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</div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2208.05322">arXiv:2208.05322</a> <span> [<a href="https://arxiv.org/pdf/2208.05322">pdf</a>, <a href="https://arxiv.org/format/2208.05322">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.107.094501">10.1103/PhysRevD.107.094501 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Neutrinoless Double Beta Decay from Lattice QCD: The Short-Distance $蟺^-\rightarrow蟺^+ e^- e^-$ Amplitude </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Detmold%2C+W">William Detmold</a>, <a href="/search/hep-lat?searchtype=author&query=Jay%2C+W+I">William I. Jay</a>, <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">David J. Murphy</a>, <a href="/search/hep-lat?searchtype=author&query=Oare%2C+P+R">Patrick R. Oare</a>, <a href="/search/hep-lat?searchtype=author&query=Shanahan%2C+P+E">Phiala E. Shanahan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2208.05322v2-abstract-short" style="display: inline;"> This work presents a determination of potential short-distance contributions to the unphysical $蟺^-\rightarrow蟺^+ e^- e^-$ decay through lattice QCD calculations. The hadronic contributions to the transition amplitude are described by the pion matrix elements of five Standard Model Effective Field Theory operators, which are computed on five ensembles of domain-wall fermions with $N_f = 2 + 1$ qua… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.05322v2-abstract-full').style.display = 'inline'; document.getElementById('2208.05322v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2208.05322v2-abstract-full" style="display: none;"> This work presents a determination of potential short-distance contributions to the unphysical $蟺^-\rightarrow蟺^+ e^- e^-$ decay through lattice QCD calculations. The hadronic contributions to the transition amplitude are described by the pion matrix elements of five Standard Model Effective Field Theory operators, which are computed on five ensembles of domain-wall fermions with $N_f = 2 + 1$ quark flavors with a range of heavier-than-physical values of the light quark masses. The matrix elements are extrapolated to the continuum, physical light-quark mass, and infinite volume limit using a functional form derived in chiral Effective Field Theory ($蠂\mathrm{EFT}$). This extrapolation also yields the relevant low-energy constants of $蠂\mathrm{EFT}$, which are necessary input for $蠂\mathrm{EFT}$ calculations of neutrinoless double beta decay of nuclei. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.05322v2-abstract-full').style.display = 'none'; document.getElementById('2208.05322v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">24 pages, 17 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MIT-CTP/5414 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2103.15131">arXiv:2103.15131</a> <span> [<a href="https://arxiv.org/pdf/2103.15131">pdf</a>, <a href="https://arxiv.org/format/2103.15131">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.104.114506">10.1103/PhysRevD.104.114506 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Lattice determination of $I= 0$ and 2 $蟺蟺$ scattering phase shifts with a physical pion mass </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">T. Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Boyle%2C+P+A">P. A. Boyle</a>, <a href="/search/hep-lat?searchtype=author&query=Bruno%2C+M">M. Bruno</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">N. H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Hoying%2C+D">D. Hoying</a>, <a href="/search/hep-lat?searchtype=author&query=Kelly%2C+C">C. Kelly</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">C. Lehner</a>, <a href="/search/hep-lat?searchtype=author&query=Mawhinney%2C+R+D">R. D. Mawhinney</a>, <a href="/search/hep-lat?searchtype=author&query=Meyer%2C+A+S">A. S. Meyer</a>, <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">D. J. Murphy</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">C. T. Sachrajda</a>, <a href="/search/hep-lat?searchtype=author&query=Soni%2C+A">A. Soni</a>, <a href="/search/hep-lat?searchtype=author&query=Wang%2C+T">T. Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2103.15131v3-abstract-short" style="display: inline;"> Phase shifts for $s$-wave $蟺蟺$ scattering in both the $I=0$ and $I=2$ channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of $32^3\times 64$. These results support our recent study of direct CP violation in $K\to蟺蟺$ decay \cite{Abbott:2020hxn}, improving our earlier 2015 calcula… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.15131v3-abstract-full').style.display = 'inline'; document.getElementById('2103.15131v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2103.15131v3-abstract-full" style="display: none;"> Phase shifts for $s$-wave $蟺蟺$ scattering in both the $I=0$ and $I=2$ channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of $32^3\times 64$. These results support our recent study of direct CP violation in $K\to蟺蟺$ decay \cite{Abbott:2020hxn}, improving our earlier 2015 calculation \cite{Bai:2015nea}. The phase shifts are determined for both stationary and moving $蟺蟺$ systems, at three ($I=0$) and four ($I=2$) different total momenta. We implement several $蟺蟺$ interpolating operators including a scalar bilinear "$蟽$" operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fitting and a bootstrap determination of p-values have been used to refine the results and a comparison with the generalized eigenvalue problem (GEVP) method is given. A detailed systematic error analysis is performed which allows phase shift results to be presented at a fixed energy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.15131v3-abstract-full').style.display = 'none'; document.getElementById('2103.15131v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 March, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v3: Add a subsection "Higher partial wave correction", and correct the unit of scattering length. 88 pages and 14 figures v2: 1). Add reference 29 as an example of pipi scattering calculation above 4mpi threshold. 2). Modify the wording on page 3 for the footage. 3). Correct the 蟽operator on page 17</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CERN-TH-2021-039 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2009.12357">arXiv:2009.12357</a> <span> [<a href="https://arxiv.org/pdf/2009.12357">pdf</a>, <a href="https://arxiv.org/format/2009.12357">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.103.054508">10.1103/PhysRevD.103.054508 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Low-energy Scattering and Effective Interactions of Two Baryons at $m_蟺\sim 450$ MeV from Lattice Quantum Chromodynamics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Illa%2C+M">Marc Illa</a>, <a href="/search/hep-lat?searchtype=author&query=Beane%2C+S+R">Silas R. Beane</a>, <a href="/search/hep-lat?searchtype=author&query=Chang%2C+E">Emmanuel Chang</a>, <a href="/search/hep-lat?searchtype=author&query=Davoudi%2C+Z">Zohreh Davoudi</a>, <a href="/search/hep-lat?searchtype=author&query=Detmold%2C+W">William Detmold</a>, <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">David J. Murphy</a>, <a href="/search/hep-lat?searchtype=author&query=Orginos%2C+K">Kostas Orginos</a>, <a href="/search/hep-lat?searchtype=author&query=Parre%C3%B1o%2C+A">Assumpta Parre帽o</a>, <a href="/search/hep-lat?searchtype=author&query=Savage%2C+M+J">Martin J. Savage</a>, <a href="/search/hep-lat?searchtype=author&query=Shanahan%2C+P+E">Phiala E. Shanahan</a>, <a href="/search/hep-lat?searchtype=author&query=Wagman%2C+M+L">Michael L. Wagman</a>, <a href="/search/hep-lat?searchtype=author&query=Winter%2C+F">Frank Winter</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2009.12357v3-abstract-short" style="display: inline;"> The interactions between two octet baryons are studied at low energies using lattice QCD (LQCD) with larger-than-physical quark masses corresponding to a pion mass of $m_蟺\sim 450$ MeV and a kaon mass of $m_{K}\sim 596$ MeV. The two-baryon systems that are analyzed range from strangeness $S=0$ to $S=-4$ and include the spin-singlet and triplet $NN$, $危N$ ($I=3/2$), and $螢螢$ states, the spin-single… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2009.12357v3-abstract-full').style.display = 'inline'; document.getElementById('2009.12357v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2009.12357v3-abstract-full" style="display: none;"> The interactions between two octet baryons are studied at low energies using lattice QCD (LQCD) with larger-than-physical quark masses corresponding to a pion mass of $m_蟺\sim 450$ MeV and a kaon mass of $m_{K}\sim 596$ MeV. The two-baryon systems that are analyzed range from strangeness $S=0$ to $S=-4$ and include the spin-singlet and triplet $NN$, $危N$ ($I=3/2$), and $螢螢$ states, the spin-singlet $危危$ ($I=2$) and $螢危$ ($I=3/2$) states, and the spin-triplet $螢N$ ($I=0$) state. The $s$-wave scattering phase shifts, low-energy scattering parameters, and binding energies when applicable, are extracted using L眉scher's formalism. While the results are consistent with most of the systems being bound at this pion mass, the interactions in the spin-triplet $危N$ and $螢螢$ channels are found to be repulsive and do not support bound states. Using results from previous studies at a larger pion mass, an extrapolation of the binding energies to the physical point is performed and is compared with experimental values and phenomenological predictions. The low-energy coefficients in pionless EFT relevant for two-baryon interactions, including those responsible for $SU(3)$ flavor-symmetry breaking, are constrained. The $SU(3)$ symmetry is observed to hold approximately at the chosen values of the quark masses, as well as the $SU(6)$ spin-flavor symmetry, predicted at large $N_c$. A remnant of an accidental $SU(16)$ symmetry found previously at a larger pion mass is further observed. The $SU(6)$-symmetric EFT constrained by these LQCD calculations is used to make predictions for two-baryon systems for which the low-energy scattering parameters could not be determined with LQCD directly in this study, and to constrain the coefficients of all leading $SU(3)$ flavor-symmetric interactions, demonstrating the predictive power of two-baryon EFTs matched to LQCD. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2009.12357v3-abstract-full').style.display = 'none'; document.getElementById('2009.12357v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 March, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 25 September, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">69 pages, 31 figures and 25 tables; published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> ICCUB-20-020, UMD-PP-020-7, MIT-CTP/5238, INT-PUB-20-038, FERMILAB-PUB-20-498-T </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 103, 054508 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2009.05522">arXiv:2009.05522</a> <span> [<a href="https://arxiv.org/pdf/2009.05522">pdf</a>, <a href="https://arxiv.org/format/2009.05522">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.126.202001">10.1103/PhysRevLett.126.202001 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Lattice QCD constraints on the parton distribution functions of ${}^3\text{He}$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Detmold%2C+W">William Detmold</a>, <a href="/search/hep-lat?searchtype=author&query=Illa%2C+M">Marc Illa</a>, <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">David J. Murphy</a>, <a href="/search/hep-lat?searchtype=author&query=Oare%2C+P">Patrick Oare</a>, <a href="/search/hep-lat?searchtype=author&query=Orginos%2C+K">Kostas Orginos</a>, <a href="/search/hep-lat?searchtype=author&query=Shanahan%2C+P+E">Phiala E. Shanahan</a>, <a href="/search/hep-lat?searchtype=author&query=Wagman%2C+M+L">Michael L. Wagman</a>, <a href="/search/hep-lat?searchtype=author&query=Winter%2C+F">Frank Winter</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2009.05522v1-abstract-short" style="display: inline;"> The fraction of the longitudinal momentum of ${}^3\text{He}$ that is carried by the isovector combination of $u$ and $d$ quarks is determined using lattice QCD for the first time. The ratio of this combination to that in the constituent nucleons is found to be consistent with unity at the few-percent level from calculations with quark masses corresponding to $m_蟺\sim 800$ MeV, extrapolated to the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2009.05522v1-abstract-full').style.display = 'inline'; document.getElementById('2009.05522v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2009.05522v1-abstract-full" style="display: none;"> The fraction of the longitudinal momentum of ${}^3\text{He}$ that is carried by the isovector combination of $u$ and $d$ quarks is determined using lattice QCD for the first time. The ratio of this combination to that in the constituent nucleons is found to be consistent with unity at the few-percent level from calculations with quark masses corresponding to $m_蟺\sim 800$ MeV, extrapolated to the physical quark masses. This constraint is consistent with, and significantly more precise than, determinations from global nuclear parton distribution function fits. Including the lattice QCD determination of the momentum fraction in the nNNPDF global fitting framework results in the uncertainty on the isovector momentum fraction ratio being reduced by a factor of 2.5, and thereby enables a more precise extraction of the $u$ and $d$ parton distributions in ${}^3\text{He}$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2009.05522v1-abstract-full').style.display = 'none'; document.getElementById('2009.05522v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 September, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MIT-CTP/5234, ICCUB-20-019, FERMILAB-PUB-20-466-T </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 126, 202001 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2004.09440">arXiv:2004.09440</a> <span> [<a href="https://arxiv.org/pdf/2004.09440">pdf</a>, <a href="https://arxiv.org/format/2004.09440">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.102.054509">10.1103/PhysRevD.102.054509 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Direct CP violation and the $螖I=1/2$ rule in $K\to蟺蟺$ decay from the Standard Model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Abbott%2C+R">Ryan Abbott</a>, <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">Thomas Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Boyle%2C+P+A">Peter A. Boyle</a>, <a href="/search/hep-lat?searchtype=author&query=Bruno%2C+M">Mattia Bruno</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Hoying%2C+D">Daniel Hoying</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">Chulwoo Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Kelly%2C+C">Christopher Kelly</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">Christoph Lehner</a>, <a href="/search/hep-lat?searchtype=author&query=Mawhinney%2C+R+D">Robert D. Mawhinney</a>, <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">David J. Murphy</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">Christopher T. Sachrajda</a>, <a href="/search/hep-lat?searchtype=author&query=Soni%2C+A">Amarjit Soni</a>, <a href="/search/hep-lat?searchtype=author&query=Tomii%2C+M">Masaaki Tomii</a>, <a href="/search/hep-lat?searchtype=author&query=Wang%2C+T">Tianle Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2004.09440v2-abstract-short" style="display: inline;"> We present a lattice QCD calculation of the $螖I=1/2$, $K\to蟺蟺$ decay amplitude $A_0$ and $\varepsilon'$, the measure of direct CP-violation in $K\to蟺蟺$ decay, improving our 2015 calculation of these quantities. Both calculations were performed with physical kinematics on a $32^3\times 64$ lattice with an inverse lattice spacing of $a^{-1}=1.3784(68)$ GeV. However, the current calculation includes… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.09440v2-abstract-full').style.display = 'inline'; document.getElementById('2004.09440v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2004.09440v2-abstract-full" style="display: none;"> We present a lattice QCD calculation of the $螖I=1/2$, $K\to蟺蟺$ decay amplitude $A_0$ and $\varepsilon'$, the measure of direct CP-violation in $K\to蟺蟺$ decay, improving our 2015 calculation of these quantities. Both calculations were performed with physical kinematics on a $32^3\times 64$ lattice with an inverse lattice spacing of $a^{-1}=1.3784(68)$ GeV. However, the current calculation includes nearly four times the statistics and numerous technical improvements allowing us to more reliably isolate the $蟺蟺$ ground-state and more accurately relate the lattice operators to those defined in the Standard Model. We find ${\rm Re}(A_0)=2.99(0.32)(0.59)\times 10^{-7}$ GeV and ${\rm Im}(A_0)=-6.98(0.62)(1.44)\times 10^{-11}$ GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result ${\rm Re}(A_0)=3.3201(18)\times 10^{-7}$ GeV. These results for $A_0$ can be combined with our earlier lattice calculation of $A_2$ to obtain ${\rm Re}(\varepsilon'/\varepsilon)=21.7(2.6)(6.2)(5.0) \times 10^{-4}$, where the third error represents omitted isospin breaking effects, and Re$(A_0)$/Re$(A_2) = 19.9(2.3)(4.4)$. The first agrees well with the experimental result of ${\rm Re}(\varepsilon'/\varepsilon)=16.6(2.3)\times 10^{-4}$. A comparison of the second with the observed ratio Re$(A_0)/$Re$(A_2) = 22.45(6)$, demonstrates the Standard Model origin of this "$螖I = 1/2$ rule" enhancement. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.09440v2-abstract-full').style.display = 'none'; document.getElementById('2004.09440v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 April, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Updated to published version. 95 pages, 12 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CERN-TH-2020-058, MIT-CTP/5197 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 102, 054509 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2004.07404">arXiv:2004.07404</a> <span> [<a href="https://arxiv.org/pdf/2004.07404">pdf</a>, <a href="https://arxiv.org/format/2004.07404">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> </div> <p class="title is-5 mathjax"> Neutrinoless Double Beta Decay from Lattice QCD: The Long-Distance $蟺^{-} \rightarrow 蟺^{+} e^{-} e^{-}$ Amplitude </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Detmold%2C+W">W. Detmold</a>, <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">D. J. Murphy</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2004.07404v1-abstract-short" style="display: inline;"> Neutrinoless double beta decay ($ 0 谓尾尾$) is a hypothetical nuclear decay mode with important implications. In particular, observation of this decay would demonstrate that the neutrino is a Majorana particle and that lepton number conservation is violated in nature. Relating experimental constraints on $0 谓尾尾$ decay rates to the neutrino masses requires theoretical input in the form of non-per… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.07404v1-abstract-full').style.display = 'inline'; document.getElementById('2004.07404v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2004.07404v1-abstract-full" style="display: none;"> Neutrinoless double beta decay ($ 0 谓尾尾$) is a hypothetical nuclear decay mode with important implications. In particular, observation of this decay would demonstrate that the neutrino is a Majorana particle and that lepton number conservation is violated in nature. Relating experimental constraints on $0 谓尾尾$ decay rates to the neutrino masses requires theoretical input in the form of non-perturbative nuclear matrix elements which remain difficult to calculate reliably. This work marks a first step toward providing a general lattice QCD framework for computing long-distance $0 谓尾尾$ matrix elements in the case where the decay is mediated by a light Majorana neutrino. The relevant formalism is developed and then tested by computing the simplest such matrix element describing an unphysical $ 蟺^{-} \rightarrow 蟺^{+} e^{-} e^{-} $ transition on a series of domain wall fermion ensembles. The resulting lattice data is then fit to next-to-leading-order chiral perturbation theory, allowing a fully-controlled extraction of the low energy constant governing the transition rate, $g_谓^{蟺蟺}(渭= 770 \,\, \mathrm{MeV}) = -10.78(12)_{\rm stat}(51)_{\rm sys}$. Finally, future prospects for calculations of more complicated processes, such as the phenomenologically important $n^{0} n^{0} \rightarrow p^{+} p^{+} e^{-} e^{-}$ decay, are discussed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.07404v1-abstract-full').style.display = 'none'; document.getElementById('2004.07404v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 April, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">26 pages, 10 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MIT-CTP/5196 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2003.12130">arXiv:2003.12130</a> <span> [<a href="https://arxiv.org/pdf/2003.12130">pdf</a>, <a href="https://arxiv.org/format/2003.12130">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.103.054504">10.1103/PhysRevD.103.054504 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Charged multi-hadron systems in lattice QCD+QED </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Beane%2C+S+R">S. R. Beane</a>, <a href="/search/hep-lat?searchtype=author&query=Detmold%2C+W">W. Detmold</a>, <a href="/search/hep-lat?searchtype=author&query=Horsley%2C+R">R. Horsley</a>, <a href="/search/hep-lat?searchtype=author&query=Illa%2C+M">M. Illa</a>, <a href="/search/hep-lat?searchtype=author&query=Jafry%2C+M">M. Jafry</a>, <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">D. J. Murphy</a>, <a href="/search/hep-lat?searchtype=author&query=Nakamura%2C+Y">Y. Nakamura</a>, <a href="/search/hep-lat?searchtype=author&query=Perlt%2C+H">H. Perlt</a>, <a href="/search/hep-lat?searchtype=author&query=Rakow%2C+P+E+L">P. E. L. Rakow</a>, <a href="/search/hep-lat?searchtype=author&query=Schierholz%2C+G">G. Schierholz</a>, <a href="/search/hep-lat?searchtype=author&query=Shanahan%2C+P+E">P. E. Shanahan</a>, <a href="/search/hep-lat?searchtype=author&query=St%C3%BCben%2C+H">H. St眉ben</a>, <a href="/search/hep-lat?searchtype=author&query=Wagman%2C+M+L">M. L. Wagman</a>, <a href="/search/hep-lat?searchtype=author&query=Winter%2C+F">F. Winter</a>, <a href="/search/hep-lat?searchtype=author&query=Young%2C+R+D">R. D. Young</a>, <a href="/search/hep-lat?searchtype=author&query=Zanotti%2C+J+M">J. M. Zanotti</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2003.12130v3-abstract-short" style="display: inline;"> Systems with the quantum numbers of up to twelve charged and neutral pseudoscalar mesons, as well as one-, two-, and three-nucleon systems, are studied using dynamical lattice quantum chromodynamics and quantum electrodynamics (QCD+QED) calculations and effective field theory. QED effects on hadronic interactions are determined by comparing systems of charged and neutral hadrons after tuning the q… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.12130v3-abstract-full').style.display = 'inline'; document.getElementById('2003.12130v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2003.12130v3-abstract-full" style="display: none;"> Systems with the quantum numbers of up to twelve charged and neutral pseudoscalar mesons, as well as one-, two-, and three-nucleon systems, are studied using dynamical lattice quantum chromodynamics and quantum electrodynamics (QCD+QED) calculations and effective field theory. QED effects on hadronic interactions are determined by comparing systems of charged and neutral hadrons after tuning the quark masses to remove strong isospin breaking effects. A non-relativistic effective field theory, which perturbatively includes finite-volume Coulomb effects, is analyzed for systems of multiple charged hadrons and found to accurately reproduce the lattice QCD+QED results. QED effects on charged multi-hadron systems beyond Coulomb photon exchange are determined by comparing the two- and three-body interaction parameters extracted from the lattice QCD+QED results for charged and neutral multi-hadron systems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.12130v3-abstract-full').style.display = 'none'; document.getElementById('2003.12130v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 March, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 March, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">67 pages, 29 figures. Published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 20-28, FERMILAB-PUB-20-123-T, ICCUB-20-007, MIT-CTP/5183, NT@UW-20-03 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 103, 054504 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1908.07050">arXiv:1908.07050</a> <span> [<a href="https://arxiv.org/pdf/1908.07050">pdf</a>, <a href="https://arxiv.org/format/1908.07050">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.104.034502">10.1103/PhysRevD.104.034502 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Sparsening Algorithm for Multi-Hadron Lattice QCD Correlation Functions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Detmold%2C+W">W. Detmold</a>, <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">D. J. Murphy</a>, <a href="/search/hep-lat?searchtype=author&query=Pochinsky%2C+A+V">A. V. Pochinsky</a>, <a href="/search/hep-lat?searchtype=author&query=Savage%2C+M+J">M. J. Savage</a>, <a href="/search/hep-lat?searchtype=author&query=Shanahan%2C+P+E">P. E. Shanahan</a>, <a href="/search/hep-lat?searchtype=author&query=Wagman%2C+M+L">M. L. Wagman</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1908.07050v1-abstract-short" style="display: inline;"> Modern advances in algorithms for lattice QCD calculations have steadily driven down the resources required to generate gauge field ensembles and calculate quark propagators, such that, in cases relevant to nuclear physics, performing quark contractions to assemble correlation functions from propagators has become the dominant cost. This work explores a propagator sparsening algorithm for forming… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.07050v1-abstract-full').style.display = 'inline'; document.getElementById('1908.07050v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1908.07050v1-abstract-full" style="display: none;"> Modern advances in algorithms for lattice QCD calculations have steadily driven down the resources required to generate gauge field ensembles and calculate quark propagators, such that, in cases relevant to nuclear physics, performing quark contractions to assemble correlation functions from propagators has become the dominant cost. This work explores a propagator sparsening algorithm for forming correlation functions describing multi-hadron systems, such as light nuclei, with reduced computational cost. The algorithm constructs correlation functions from sparsened propagators defined on a coarsened lattice geometry, where the sparsened propagators are obtained from propagators computed on the full lattice. This algorithm is used to study the low-energy QCD ground-state spectrum using a single Wilson-clover lattice ensemble with $m_蟺 \approx 800$ MeV. It is found that the extracted ground state masses and binding energies, as well as their statistical uncertainties, are consistent when determined from correlation functions constructed from sparsened and full propagators. In addition, while evidence of modified couplings to excited states is observed in sparsened correlation functions, it is demonstrated that these effects can be removed, if desired, with an inexpensive modification to the sparsened estimator. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.07050v1-abstract-full').style.display = 'none'; document.getElementById('1908.07050v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 August, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">18 pages, 5 figures, 4 tables</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MIT-CTP/5127, INT-PUB-19-026 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 104, 034502 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1811.05554">arXiv:1811.05554</a> <span> [<a href="https://arxiv.org/pdf/1811.05554">pdf</a>, <a href="https://arxiv.org/format/1811.05554">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> </div> <p class="title is-5 mathjax"> Nuclear Matrix Elements for Neutrinoless Double Beta Decay from Lattice QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Detmold%2C+W">W. Detmold</a>, <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">D. J. Murphy</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1811.05554v1-abstract-short" style="display: inline;"> While neutrino oscillation experiments have demonstrated that neutrinos have small, nonzero masses, much remains unknown about their properties and decay modes. One potential decay mode --- neutrinoless double beta decay ($0 谓尾尾$) --- is a particularly interesting target of experimental searches, since its observation would imply that the neutrino is a Majorana particle, demonstrate that lepton nu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1811.05554v1-abstract-full').style.display = 'inline'; document.getElementById('1811.05554v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1811.05554v1-abstract-full" style="display: none;"> While neutrino oscillation experiments have demonstrated that neutrinos have small, nonzero masses, much remains unknown about their properties and decay modes. One potential decay mode --- neutrinoless double beta decay ($0 谓尾尾$) --- is a particularly interesting target of experimental searches, since its observation would imply that the neutrino is a Majorana particle, demonstrate that lepton number conservation is violated in nature, and give further constraints on the neutrino masses and mixing angles. Relating experimental constraints on $0 谓尾尾$ decay rates to the neutrino masses, however, requires theoretical input in the form of non-perturbative nuclear matrix elements which remain difficult to calculate reliably. In this talk we will discuss progress towards first-principles calculations of relevant nuclear matrix elements using lattice QCD and effective field theory techniques, assuming neutrinoless double beta decay mediated by a light Majorana neutrino. We will show preliminary results for the $蟺^{-} \rightarrow 蟺^{+} e^{-} e^{-}$ transition amplitude computed on a $16^{3} \times 32$ domain wall fermion lattice with a pion mass of 420 MeV, and discuss improved methods applicable to general lattice calculations of $0 谓尾尾$ decay amplitudes. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1811.05554v1-abstract-full').style.display = 'none'; document.getElementById('1811.05554v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 November, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 3 figures, talk presented at the 36th Annual International Symposium on Lattice Field Theory (Lattice 2018)</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1706.05843">arXiv:1706.05843</a> <span> [<a href="https://arxiv.org/pdf/1706.05843">pdf</a>, <a href="https://arxiv.org/format/1706.05843">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.97.054503">10.1103/PhysRevD.97.054503 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Domain Wall Fermion QCD with the Exact One Flavor Algorithm </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">C. Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Kelly%2C+C">C. Kelly</a>, <a href="/search/hep-lat?searchtype=author&query=Mawhinney%2C+R+D">R. D. Mawhinney</a>, <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">D. J. Murphy</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1706.05843v2-abstract-short" style="display: inline;"> Lattice QCD calculations including the effects of one or more non-degenerate sea quark flavors are conventionally performed using the Rational Hybrid Monte Carlo (RHMC) algorithm, which computes the square root of the determinant of $\mathscr{D}^{\dagger} \mathscr{D}$, where $\mathscr{D}$ is the Dirac operator. The special case of two degenerate quark flavors with the same mass is described direct… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1706.05843v2-abstract-full').style.display = 'inline'; document.getElementById('1706.05843v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1706.05843v2-abstract-full" style="display: none;"> Lattice QCD calculations including the effects of one or more non-degenerate sea quark flavors are conventionally performed using the Rational Hybrid Monte Carlo (RHMC) algorithm, which computes the square root of the determinant of $\mathscr{D}^{\dagger} \mathscr{D}$, where $\mathscr{D}$ is the Dirac operator. The special case of two degenerate quark flavors with the same mass is described directly by the determinant of $\mathscr{D}^{\dagger} \mathscr{D}$ --- in particular, no square root is necessary --- enabling a variety of algorithmic developments, which have driven down the cost of simulating the light (up and down) quarks in the isospin-symmetric limit of equal masses. As a result, the relative cost of single quark flavors --- such as the strange or charm --- computed with RHMC has become more expensive. This problem is even more severe in the context of our measurements of the $螖I = 1/2$ $K \rightarrow 蟺蟺$ matrix elements on lattice ensembles with $G$-parity boundary conditions, since $G$-parity is associated with a doubling of the number of quark flavors described by $\mathscr{D}$, and thus RHMC is needed for the isospin-symmetric light quarks as well. In this paper we report on our implementation of the exact one flavor algorithm (EOFA) introduced by the TWQCD collaboration for simulations including single flavors of domain wall quarks. We have developed a new preconditioner for the EOFA Dirac equation, which both reduces the cost of solving the Dirac equation and allows us to re-use the bulk of our existing high-performance code. Coupling these improvements with careful tuning of our integrator, the time per accepted trajectory in the production of our 2+1 flavor $G$-parity ensembles with physical pion and kaon masses has been decreased by a factor of 4.2. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1706.05843v2-abstract-full').style.display = 'none'; document.getElementById('1706.05843v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 August, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 19 June, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">61 pages, 18 figures, 14 tables. v2: minor updates for journal submission</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 97, 054503 (2018) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1611.00298">arXiv:1611.00298</a> <span> [<a href="https://arxiv.org/pdf/1611.00298">pdf</a>, <a href="https://arxiv.org/format/1611.00298">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Domain Wall Fermion Simulations with the Exact One-Flavor Algorithm </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">D. J. Murphy</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1611.00298v2-abstract-short" style="display: inline;"> As algorithmic developments have driven down the cost of simulating degenerate light quark flavors the relative cost of simulating single quark flavors with the Rational Hybrid Monte Carlo (RHMC) algorithm has become more expensive. TWQCD has proposed an exact one-flavor algorithm (EOFA) that allows for HMC simulations of a single quark flavor without taking a square root of the fermion determinan… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.00298v2-abstract-full').style.display = 'inline'; document.getElementById('1611.00298v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1611.00298v2-abstract-full" style="display: none;"> As algorithmic developments have driven down the cost of simulating degenerate light quark flavors the relative cost of simulating single quark flavors with the Rational Hybrid Monte Carlo (RHMC) algorithm has become more expensive. TWQCD has proposed an exact one-flavor algorithm (EOFA) that allows for HMC simulations of a single quark flavor without taking a square root of the fermion determinant. We have independently implemented EOFA in the Columbia Physics System (CPS) and BAGEL Fermion Sparse-Matrix Library (BFM) for Shamir and M枚bius domain wall fermions, and begun to optimize and test our implementation against RHMC. In this talk we discuss the derivation of the EOFA action, our tests of its equivalence to RHMC, and the current state of our implementation and optimization. We find, after introducing a novel preconditioning technique for the EOFA Dirac operator, that EOFA is a factor of 2.4 times faster than RHMC per molecular dynamics trajectory for the strange quark determinant on an $N_{f} = 2+1$ M枚bius DWF ensemble with physical quark masses and a $24^{3} \times 64 \times 24$ volume. We expect that further improvement is possible by retuning the integrator parameters for EOFA and by continuing to optimize our code. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.00298v2-abstract-full').style.display = 'none'; document.getElementById('1611.00298v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 November, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 1 November, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 2 figures. Talk presented at the 34th International Symposium on Lattice Field Theory (LATTICE 2016), 24-30 July 2016, University of Southampton, UK. Updated to published version</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1511.04419">arXiv:1511.04419</a> <span> [<a href="https://arxiv.org/pdf/1511.04419">pdf</a>, <a href="https://arxiv.org/format/1511.04419">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> NLO and NNLO Low Energy Constants for $SU(2)$ Chiral Perturbation Theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Mawhinney%2C+R+D">R. D. Mawhinney</a>, <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">D. J. Murphy</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1511.04419v1-abstract-short" style="display: inline;"> We have performed global fits of $f_蟺$ and $m_蟺$, from a variety of RBC-UKQCD domain wall fermion ensembles, to $SU(2)$ partially quenched chiral perturbation theory at NNLO. We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched low energy constants, which we compare to other lattice and phenomenological determinations. We discuss the convergence of the expa… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1511.04419v1-abstract-full').style.display = 'inline'; document.getElementById('1511.04419v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1511.04419v1-abstract-full" style="display: none;"> We have performed global fits of $f_蟺$ and $m_蟺$, from a variety of RBC-UKQCD domain wall fermion ensembles, to $SU(2)$ partially quenched chiral perturbation theory at NNLO. We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched low energy constants, which we compare to other lattice and phenomenological determinations. We discuss the convergence of the expansion and use our large set of low energy constants to make predictions for the pion mass splitting due to QCD isospin breaking effects and the s-wave $蟺蟺$ scattering lengths. We conclude that, for the range of pseudoscalar masses explored in this work, $115~\mathrm{MeV} \lesssim m_{\rm PS} \lesssim 430~\mathrm{MeV}$, the NNLO $SU(2)$ expansion is quite robust and can fit lattice data with percent-scale accuracy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1511.04419v1-abstract-full').style.display = 'none'; document.getElementById('1511.04419v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 November, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 4 figures. Proceedings of the 33rd International Symposium on Lattice Field Theory, 14-18 July 2015, Kobe, Japan</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1511.01950">arXiv:1511.01950</a> <span> [<a href="https://arxiv.org/pdf/1511.01950">pdf</a>, <a href="https://arxiv.org/format/1511.01950">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.93.054502">10.1103/PhysRevD.93.054502 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Low Energy Constants of $SU(2)$ Partially Quenched Chiral Perturbation Theory from $N_{f}=2+1$ Domain Wall QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Boyle%2C+P+A">P. A. Boyle</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">N. H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Garron%2C+N">N. Garron</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">C. Jung</a>, <a href="/search/hep-lat?searchtype=author&query=J%C3%BCttner%2C+A">A. J眉ttner</a>, <a href="/search/hep-lat?searchtype=author&query=Kelly%2C+C">C. Kelly</a>, <a href="/search/hep-lat?searchtype=author&query=Mawhinney%2C+R+D">R. D. Mawhinney</a>, <a href="/search/hep-lat?searchtype=author&query=McGlynn%2C+G">G. McGlynn</a>, <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">D. J. Murphy</a>, <a href="/search/hep-lat?searchtype=author&query=Ohta%2C+S">S. Ohta</a>, <a href="/search/hep-lat?searchtype=author&query=Portelli%2C+A">A. Portelli</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">C. T. Sachrajda</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1511.01950v1-abstract-short" style="display: inline;"> We have performed fits of the pseudoscalar masses and decay constants, from a variety of RBC-UKQCD domain wall fermion ensembles, to $SU(2)$ partially quenched chiral perturbation theory at next-to leading order (NLO) and next-to-next-to leading order (NNLO). We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched low energy constants, which we compare to othe… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1511.01950v1-abstract-full').style.display = 'inline'; document.getElementById('1511.01950v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1511.01950v1-abstract-full" style="display: none;"> We have performed fits of the pseudoscalar masses and decay constants, from a variety of RBC-UKQCD domain wall fermion ensembles, to $SU(2)$ partially quenched chiral perturbation theory at next-to leading order (NLO) and next-to-next-to leading order (NNLO). We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched low energy constants, which we compare to other lattice and phenomenological determinations. We discuss the size of successive terms in the chiral expansion and use our large set of low energy constants to make predictions for mass splittings due to QCD isospin breaking effects and the S-wave $蟺蟺$ scattering lengths. We conclude that, for the range of pseudoscalar masses explored in this work, $115~\mathrm{MeV} \lesssim m_{\rm PS} \lesssim 430~\mathrm{MeV}$, the NNLO $SU(2)$ expansion is quite robust and can fit lattice data with percent-scale accuracy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1511.01950v1-abstract-full').style.display = 'none'; document.getElementById('1511.01950v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 November, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 93, 054502 (2016) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1411.7017">arXiv:1411.7017</a> <span> [<a href="https://arxiv.org/pdf/1411.7017">pdf</a>, <a href="https://arxiv.org/ps/1411.7017">ps</a>, <a href="https://arxiv.org/format/1411.7017">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.93.074505">10.1103/PhysRevD.93.074505 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Domain wall QCD with physical quark masses </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=RBC"> RBC</a>, <a href="/search/hep-lat?searchtype=author&query=collaborations%2C+U">UKQCD collaborations</a>, <a href="/search/hep-lat?searchtype=author&query=%3A"> :</a>, <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">T. Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Boyle%2C+P+A">P. A. Boyle</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">N. H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Frison%2C+J">J. Frison</a>, <a href="/search/hep-lat?searchtype=author&query=Garron%2C+N">N. Garron</a>, <a href="/search/hep-lat?searchtype=author&query=Hudspith%2C+R+J">R. J. Hudspith</a>, <a href="/search/hep-lat?searchtype=author&query=Izubuchi%2C+T">T. Izubuchi</a>, <a href="/search/hep-lat?searchtype=author&query=Janowski%2C+T">T. Janowski</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">C. Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Juettner%2C+A">A. Juettner</a>, <a href="/search/hep-lat?searchtype=author&query=Kelly%2C+C">C. Kelly</a>, <a href="/search/hep-lat?searchtype=author&query=Kenway%2C+R+D">R. D. Kenway</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">C. Lehner</a>, <a href="/search/hep-lat?searchtype=author&query=Marinkovic%2C+M">M. Marinkovic</a>, <a href="/search/hep-lat?searchtype=author&query=Mawhinney%2C+R+D">R. D. Mawhinney</a>, <a href="/search/hep-lat?searchtype=author&query=McGlynn%2C+G">G. McGlynn</a>, <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">D. J. Murphy</a>, <a href="/search/hep-lat?searchtype=author&query=Ohta%2C+S">S. Ohta</a>, <a href="/search/hep-lat?searchtype=author&query=Portelli%2C+A">A. Portelli</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">C. T. Sachrajda</a>, <a href="/search/hep-lat?searchtype=author&query=Soni%2C+A">A. Soni</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1411.7017v2-abstract-short" style="display: inline;"> We present results for several light hadronic quantities ($f_蟺$, $f_K$, $B_K$, $m_{ud}$, $m_s$, $t_0^{1/2}$, $w_0$) obtained from simulations of 2+1 flavor domain wall lattice QCD with large physical volumes and nearly-physical pion masses at two lattice spacings. We perform a short, O(3)%, extrapolation in pion mass to the physical values by combining our new data in a simultaneous chiral/continu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1411.7017v2-abstract-full').style.display = 'inline'; document.getElementById('1411.7017v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1411.7017v2-abstract-full" style="display: none;"> We present results for several light hadronic quantities ($f_蟺$, $f_K$, $B_K$, $m_{ud}$, $m_s$, $t_0^{1/2}$, $w_0$) obtained from simulations of 2+1 flavor domain wall lattice QCD with large physical volumes and nearly-physical pion masses at two lattice spacings. We perform a short, O(3)%, extrapolation in pion mass to the physical values by combining our new data in a simultaneous chiral/continuum `global fit' with a number of other ensembles with heavier pion masses. We use the physical values of $m_蟺$, $m_K$ and $m_惟$ to determine the two quark masses and the scale - all other quantities are outputs from our simulations. We obtain results with sub-percent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including: $f_蟺$ = 130.2(9) MeV; $f_K$ = 155.5(8) MeV; the average up/down quark mass and strange quark mass in the $\bar {\rm MS}$ scheme at 3 GeV, 2.997(49) and 81.64(1.17) MeV respectively; and the neutral kaon mixing parameter, $B_K$, in the RGI scheme, 0.750(15) and the $\bar{\rm MS}$ scheme at 3 GeV, 0.530(11). <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1411.7017v2-abstract-full').style.display = 'none'; document.getElementById('1411.7017v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 May, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 25 November, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">131 pages, 30 figures. Updated to match published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 93, 074505 (2016) </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/license/index.html">Copyright</a></li> <li><a href="https://info.arxiv.org/help/policies/privacy_policy.html">Privacy Policy</a></li> </ul> </div> <div class="column sorry-app-links"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/web_accessibility.html">Web Accessibility Assistance</a></li> <li> <p class="help"> <a class="a11y-main-link" href="https://status.arxiv.org" target="_blank">arXiv Operational Status <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512" class="icon filter-dark_grey" role="presentation"><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></a><br> Get status notifications via <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/email/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg>email</a> or <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/slack/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon filter-black" role="presentation"><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"/></svg>slack</a> </p> </li> </ul> </div> </div> </div>  </div> </footer> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/member_acknowledgement.js"></script> </body> </html>

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