="685" height="88"></picture></div></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-q-desc"></div></div></figure></div><p>If we integrate out the mediator in Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-09712-6#Equ45">45</a>), the interaction term becomes</p><div id="Equ46" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} {\mathcal {L}}_{\mathrm{int}}^{\mathrm{eff}} \supset \frac{g_\chi g_b}{m_V^2} \, \left( {\overline{\chi }} \gamma _\mu \chi \sum _{q \,=\, d,s,b} {\overline{q}} \gamma ^\mu q \right) . \end{aligned}$$</span></div><div class="c-article-equation__number"> (46) </div></div><p>The operator in <span class="u-sans-serif">DirectDM</span> corresponding to this interaction is <img src="//media.springernature.com/lw158/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_IEq682_HTML.gif" style="width:158px;max-width:none;" alt="">. We identify the relevant coefficient to pass to <span class="u-sans-serif">DirectDM</span> as <span class="mathjax-tex">$g_\chi g_b / m_V^2$</span>. This is simply implemented in <span class="u-sans-serif">DarkBit</span> by the following source code:</p><div class="c-article-section__figure c-article-section__figure--no-border" data-test="figure" data-container-section="figure" id="figure-r"><figure><div class="c-article-section__figure-content" id="Figr"><div class="c-article-section__figure-item"><div class="c-article-section__figure-content"><picture><img aria-describedby="Figr" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figr_HTML.png" alt="figure r" loading="lazy" width="685" height="350"></picture></div></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-r-desc"></div></div></figure></div><p>plus a new matching entry in <img src="//media.springernature.com/lw154/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figs_HTML.gif" style="width:154px;max-width:none;" alt="">,</p><div class="c-article-section__figure c-article-section__figure--no-border" data-test="figure" data-container-section="figure" id="figure-t"><figure><div class="c-article-section__figure-content" id="Figt"><div class="c-article-section__figure-item"><div class="c-article-section__figure-content"><picture><img aria-describedby="Figt" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figt_HTML.png" alt="figure t" loading="lazy" width="685" height="180"></picture></div></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-t-desc"></div></div></figure></div><p>For a full definition of the operator basis used in <span class="u-sans-serif">DirectDM</span>, we refer the reader to Refs. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 67" title="F. Bishara, J. Brod, B. Grinstein, J. Zupan, DirectDM: a tool for dark matter direct detection. 
 arXiv:1708.02678
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR67" id="ref-link-section-d52098281e25473">67</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 68" title="J. Brod, A. Gootjes-Dreesbach, M. Tammaro, J. Zupan, Effective field theory for dark matter direct detection up to dimension seven. JHEP 10, 065 (2018). 
 arXiv:1710.10218
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR68" id="ref-link-section-d52098281e25476">68</a>].</p><p>When <span class="u-sans-serif">DirectDM</span> is used, the user must also scan over the model <img src="//media.springernature.com/lw247/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figu_HTML.gif" style="width:247px;max-width:none;" alt="">, which contains (nuisance) parameters used in the matching and running routines in <span class="u-sans-serif">DirectDM</span>. These are defined in Table 1 of Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 67" title="F. Bishara, J. Brod, B. Grinstein, J. Zupan, DirectDM: a tool for dark matter direct detection. 
 arXiv:1708.02678
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR67" id="ref-link-section-d52098281e25493">67</a>]. We provide a <span class="u-sans-serif">YAML</span> file containing the default values used in <span class="u-sans-serif">DirectDM</span> (see the <img src="//media.springernature.com/lw329/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figv_HTML.gif" alt=""> file in the <span class="u-monospace">$</span><img src="//media.springernature.com/lw220/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figw_HTML.gif" style="width:220px;max-width:none;" alt=""> directory).</p><h3 class="c-article__sub-heading" id="App2">Appendix B: UFO to CalcHEP</h3><p><span class="u-sans-serif">ufo_to_mdl</span> is a simple <span class="u-sans-serif">Python</span> tool distributed with <span class="u-sans-serif">GAMBIT</span> <span class="u-sans-serif">v2.1</span> and above, and is integrated in the <span class="u-sans-serif">GUM</span> framework. <span class="u-sans-serif">ufo_to_mdl</span> is located at <span class="u-monospace">$</span><img src="//media.springernature.com/lw237/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figx_HTML.gif" style="width:237px;max-width:none;" alt="">. It can also be run as a standalone tool, using either <span class="u-sans-serif">Python2</span> or <span class="u-sans-serif">Python3</span>. Below we briefly describe the motivation for <span class="u-sans-serif">ufo_to_mdl</span> and how to use it.</p><p>The purpose of <span class="u-sans-serif">ufo_to_mdl</span> is to generate <span class="u-sans-serif">CalcHEP</span> input (<span class="u-monospace">.mdl</span> files) from <span class="u-sans-serif">UFO</span> files. The motivation for this tool’s creation is that <span class="u-sans-serif">FeynRules</span> does not generate four-fermion <span class="u-sans-serif">CalcHEP</span> output, but it can create such output for <span class="u-sans-serif">MadGraph</span>. In fact, at the time of writing, <span class="u-sans-serif">LanHEP</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 189" title="A. Semenov, LanHEP: a package for the automatic generation of Feynman rules in field theory. Version 3.0. Comput. Phys. Commun. 180, 431–454 (2009). 
 arXiv:0805.0555
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR189" id="ref-link-section-d52098281e25588">189</a>] is the only package that supports automatic generation of four-fermion contact interactions for <span class="u-sans-serif">CalcHEP</span> files. <span class="u-sans-serif">ufo_to_mdl</span> allows the user to study four-fermion interactions using <span class="u-sans-serif">CalcHEP</span> (and correspondingly, <span class="u-sans-serif">micrOMEGAs</span>), effectively creating a pathway from <span class="u-sans-serif">FeynRules</span> to <span class="u-sans-serif">CalcHEP</span> for effective theories of this kind. In the context of <span class="u-sans-serif">GAMBIT</span> and the <span class="u-sans-serif">GUM</span> pipeline, <span class="u-sans-serif">ufo_to_mdl</span> allows the user to study EFTs of DM using the routines provided by <span class="u-sans-serif">micrOMEGAs</span> and <span class="u-sans-serif">CalcHEP</span> inside of the <span class="u-sans-serif">GAMBIT</span> framework, such as relic density calculations, direct detection rates, and indirect detection via the Process Catalogue (see the <span class="u-sans-serif">DarkBit</span> manual [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 52" title="GAMBIT Dark Matter Workgroup: T. Bringmann, J. Conrad et al., DarkBit: a GAMBIT module for computing dark matter observables and likelihoods. Eur. Phys. J. C 77, 831 (2017). 
 arXiv:1705.07920
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR52" id="ref-link-section-d52098281e25632">52</a>] for details).</p><p>Usage of <span class="u-sans-serif">ufo_to_mdl</span> is straightforward. There are two modes <span class="u-sans-serif">ufo_to_mdl</span> can be operated in: comparison mode and conversion mode. The mode integrated into the <span class="u-sans-serif">GUM</span> pipeline is the comparison mode, which compares two directories containing <span class="u-monospace">.ufo</span> and <span class="u-monospace">.mdl</span> files generated by <span class="u-sans-serif">FeynRules</span>:</p><div class="c-article-section__figure c-article-section__figure--no-border" data-test="figure" data-container-section="figure" id="figure-y"><figure><div class="c-article-section__figure-content" id="Figy"><div class="c-article-section__figure-item"><div class="c-article-section__figure-content"><picture><img aria-describedby="Figy" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figy_HTML.png" alt="figure y" loading="lazy" width="685" height="23"></picture></div></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-y-desc"></div></div></figure></div><p>This ensures that all vertices in the <span class="u-sans-serif">MadGraph</span> files are present in the <span class="u-sans-serif">CalcHEP</span> files. <span class="u-sans-serif">ufo_to_mdl</span> does not explicitly check that the vertex functions and Lorentz indices are in agreement; it solely checks the particle content of the vertices. If there are vertices missing from the <span class="u-sans-serif">CalcHEP</span> files,<sup><a href="#Fn19"><span class="u-visually-hidden">Footnote </span>19</a></sup><span class="u-sans-serif">ufo_to_mdl</span> generates these vertices and writes a set of corrected <span class="u-sans-serif">CalcHEP</span> files to a new directory <img src="//media.springernature.com/lw134/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figz_HTML.gif" style="width:134px;max-width:none;" alt="">.</p><p>In the case of four-fermion operators, <span class="u-sans-serif">ufo_to_mdl</span> adds an additional auxiliary field to the particle content, and creates two 3-field interactions by way of this new auxiliary mediator particle, following the prescription described in Chapter 8 of the <span class="u-sans-serif">CalcHEP</span> manual [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 128" title="A. Belyaev, N.D. Christensen, A. Pukhov, CalcHEP 3.4 for collider physics within and beyond the Standard Model. Comput. Phys. Commun. 184, 1729–1769 (2013). 
 arXiv:1207.6082
 
 " href="/article/10.1140/epjc/s10052-021-09712-6#ref-CR128" id="ref-link-section-d52098281e25715">128</a>]. An auxiliary field has no momentum dependence and serves only to split the vertex into a form in which <span class="u-sans-serif">CalcHEP</span> can use. The order of fields generated by <span class="u-sans-serif">ufo_to_mdl</span> will be identical to those in the <span class="u-sans-serif">MadGraph</span> files, i.e. a vertex</p><div id="Equ47" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} i \left( {\overline{\chi }} {\varGamma }_\chi \chi \right) \left( {\overline{\psi }} {\varGamma }_\psi \psi \right) \end{aligned}$$</span></div><div class="c-article-equation__number"> (47) </div></div><p>would be broken up into two vertices,</p><div id="Equ48" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} i \left( {\overline{\chi }} {\varGamma }_\chi \chi \right) \phi \quad \text {and}\quad i \left( {\overline{\psi }} {\varGamma }_\psi \psi \right) \phi , \end{aligned}$$</span></div><div class="c-article-equation__number"> (48) </div></div><p>where <span class="mathjax-tex">${\varGamma }_\chi $</span> is a generic Dirac structure contracted with the field <span class="mathjax-tex">$\chi $</span>, and <span class="mathjax-tex">$\phi $</span> is the auxiliary field, with Lorentz indices corresponding to <span class="mathjax-tex">${\varGamma }$</span> (either scalar, vector or tensor). As a result, operators in <span class="u-sans-serif">FeynRules</span> files should be written pairwise.</p><p>As noted above, <span class="u-sans-serif">ufo_to_mdl</span> can also be used as a standalone tool independent of the <span class="u-sans-serif">GUM</span> pipeline. Running <span class="u-sans-serif">ufo_to_mdl</span> in conversion mode, with only a directory containing <span class="u-sans-serif">MadGraph</span> files as input,</p><div class="c-article-section__figure c-article-section__figure--no-border" data-test="figure" data-container-section="figure" id="figure-aa"><figure><div class="c-article-section__figure-content" id="Figaa"><div class="c-article-section__figure-item"><div class="c-article-section__figure-content"><picture><img aria-describedby="Figaa" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figaa_HTML.png" alt="figure aa" loading="lazy" width="685" height="23"></picture></div></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-aa-desc"></div></div></figure></div><p> will generate <span class="u-monospace">.mdl</span> files from scratch and save them in a new directory with name <img src="//media.springernature.com/lw134/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figab_HTML.gif" style="width:134px;max-width:none;" alt="">. The version of <span class="u-sans-serif">ufo_to_mdl</span> released with <span class="u-sans-serif">GAMBIT</span> <span class="u-sans-serif">v2.1</span> does not support non-trivial colour structures and will throw an error if it is asked to generate a vertex with implicit colour structure.</p><h3 class="c-article__sub-heading" id="App3">Appendix C: CMB energy injection</h3><p>In order to provide CMB constraints from energy injection through decays and annihilation of DM, the yields <i>dN</i>/<i>dE</i> of photons, positrons and electrons produced in these processes need to be known. With <span class="u-sans-serif">GAMBIT</span> <span class="u-sans-serif">v2.1</span>, the existing capabilities for the calculation of photon yields (<img src="//media.springernature.com/lw64/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figac_HTML.gif" style="width:64px;max-width:none;" alt=""><sup><a href="#Fn20"><span class="u-visually-hidden">Footnote </span>20</a></sup>) were generalised and capabilities that calculate the yields of positrons (<img src="//media.springernature.com/lw109/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figae_HTML.gif" style="width:109px;max-width:none;" alt="">) and electrons (<img src="//media.springernature.com/lw109/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figaf_HTML.gif" style="width:109px;max-width:none;" alt="">) were introduced. To support future analyses of charged cosmic rays, we also introduced the capabilities <img src="//media.springernature.com/lw125/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figag_HTML.gif" style="width:125px;max-width:none;" alt=""> and <img src="//media.springernature.com/lw141/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figah_HTML.gif" style="width:141px;max-width:none;" alt=""> that calculate the yields of anti-protons and anti-deuterons, respectively. These capabilities are, however, not used for the CMB energy injection calculations.</p><p>Once the yields are known, they need to be passed to <span class="u-sans-serif">DarkAges</span> via the capability <img src="//media.springernature.com/lw192/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figai_HTML.gif" style="width:192px;max-width:none;" alt=""> to derive the effective efficiency function <span class="mathjax-tex">$ f_{\mathrm{eff}} (z) $</span>. For maximal flexibility, we have implemented the function <img src="//media.springernature.com/lw307/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figaj_HTML.gif" alt=""> that automatically provides the inputs for <span class="u-sans-serif">DarkAges</span> based on the model-dependent <img src="//media.springernature.com/lw130/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figak_HTML.gif" style="width:130px;max-width:none;" alt="">, and the yields for photons, electrons and positrons. Once these capabilities have been provided, no further input from the user is needed.</p><p>To enable CMB energy injection constraints, the user also needs to declare that the model in question can be mapped to one of the energy injection “flag” models (<img src="//media.springernature.com/lw175/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figal_HTML.gif" style="width:175px;max-width:none;" alt=""> or <img src="//media.springernature.com/lw157/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figam_HTML.gif" style="width:157px;max-width:none;" alt="">) and their parameters. This can be done via a friend relationship to the appropriate “flag” model.</p><p>Assuming that the model under consideration contains annihilating DM particles, the user has to define a relation to <img src="//media.springernature.com/lw175/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figan_HTML.gif" style="width:175px;max-width:none;" alt="">, and its two parameters <img src="//media.springernature.com/lw50/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figao_HTML.gif" style="width:50px;max-width:none;" alt=""> and <img src="//media.springernature.com/lw34/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figap_HTML.gif" style="width:34px;max-width:none;" alt="">. It is important to note that the model <img src="//media.springernature.com/lw175/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figaq_HTML.gif" style="width:175px;max-width:none;" alt=""> implicitly assumes that the DM particle constitutes all of DM (<span class="mathjax-tex">$ f_\chi =1 $</span>) and that it is self-conjugate. In case that the particle is not self-conjugate, the parameter <img src="//media.springernature.com/lw50/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figar_HTML.gif" style="width:50px;max-width:none;" alt=""> needs to be rescaled by <span class="mathjax-tex">$ \kappa =1/2 $</span>. Likewise, if the DM candidate does not constitute all of DM, <img src="//media.springernature.com/lw50/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figas_HTML.gif" style="width:50px;max-width:none;" alt=""> needs to be rescaled by <span class="mathjax-tex">$ f_\chi ^2 $</span>.</p><p>To define the translation function, the user has to make sure that the definition of the model <img src="//media.springernature.com/lw175/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figat_HTML.gif" style="width:175px;max-width:none;" alt=""> is known, i.e. the following header is included:</p><div class="c-article-section__figure c-article-section__figure--no-border" data-test="figure" data-container-section="figure" id="figure-au"><figure><div class="c-article-section__figure-content" id="Figau"><div class="c-article-section__figure-item"><div class="c-article-section__figure-content"><picture><img aria-describedby="Figau" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figau_HTML.png" alt="figure au" loading="lazy" width="685" height="23"></picture></div></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-au-desc"></div></div></figure></div><p>Furthermore, the translation function and its dependencies need to be defined by including the following lines to the definition of the model in question:</p><div class="c-article-section__figure c-article-section__figure--no-border" data-test="figure" data-container-section="figure" id="figure-av"><figure><div class="c-article-section__figure-content" id="Figav"><div class="c-article-section__figure-item"><div class="c-article-section__figure-content"><picture><img aria-describedby="Figav" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figav_HTML.png" alt="figure av" loading="lazy" width="685" height="114"></picture></div></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-av-desc"></div></div></figure></div><p>Note that this definition makes use of the <img src="//media.springernature.com/lw41/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figaw_HTML.gif" style="width:41px;max-width:none;" alt=""><img src="//media.springernature.com/lw79/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figax_HTML.gif" style="width:79px;max-width:none;" alt=""> capability, described in App. A, in order to get the mass of the DM candidate and the information whether the DM candidate is self-conjugate or not. In case that this capability is not defined for the model in question, this dependency has to be replaced by equivalent dependencies. For the translation function defined above, the source code looks like this:</p><div class="c-article-section__figure c-article-section__figure--no-border" data-test="figure" data-container-section="figure" id="figure-ay"><figure><div class="c-article-section__figure-content" id="Figay"><div class="c-article-section__figure-item"><div class="c-article-section__figure-content"><picture><img aria-describedby="Figay" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figay_HTML.png" alt="figure ay" loading="lazy" width="685" height="193"></picture></div></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-ay-desc"></div></div></figure></div><p>Note that this has to be placed in the correct namespace:</p><div class="c-article-section__figure c-article-section__figure--no-border" data-test="figure" data-container-section="figure" id="figure-az"><figure><div class="c-article-section__figure-content" id="Figaz"><div class="c-article-section__figure-item"><div class="c-article-section__figure-content"><picture><img aria-describedby="Figaz" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-09712-6/MediaObjects/10052_2021_9712_Figaz_HTML.png" alt="figure az" loading="lazy" width="685" height="101"></picture></div></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-az-desc"></div></div></figure></div></div></div></section><section data-title="Rights and permissions"><div class="c-article-section" id="rightslink-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="rightslink">Rights and permissions</h2><div class="c-article-section__content" id="rightslink-content"> <p><b>Open Access</b> This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. 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