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</div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Blumlein%2C+J&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Blumlein%2C+J&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Blumlein%2C+J&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> <li> <a href="/search/?searchtype=author&query=Blumlein%2C+J&start=100" class="pagination-link " aria-label="Page 3" aria-current="page">3 </a> </li> <li> <a href="/search/?searchtype=author&query=Blumlein%2C+J&start=150" class="pagination-link " aria-label="Page 4" aria-current="page">4 </a> </li> <li> <a href="/search/?searchtype=author&query=Blumlein%2C+J&start=200" class="pagination-link " aria-label="Page 5" aria-current="page">5 </a> </li> <li> <a href="/search/?searchtype=author&query=Blumlein%2C+J&start=250" class="pagination-link " aria-label="Page 6" aria-current="page">6 </a> </li> <li> <a href="/search/?searchtype=author&query=Blumlein%2C+J&start=300" class="pagination-link " aria-label="Page 7" aria-current="page">7 </a> </li> </ul> </nav> <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/2408.07046">arXiv:2408.07046</a> <span> [<a href="https://arxiv.org/pdf/2408.07046">pdf</a>, <a href="https://arxiv.org/format/2408.07046">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Symbolic Computation">cs.SC</span> </div> </div> <p class="title is-5 mathjax"> Challenges for analytic calculations of the massive three-loop form factors </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=Marquard%2C+P">P. Marquard</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</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="2408.07046v1-abstract-short" style="display: inline;"> The calculation of massive three-loop QCD form factors using in particular the large moments method has been successfully applied to quarkonic contributions in [1]. We give a brief review of the different steps of the calculation and report on improvements of our methods that enabled us to push forward the calculations of the gluonic contributions to the form factors. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2408.07046v1-abstract-full" style="display: none;"> The calculation of massive three-loop QCD form factors using in particular the large moments method has been successfully applied to quarkonic contributions in [1]. We give a brief review of the different steps of the calculation and report on improvements of our methods that enabled us to push forward the calculations of the gluonic contributions to the form factors. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.07046v1-abstract-full').style.display = 'none'; document.getElementById('2408.07046v1-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 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY-24-121, RISC Report number 24-05, PoS (LL2024) 031 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2407.02006">arXiv:2407.02006</a> <span> [<a href="https://arxiv.org/pdf/2407.02006">pdf</a>, <a href="https://arxiv.org/format/2407.02006">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> </div> </div> <p class="title is-5 mathjax"> The three-loop single-mass heavy flavor corrections to deep-inelastic scattering </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Ablinger%2C+J">J. Ablinger</a>, <a href="/search/hep-ph?searchtype=author&query=Behring%2C+A">A. Behring</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=von+Manteuffel%2C+A">A. von Manteuffel</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Schoenwald%2C+K">K. Schoenwald</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="2407.02006v1-abstract-short" style="display: inline;"> We report on the status of the calculation of the massive Wilson coefficients and operator matrix elements for deep-inelastic scatterung to three-loop order. We discuss both the unpolarized and the polarized case, for which all the single-mass and nearly all two-mass contributions have been calculated. Numerical results on the structure function $F_2(x,Q^2)$ are presented. In the polarized case, w… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.02006v1-abstract-full').style.display = 'inline'; document.getElementById('2407.02006v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2407.02006v1-abstract-full" style="display: none;"> We report on the status of the calculation of the massive Wilson coefficients and operator matrix elements for deep-inelastic scatterung to three-loop order. We discuss both the unpolarized and the polarized case, for which all the single-mass and nearly all two-mass contributions have been calculated. Numerical results on the structure function $F_2(x,Q^2)$ are presented. In the polarized case, we work in the Larin scheme and refer to parton distribution functions in this scheme. Furthermore, results on the three-loop variable flavor number scheme are presented <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.02006v1-abstract-full').style.display = 'none'; document.getElementById('2407.02006v1-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> 2 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2024. </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">12 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CERN-TH-2024-100, ZU-TH 31/24, RISC Report number 24-04, PoS (LL2024) 047, DESY-24-096, </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2405.17252">arXiv:2405.17252</a> <span> [<a href="https://arxiv.org/pdf/2405.17252">pdf</a>, <a href="https://arxiv.org/format/2405.17252">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 - Phenomenology">hep-ph</span> </div> </div> <p class="title is-5 mathjax"> Next-to-Next-to-Leading Order Evolution of Polarized Parton Densities in the Larin Scheme </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Saragnese%2C+M">M. Saragnese</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="2405.17252v1-abstract-short" style="display: inline;"> In many calculations involving polarized twist-2 parton densities to higher order in the strong coupling constant one uses the Larin scheme to describe chiral effects in dimensional regularization. Upon forming observables, the scheme dependence cancels. Still one needs a corresponding regularization scheme to compute the contributing building blocks, like massless and massive Wilson coefficients,… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.17252v1-abstract-full').style.display = 'inline'; document.getElementById('2405.17252v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2405.17252v1-abstract-full" style="display: none;"> In many calculations involving polarized twist-2 parton densities to higher order in the strong coupling constant one uses the Larin scheme to describe chiral effects in dimensional regularization. Upon forming observables, the scheme dependence cancels. Still one needs a corresponding regularization scheme to compute the contributing building blocks, like massless and massive Wilson coefficients, as well as the massive 3-loop operator matrix elements used in the variable flavor number scheme. These are matched to the evolved parton distribution functions in the Larin scheme. Starting with suitable input distributions we provide the solution of scale evolution of the different polarized parton distribution functions in Bjorken $x$ space for a wide range of virtualities $Q^2$ in the Larin scheme, at next-to-leading, and to next-to-next-to-leading order for the first time. We also illustrate the deviation between the parton distributions in the Larin and $\overline{\rm MS}$ schemes numerically. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.17252v1-abstract-full').style.display = 'none'; document.getElementById('2405.17252v1-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> 27 May, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2024. </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">13 pages Latex, 9 Figures, ancillary files</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 24--066 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2403.00513">arXiv:2403.00513</a> <span> [<a href="https://arxiv.org/pdf/2403.00513">pdf</a>, <a href="https://arxiv.org/format/2403.00513">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 - 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/10.1016/j.physletb.2024.138713">10.1016/j.physletb.2024.138713 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $螖A_{Qg}^{(3)}$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Ablinger%2C+J">J. Ablinger</a>, <a href="/search/hep-ph?searchtype=author&query=Behring%2C+A">A. Behring</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=von+Manteuffel%2C+A">A. von Manteuffel</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2403.00513v1-abstract-short" style="display: inline;"> The non-first-order-factorizable contributions (The terms 'first-order-factorizable contributions' and 'non-first-order-factorizable contributions' have been introduced and discussed in Refs. \cite{Behring:2023rlq,Ablinger:2023ahe}. They describe the factorization behaviour of the difference- or differential equations for a subset of master integrals of a given problem.) to the unpolarized and pol… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.00513v1-abstract-full').style.display = 'inline'; document.getElementById('2403.00513v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.00513v1-abstract-full" style="display: none;"> The non-first-order-factorizable contributions (The terms 'first-order-factorizable contributions' and 'non-first-order-factorizable contributions' have been introduced and discussed in Refs. \cite{Behring:2023rlq,Ablinger:2023ahe}. They describe the factorization behaviour of the difference- or differential equations for a subset of master integrals of a given problem.) to the unpolarized and polarized massive operator matrix elements to three-loop order, $A_{Qg}^{(3)}$ and $螖A_{Qg}^{(3)}$, are calculated in the single-mass case. For the $_2F_1$-related master integrals of the problem, we use a semi-analytic method based on series expansions and utilize the first-order differential equations for the master integrals which does not need a special basis of the master integrals. Due to the singularity structure of this basis a part of the integrals has to be computed to $O(\varepsilon^5)$ in the dimensional parameter. The solutions have to be matched at a series of thresholds and pseudo-thresholds in the region of the Bjorken variable $x \in ]0,\infty[$ using highly precise series expansions to obtain the imaginary part of the physical amplitude for $x \in ]0,1]$ at a high relative accuracy. We compare the present results both with previous analytic results, the results for fixed Mellin moments, and a prediction in the small-$x$ region. We also derive expansions in the region of small and large values of $x$. With this paper, all three-loop single-mass unpolarized and polarized operator matrix elements are calculated. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.00513v1-abstract-full').style.display = 'none'; document.getElementById('2403.00513v1-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> 1 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DO--TH 23/15. DESY 24--027, RISC Report series 24--02, ZU-TH 13/24, CERN-TH-2024-30 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2311.00644">arXiv:2311.00644</a> <span> [<a href="https://arxiv.org/pdf/2311.00644">pdf</a>, <a href="https://arxiv.org/format/2311.00644">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-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/10.1016/j.nuclphysb.2023.116427">10.1016/j.nuclphysb.2023.116427 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The first-order factorizable contributions to the three-loop massive operator matrix elements $A_{Qg}^{(3)}$ and $螖A_{Qg}^{(3)}$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Ablinger%2C+J">J. Ablinger</a>, <a href="/search/hep-ph?searchtype=author&query=Behring%2C+A">A. Behring</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=von+Manteuffel%2C+A">A. von Manteuffel</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2311.00644v1-abstract-short" style="display: inline;"> The unpolarized and polarized massive operator matrix elements $A_{Qg}^{(3)}$ and $螖A_{Qg}^{(3)}$ contain first-order factorizable and non-first-order factorizable contributions in the determining difference or differential equations of their master integrals. We compute their first-order factorizable contributions in the single heavy mass case for all contributing Feynman diagrams. Moreover, we p… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2311.00644v1-abstract-full').style.display = 'inline'; document.getElementById('2311.00644v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2311.00644v1-abstract-full" style="display: none;"> The unpolarized and polarized massive operator matrix elements $A_{Qg}^{(3)}$ and $螖A_{Qg}^{(3)}$ contain first-order factorizable and non-first-order factorizable contributions in the determining difference or differential equations of their master integrals. We compute their first-order factorizable contributions in the single heavy mass case for all contributing Feynman diagrams. Moreover, we present the complete color-$味$ factors for the cases in which also non-first-order factorizable contributions emerge in the master integrals, but cancel in the final result as found by using the method of arbitrary high Mellin moments. Individual contributions depend also on generalized harmonic sums and on nested finite binomial and inverse binomial sums in Mellin $N$-space, and correspondingly, on Kummer-Poincar茅 and square-root valued alphabets in Bjorken-$x$ space. We present a complete discussion of the possibilities of solving the present problem in $N$-space analytically and we also discuss the limitations in the present case to analytically continue the given $N$-space expressions to $N \in \mathbb{C}$ by strict methods. The representation through generating functions allows a well synchronized representation of the first-order factorizable results over a 17-letter alphabet. We finally obtain representations in terms of iterated integrals over the corresponding alphabet in $x$-space, also containing up to weight {\sf w = 5} special constants, which can be rationalized to Kummer-Poincar茅 iterated integrals at special arguments. The analytic $x$-space representation requires separate analyses for the intervals $x \in [0,1/4], [1/4,1/2], [1/2,1]$ and $x > 1$. We also derive the small and large $x$ limits of the first-order factorizable contributions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2311.00644v1-abstract-full').style.display = 'none'; document.getElementById('2311.00644v1-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> 1 November, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2023. </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">58 pages, 4 Figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DO-TH 23/12, DESY 23-142, CERN-TH-2023-164,RISC Report series 23-12, ZU-TH 60/23, MSUHEP-23-025 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2308.06042">arXiv:2308.06042</a> <span> [<a href="https://arxiv.org/pdf/2308.06042">pdf</a>, <a href="https://arxiv.org/ps/2308.06042">ps</a>, <a href="https://arxiv.org/format/2308.06042">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Symbolic Computation">cs.SC</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/10.1145/3614408.3614410">10.1145/3614408.3614410 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Computing Mellin representations and asymptotics of nested binomial sums in a symbolic way: the RICA package </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bluemlein%2C+J">Johannes Bluemlein</a>, <a href="/search/hep-ph?searchtype=author&query=Fadeev%2C+N">Nikolai Fadeev</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">Carsten Schneider</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="2308.06042v1-abstract-short" style="display: inline;"> Nested binomial sums form a particular class of sums that arise in the context of particle physics computations at higher orders in perturbation theory within QCD and QED, but that are also mathematically relevant, e.g., in combinatorics. We present the package RICA (Rule Induced Convolutions for Asymptotics), which aims at calculating Mellin representations and asymptotic expansions at infinity o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2308.06042v1-abstract-full').style.display = 'inline'; document.getElementById('2308.06042v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2308.06042v1-abstract-full" style="display: none;"> Nested binomial sums form a particular class of sums that arise in the context of particle physics computations at higher orders in perturbation theory within QCD and QED, but that are also mathematically relevant, e.g., in combinatorics. We present the package RICA (Rule Induced Convolutions for Asymptotics), which aims at calculating Mellin representations and asymptotic expansions at infinity of those objects. These representations are of particular interest to perform analytic continuations of such sums. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2308.06042v1-abstract-full').style.display = 'none'; document.getElementById('2308.06042v1-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 August, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> RISC Report Series 23-11 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> ACM Communications in Computer Algebra, Vol. 57, No. 2, Issue 224, June 2023 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2307.02983">arXiv:2307.02983</a> <span> [<a href="https://arxiv.org/pdf/2307.02983">pdf</a>, <a href="https://arxiv.org/format/2307.02983">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> Analytic results on the massive three-loop form factors: quarkonic contributions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">Johannes Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">Abilio De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=Marquard%2C+P">Peter Marquard</a>, <a href="/search/hep-ph?searchtype=author&query=Rana%2C+N">Narayan Rana</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">Carsten Schneider</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="2307.02983v1-abstract-short" style="display: inline;"> The quarkonic contributions to the three-loop heavy-quark form factors for vector, axial-vector, scalar and pseudoscalar currents are described by closed form difference equations for the expansion coefficients in the limit of small virtualities $q^2/m^2$. A part of the contributions can be solved analytically and expressed in terms of harmonic and cyclotomic harmonic polylogarithms and square-roo… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2307.02983v1-abstract-full').style.display = 'inline'; document.getElementById('2307.02983v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2307.02983v1-abstract-full" style="display: none;"> The quarkonic contributions to the three-loop heavy-quark form factors for vector, axial-vector, scalar and pseudoscalar currents are described by closed form difference equations for the expansion coefficients in the limit of small virtualities $q^2/m^2$. A part of the contributions can be solved analytically and expressed in terms of harmonic and cyclotomic harmonic polylogarithms and square-root valued iterated integrals. Other contributions obey equations which are not first-order factorizable. For them still infinite series expansions around the singularities of the form factors can be obtained by matching the expansions at intermediate points and using differential equations which are obeyed directly by the form factors and are derived by guessing algorithms. One may determine all expansion coefficients for $q^2 /m^2 \to \infty$ analytically in terms of multiple zeta values. By expanding around the threshold and pseudo-threshold, the corresponding constants are multiple zeta values supplemented by a finite amount of new constants, which can be computed at high precision. For a part of these coefficients, the infinite series in front of these constants may be even resummed into harmonic polylogarithms. In this way, one obtains a deeper analytic description of the massive form factors, beyond their pure numerical evaluation. The calculations of these analytic results are based on sophisticated computer algebra techniques. We also compare our results with numerical results in the literature. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2307.02983v1-abstract-full').style.display = 'none'; document.getElementById('2307.02983v1-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> 6 July, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2023. </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">92 pages, 14 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 23--012, DO--TH 23/02, RISC Report Series 23-08 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.16550">arXiv:2306.16550</a> <span> [<a href="https://arxiv.org/pdf/2306.16550">pdf</a>, <a href="https://arxiv.org/format/2306.16550">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> </div> </div> <p class="title is-5 mathjax"> Recent 3-Loop Heavy Flavor Corrections to Deep-Inelastic Scattering </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Ablinger%2C+J">J. Ablinger</a>, <a href="/search/hep-ph?searchtype=author&query=Behring%2C+A">A. Behring</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=Goedicke%2C+A">A. Goedicke</a>, <a href="/search/hep-ph?searchtype=author&query=von+Manteuffel%2C+A">A. von Manteuffel</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2306.16550v1-abstract-short" style="display: inline;"> We report on recent progress in calculating the three loop QCD corrections of the heavy flavor contributions in deep--inelastic scattering and the massive operator matrix elements of the variable flavor number scheme. Notably we deal with the operator matrix elements $A_{gg,Q}^{(3)}$ and $A_{Qg}^{(3)}$ and technical steps to their calculation. In particular, a new method to obtain the inverse Mell… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.16550v1-abstract-full').style.display = 'inline'; document.getElementById('2306.16550v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.16550v1-abstract-full" style="display: none;"> We report on recent progress in calculating the three loop QCD corrections of the heavy flavor contributions in deep--inelastic scattering and the massive operator matrix elements of the variable flavor number scheme. Notably we deal with the operator matrix elements $A_{gg,Q}^{(3)}$ and $A_{Qg}^{(3)}$ and technical steps to their calculation. In particular, a new method to obtain the inverse Mellin transform without computing the corresponding $N$--space expressions is discussed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.16550v1-abstract-full').style.display = 'none'; document.getElementById('2306.16550v1-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> 28 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </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">Proc RADCOR 2023, 7 pages, 1 figure</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY-23-089, DO-TH 23/09, CERN-TH-2023-122, ZU-TH 29/23, RISC Report Series 23-09, MSUHEP-23-018 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.14578">arXiv:2306.14578</a> <span> [<a href="https://arxiv.org/pdf/2306.14578">pdf</a>, <a href="https://arxiv.org/format/2306.14578">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Experiment">nucl-ex</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"> Radiative Corrections: From Medium to High Energy Experiments </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Afanasev%2C+A">Andrei Afanasev</a>, <a href="/search/hep-ph?searchtype=author&query=Bernauer%2C+J+C">Jan C. Bernauer</a>, <a href="/search/hep-ph?searchtype=author&query=Blunden%2C+P">Peter Blunden</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">Johannes Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Cline%2C+E+W">Ethan W. Cline</a>, <a href="/search/hep-ph?searchtype=author&query=Friedrich%2C+J+M">Jan M. Friedrich</a>, <a href="/search/hep-ph?searchtype=author&query=Hagelstein%2C+F">Franziska Hagelstein</a>, <a href="/search/hep-ph?searchtype=author&query=Husek%2C+T">Tom谩拧 Husek</a>, <a href="/search/hep-ph?searchtype=author&query=Kohl%2C+M">Michael Kohl</a>, <a href="/search/hep-ph?searchtype=author&query=Myhrer%2C+F">Fred Myhrer</a>, <a href="/search/hep-ph?searchtype=author&query=Paz%2C+G">Gil Paz</a>, <a href="/search/hep-ph?searchtype=author&query=Schadmand%2C+S">Susan Schadmand</a>, <a href="/search/hep-ph?searchtype=author&query=Schmidt%2C+A">Axel Schmidt</a>, <a href="/search/hep-ph?searchtype=author&query=Sharkovska%2C+V">Vladyslava Sharkovska</a>, <a href="/search/hep-ph?searchtype=author&query=Signer%2C+A">Adrian Signer</a>, <a href="/search/hep-ph?searchtype=author&query=Tomalak%2C+O">Oleksandr Tomalak</a>, <a href="/search/hep-ph?searchtype=author&query=Tomasi-Gustafsson%2C+E">Egle Tomasi-Gustafsson</a>, <a href="/search/hep-ph?searchtype=author&query=Ulrich%2C+Y">Yannick Ulrich</a>, <a href="/search/hep-ph?searchtype=author&query=Vanderhaeghen%2C+M">Marc Vanderhaeghen</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="2306.14578v1-abstract-short" style="display: inline;"> Radiative corrections are crucial for modern high-precision physics experiments, and are an area of active research in the experimental and theoretical community. Here we provide an overview of the state of the field of radiative corrections with a focus on several topics: lepton-proton scattering, QED corrections in deep-inelastic scattering, and in radiative light-hadron decays. Particular empha… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.14578v1-abstract-full').style.display = 'inline'; document.getElementById('2306.14578v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.14578v1-abstract-full" style="display: none;"> Radiative corrections are crucial for modern high-precision physics experiments, and are an area of active research in the experimental and theoretical community. Here we provide an overview of the state of the field of radiative corrections with a focus on several topics: lepton-proton scattering, QED corrections in deep-inelastic scattering, and in radiative light-hadron decays. Particular emphasis is placed on the two-photon exchange, believed to be responsible for the proton form-factor discrepancy, and associated Monte-Carlo codes. We encourage the community to continue developing theoretical techniques to treat radiative corrections, and perform experimental tests of these corrections. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.14578v1-abstract-full').style.display = 'none'; document.getElementById('2306.14578v1-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 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </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">Review article to be submitted to the EPJ A Topical Collection on radiative corrections. 63 pages, 27 figures, 3 tables</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.01362">arXiv:2306.01362</a> <span> [<a href="https://arxiv.org/pdf/2306.01362">pdf</a>, <a href="https://arxiv.org/format/2306.01362">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 - Phenomenology">hep-ph</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 - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> Deep-Inelastic Scattering: What do we know ? </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">Johannes Bl眉mlein</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="2306.01362v1-abstract-short" style="display: inline;"> A survey is given on the current status of the theoretical description of unpolarized and polarized deep--inelastic scattering processes in Quantum Chromodynamics at large virtualities. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.01362v1-abstract-full" style="display: none;"> A survey is given on the current status of the theoretical description of unpolarized and polarized deep--inelastic scattering processes in Quantum Chromodynamics at large virtualities. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.01362v1-abstract-full').style.display = 'none'; document.getElementById('2306.01362v1-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> 2 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </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, 4 figures, Dedicated to the Memory of Harald Fritzsch</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 23--066, DO--TH 23/06 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2303.05943">arXiv:2303.05943</a> <span> [<a href="https://arxiv.org/pdf/2303.05943">pdf</a>, <a href="https://arxiv.org/ps/2303.05943">ps</a>, <a href="https://arxiv.org/format/2303.05943">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-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/10.1007/JHEP06(2023)062">10.1007/JHEP06(2023)062 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The inverse Mellin transform via analytic continuation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Behring%2C+A">A. Behring</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2303.05943v1-abstract-short" style="display: inline;"> We present a method to calculate the $x$--space expressions of massless or massive operator matrix elements in QCD and QED containing local composite operator insertions, depending on the discrete Mellin index $N$, directly, without computing the Mellin--space expressions in explicit form analytically. Here $N$ belongs either to the even or odd positive integers. The method is based on the resumma… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.05943v1-abstract-full').style.display = 'inline'; document.getElementById('2303.05943v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2303.05943v1-abstract-full" style="display: none;"> We present a method to calculate the $x$--space expressions of massless or massive operator matrix elements in QCD and QED containing local composite operator insertions, depending on the discrete Mellin index $N$, directly, without computing the Mellin--space expressions in explicit form analytically. Here $N$ belongs either to the even or odd positive integers. The method is based on the resummation of the operators into effective propagators and relies on an analytic continuation between two continuous variables. We apply it to iterated integrals as well as to the more general case of iterated non--iterative integrals, generalizing the former ones. The $x$--space expressions are needed to derive the small--$x$ behaviour of the respective quantities, which usually cannot be accessed in $N$--space. We illustrate the method for different (iterated) alphabets, including non--iterative $_2F_1$ and elliptic structures, as examples. These structures occur in different massless and massive three--loop calculations. Likewise the method applies even to the analytic closed form solutions of more general cases of differential equations which do not factorize into first--order factors. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.05943v1-abstract-full').style.display = 'none'; document.getElementById('2303.05943v1-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> 10 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2023. </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">43 pages Latex</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 20--053, DO-TH 23/01, CERN-TH-2023-020, ZU--TH 13/23 13/23 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2211.15337">arXiv:2211.15337</a> <span> [<a href="https://arxiv.org/pdf/2211.15337">pdf</a>, <a href="https://arxiv.org/format/2211.15337">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</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/10.1016/j.nuclphysb.2023.116114">10.1016/j.nuclphysb.2023.116114 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> $O(伪_s^2$) Polarized Heavy Flavor Corrections}to Deep-Inelastic Scattering at $Q^2 \gg m^2$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bierenbaum%2C+I">I. Bierenbaum</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=Goedicke%2C+A">A. Goedicke</a>, <a href="/search/hep-ph?searchtype=author&query=Klein%2C+S">S. Klein</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2211.15337v1-abstract-short" style="display: inline;"> We calculate the quarkonic $O(伪_s^2)$ massive operator matrix elements $螖A_{Qg}(N), 螖A_{Qq}^{\rm PS}(N)$ and $螖A_{qq,Q}^{\rm NS}(N)$ for the twist--2 operators and the associated heavy flavor Wilson coefficients in polarized deeply inelastic scattering in the region $Q^2 \gg m^2$ to $O(\varepsilon)$ in the case of the inclusive heavy flavor contributions. The evaluation is performed in Mellin spac… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2211.15337v1-abstract-full').style.display = 'inline'; document.getElementById('2211.15337v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2211.15337v1-abstract-full" style="display: none;"> We calculate the quarkonic $O(伪_s^2)$ massive operator matrix elements $螖A_{Qg}(N), 螖A_{Qq}^{\rm PS}(N)$ and $螖A_{qq,Q}^{\rm NS}(N)$ for the twist--2 operators and the associated heavy flavor Wilson coefficients in polarized deeply inelastic scattering in the region $Q^2 \gg m^2$ to $O(\varepsilon)$ in the case of the inclusive heavy flavor contributions. The evaluation is performed in Mellin space, without applying the integration-by-parts method. The result is given in terms of harmonic sums. This leads to a significant compactification of the operator matrix elements and massive Wilson coefficients in the region $Q^2 \gg m^2$ derived previously in \cite{BUZA2}, which we partly confirm, and also partly correct. The results allow to determine the heavy flavor Wilson coefficients for $g_1(x,Q^2)$ to $O(伪_s^2)$ for all but the power suppressed terms $\propto (m^2/Q^2)^k, k \geq 1$. The results in momentum fraction $z$-space are also presented. We also discuss the small $x$ effects in the polarized case. Numerical results are presented. We also compute the gluonic matching coefficients in the two--mass variable flavor number scheme to $O(\varepsilon)$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2211.15337v1-abstract-full').style.display = 'none'; document.getElementById('2211.15337v1-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> 28 November, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 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">58 pages Latex, 12 Figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 15--004, DO--TH 15/01, TTP 22--023, ZU-TH 57/22, SAGEX--20--11 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2211.05462">arXiv:2211.05462</a> <span> [<a href="https://arxiv.org/pdf/2211.05462">pdf</a>, <a href="https://arxiv.org/format/2211.05462">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</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/10.1007/JHEP12(2022)134">10.1007/JHEP12(2022)134 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Unpolarized and Polarized Single-Mass Three-Loop Heavy Flavor Operator Matrix Elements $A_{gg,Q}$ and $螖A_{gg,Q}$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Ablinger%2C+J">J. Ablinger</a>, <a href="/search/hep-ph?searchtype=author&query=Behring%2C+A">A. Behring</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+A+G+A+v+M+C">A. Goedicke A. von Manteuffel C. Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2211.05462v1-abstract-short" style="display: inline;"> We calculate the gluonic massive operator matrix elements in the unpolarized and polarized cases, $A_{gg,Q}(x,渭^2)$ and $螖A_{gg,Q}(x,渭^2)$, at three-loop order for a single mass. These quantities contribute to the matching of the gluon distribution in the variable flavor number scheme. The polarized operator matrix element is calculated in the Larin scheme. These operator matrix elements contain f… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2211.05462v1-abstract-full').style.display = 'inline'; document.getElementById('2211.05462v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2211.05462v1-abstract-full" style="display: none;"> We calculate the gluonic massive operator matrix elements in the unpolarized and polarized cases, $A_{gg,Q}(x,渭^2)$ and $螖A_{gg,Q}(x,渭^2)$, at three-loop order for a single mass. These quantities contribute to the matching of the gluon distribution in the variable flavor number scheme. The polarized operator matrix element is calculated in the Larin scheme. These operator matrix elements contain finite binomial and inverse binomial sums in Mellin $N$-space and iterated integrals over square root-valued alphabets in momentum fraction $x$-space. We derive the necessary analytic relations for the analytic continuation of these quantities from the even or odd Mellin moments into the complex plane, present analytic expressions in momentum fraction $x$-space and derive numerical results. The present results complete the gluon transition matrix elements both of the single- and double-mass variable flavor number scheme to three-loop order. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2211.05462v1-abstract-full').style.display = 'none'; document.getElementById('2211.05462v1-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> 10 November, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 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">48 p LATEX, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 15-112, DO-TH 22/26, CERN-TH-2022-179, ZU-TH 53/22, RISC Report Series 22-25, MSUHEP-22-036 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2208.14325">arXiv:2208.14325</a> <span> [<a href="https://arxiv.org/pdf/2208.14325">pdf</a>, <a href="https://arxiv.org/ps/2208.14325">ps</a>, <a href="https://arxiv.org/format/2208.14325">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 - Phenomenology">hep-ph</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 - Theory">hep-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/10.1007/JHEP11(2022)156">10.1007/JHEP11(2022)156 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The massless three-loop Wilson coefficients for the deep-inelastic structure functions $F_2, F_L, xF_3$ and $g_1$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Marquard%2C+P">P. Marquard</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2208.14325v1-abstract-short" style="display: inline;"> We calculate the massless unpolarized Wilson coefficients for deeply inelastic scattering for the structure functions $F_2(x,Q^2), F_L(x,Q^2), x F_3(x,Q^2)$ in the $\overline{\sf MS}$ scheme and the polarized Wilson coefficients of the structure function $g_1(x,Q^2)$ in the Larin scheme up to three--loop order in QCD in a fully automated way based on the method of arbitrary high Mellin moments. We… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.14325v1-abstract-full').style.display = 'inline'; document.getElementById('2208.14325v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2208.14325v1-abstract-full" style="display: none;"> We calculate the massless unpolarized Wilson coefficients for deeply inelastic scattering for the structure functions $F_2(x,Q^2), F_L(x,Q^2), x F_3(x,Q^2)$ in the $\overline{\sf MS}$ scheme and the polarized Wilson coefficients of the structure function $g_1(x,Q^2)$ in the Larin scheme up to three--loop order in QCD in a fully automated way based on the method of arbitrary high Mellin moments. We work in the Larin scheme in the case of contributing axial--vector couplings or polarized nucleons. For the unpolarized structure functions we compare to results given in the literature. The polarized three--loop Wilson coefficients are calculated for the first time. As a by--product we also obtain the quarkonic three--loop anomalous dimensions from the $O(1/\varepsilon)$ terms of the unrenormalized forward Compton amplitude. Expansions for small and large values of the Bjorken variable $x$ are provided. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.14325v1-abstract-full').style.display = 'none'; document.getElementById('2208.14325v1-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, 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">159 pages Latex</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 22-123, DO-TH 22/20, TTP 22-057, RISC Report Series 22-12, SAGEX-22-30 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2208.04552">arXiv:2208.04552</a> <span> [<a href="https://arxiv.org/pdf/2208.04552">pdf</a>, <a href="https://arxiv.org/format/2208.04552">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</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"> Gravity in binary systems at the fifth and sixth post-Newtonian order </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Maier%2C+A">A. Maier</a>, <a href="/search/hep-ph?searchtype=author&query=Marquard%2C+P">P. Marquard</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%A4fer%2C+G">G. Sch盲fer</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="2208.04552v1-abstract-short" style="display: inline;"> Binary sources of gravitational waves in the early inspiral phase are accurately described by a post-Newtonian expansion in small velocity and weak interaction. We compute the conservative dynamics to fifth and partial sixth order using a non-relativistic effective field theory. We give predictions for central observables and determine the required coefficients for the construction of an Effective… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.04552v1-abstract-full').style.display = 'inline'; document.getElementById('2208.04552v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2208.04552v1-abstract-full" style="display: none;"> Binary sources of gravitational waves in the early inspiral phase are accurately described by a post-Newtonian expansion in small velocity and weak interaction. We compute the conservative dynamics to fifth and partial sixth order using a non-relativistic effective field theory. We give predictions for central observables and determine the required coefficients for the construction of an Effective One-Body Hamiltonian, extending the applicability of our results to the late inspiral and merger phases. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.04552v1-abstract-full').style.display = 'none'; document.getElementById('2208.04552v1-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> 9 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">10 pages, 1 figure. Contribution to the proceedings of Loops and Legs in Quantum Field Theory - LL2022</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2207.08524">arXiv:2207.08524</a> <span> [<a href="https://arxiv.org/pdf/2207.08524">pdf</a>, <a href="https://arxiv.org/ps/2207.08524">ps</a>, <a href="https://arxiv.org/format/2207.08524">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Symbolic Computation">cs.SC</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"> Computer Algebra and Hypergeometric Structures for Feynman Integrals </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bluemlein%2C+J">Johannes Bluemlein</a>, <a href="/search/hep-ph?searchtype=author&query=Saragnese%2C+M">Marco Saragnese</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">Carsten Schneider</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="2207.08524v1-abstract-short" style="display: inline;"> We present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations. The summand of the series solutions may be built by hypergeometric products and more generally by indefinite nested sums defined over such products. Special cases are hypergeometric structures such as Appell-functions or… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.08524v1-abstract-full').style.display = 'inline'; document.getElementById('2207.08524v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2207.08524v1-abstract-full" style="display: none;"> We present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations. The summand of the series solutions may be built by hypergeometric products and more generally by indefinite nested sums defined over such products. Special cases are hypergeometric structures such as Appell-functions or generalizations of them that arise frequently when dealing with parameter Feynman integrals. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.08524v1-abstract-full').style.display = 'none'; document.getElementById('2207.08524v1-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> 18 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 22--117, DO-TH 22/18, RISC Report Series 22-08, SAGEX-22-28-E </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2207.07943">arXiv:2207.07943</a> <span> [<a href="https://arxiv.org/pdf/2207.07943">pdf</a>, <a href="https://arxiv.org/ps/2207.07943">ps</a>, <a href="https://arxiv.org/format/2207.07943">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 - Phenomenology">hep-ph</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 - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> The 3-loop anomalous dimensions from off-shell operator matrix elements </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Marquard%2C+P">P. Marquard</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2207.07943v1-abstract-short" style="display: inline;"> We report on the calculation of the three-loop polarized and unpolarized flavor non-singlet and the polarized singlet anomalous dimensions using massless off-shell operator matrix elements in a gauge-variant framework. We also reconsider the unpolarized two-loop singlet anomalous dimensions and correct errors in the foregoing literature. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2207.07943v1-abstract-full" style="display: none;"> We report on the calculation of the three-loop polarized and unpolarized flavor non-singlet and the polarized singlet anomalous dimensions using massless off-shell operator matrix elements in a gauge-variant framework. We also reconsider the unpolarized two-loop singlet anomalous dimensions and correct errors in the foregoing literature. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.07943v1-abstract-full').style.display = 'none'; document.getElementById('2207.07943v1-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 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 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">12 pages Latex, Contributeion to the Proceedings of LL2022</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 19--061, DO-TH 20/09, TTP22--048, RISC Report Series 22--09, SAGEX 20--20 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> PoS (LL2022) 048 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2203.13923">arXiv:2203.13923</a> <span> [<a href="https://arxiv.org/pdf/2203.13923">pdf</a>, <a href="https://arxiv.org/format/2203.13923">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</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/10.5506/APhysPolB.53.12-A1">10.5506/APhysPolB.53.12-A1 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Snowmass 2021 whitepaper: Proton structure at the precision frontier </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Amoroso%2C+S">S. Amoroso</a>, <a href="/search/hep-ph?searchtype=author&query=Apyan%2C+A">A. Apyan</a>, <a href="/search/hep-ph?searchtype=author&query=Armesto%2C+N">N. Armesto</a>, <a href="/search/hep-ph?searchtype=author&query=Ball%2C+R+D">R. D. Ball</a>, <a href="/search/hep-ph?searchtype=author&query=Bertone%2C+V">V. Bertone</a>, <a href="/search/hep-ph?searchtype=author&query=Bissolotti%2C+C">C. Bissolotti</a>, <a href="/search/hep-ph?searchtype=author&query=Bluemlein%2C+J">J. Bluemlein</a>, <a href="/search/hep-ph?searchtype=author&query=Boughezal%2C+R">R. Boughezal</a>, <a href="/search/hep-ph?searchtype=author&query=Bozzi%2C+G">G. Bozzi</a>, <a href="/search/hep-ph?searchtype=author&query=Britzger%2C+D">D. Britzger</a>, <a href="/search/hep-ph?searchtype=author&query=Buckley%2C+A">A. Buckley</a>, <a href="/search/hep-ph?searchtype=author&query=Candido%2C+A">A. Candido</a>, <a href="/search/hep-ph?searchtype=author&query=Carrazza%2C+S">S. Carrazza</a>, <a href="/search/hep-ph?searchtype=author&query=Celiberto%2C+F+G">F. G. Celiberto</a>, <a href="/search/hep-ph?searchtype=author&query=Cerci%2C+S">S. Cerci</a>, <a href="/search/hep-ph?searchtype=author&query=Chachamis%2C+G">G. Chachamis</a>, <a href="/search/hep-ph?searchtype=author&query=Cooper-Sarkar%2C+A+M">A. M. Cooper-Sarkar</a>, <a href="/search/hep-ph?searchtype=author&query=Courtoy%2C+A">A. Courtoy</a>, <a href="/search/hep-ph?searchtype=author&query=Cridge%2C+T">T. Cridge</a>, <a href="/search/hep-ph?searchtype=author&query=Cruz-Martinez%2C+J+M">J. M. Cruz-Martinez</a>, <a href="/search/hep-ph?searchtype=author&query=Giuli%2C+F">F. Giuli</a>, <a href="/search/hep-ph?searchtype=author&query=Guzzi%2C+M">M. Guzzi</a>, <a href="/search/hep-ph?searchtype=author&query=Gwenlan%2C+C">C. Gwenlan</a>, <a href="/search/hep-ph?searchtype=author&query=Harland-Lang%2C+L+A">L. A. Harland-Lang</a>, <a href="/search/hep-ph?searchtype=author&query=Hekhorn%2C+F">F. Hekhorn</a> , et al. (32 additional authors not shown) </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="2203.13923v3-abstract-short" style="display: inline;"> An overwhelming number of theoretical predictions for hadron colliders require parton distribution functions (PDFs), which are an important ingredient of theory infrastructure for the next generation of high-energy experiments. This whitepaper summarizes the status and future prospects for determination of high-precision PDFs applicable in a wide range of energies and experiments, in particular in… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.13923v3-abstract-full').style.display = 'inline'; document.getElementById('2203.13923v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2203.13923v3-abstract-full" style="display: none;"> An overwhelming number of theoretical predictions for hadron colliders require parton distribution functions (PDFs), which are an important ingredient of theory infrastructure for the next generation of high-energy experiments. This whitepaper summarizes the status and future prospects for determination of high-precision PDFs applicable in a wide range of energies and experiments, in particular in precision tests of the Standard Model and in new physics searches at the high-luminosity Large Hadron Collider and Electron-Ion Collider. We discuss the envisioned advancements in experimental measurements, QCD theory, global analysis methodology, and computing that are necessary to bring unpolarized PDFs in the nucleon to the N2LO and N3LO accuracy in the QCD coupling strength. Special attention is given to the new tasks that emerge in the era of the precision PDF analysis, such as those focusing on the robust control of systematic factors both in experimental measurements and theoretical computations. Various synergies between experimental and theoretical studies of the hadron structure are explored, including opportunities for studying PDFs for nuclear and meson targets, PDFs with electroweak contributions or dependence on the transverse momentum, for incisive comparisons between phenomenological models for the PDFs and computations on discrete lattice, and for cross-fertilization with machine learning/AI approaches. [Submitted to the US Community Study on the Future of Particle Physics (Snowmass 2021).] <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.13923v3-abstract-full').style.display = 'none'; document.getElementById('2203.13923v3-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 April, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 25 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 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">83 pages, 27 figures, contribution to Snowmass 2021; v.3: journal version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> Edinburgh 2022/08, FERMILAB-PUB-22-222-QIS-SCD-T, MPP-2022-32, SLAC-PUB-17652, SMU-HEP-22-02, TIF-UNIMI-2022-6 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Acta Phys.Polon.B 53 (2022) 12, A1 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2203.13015">arXiv:2203.13015</a> <span> [<a href="https://arxiv.org/pdf/2203.13015">pdf</a>, <a href="https://arxiv.org/ps/2203.13015">ps</a>, <a href="https://arxiv.org/format/2203.13015">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 - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Symbolic Computation">cs.SC</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/10.1088/1751-8121/ac8086">10.1088/1751-8121/ac8086 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">Johannes Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">Carsten Schneider</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="2203.13015v3-abstract-short" style="display: inline;"> The analytic integration and simplification of multi-loop Feynman integrals to special functions and constants plays an important role to perform higher order perturbative calculations in the Standard Model of elementary particles. In this survey article the most recent and relevant computer algebra and special function algorithms are presented that are currently used or that may play an important… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.13015v3-abstract-full').style.display = 'inline'; document.getElementById('2203.13015v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2203.13015v3-abstract-full" style="display: none;"> The analytic integration and simplification of multi-loop Feynman integrals to special functions and constants plays an important role to perform higher order perturbative calculations in the Standard Model of elementary particles. In this survey article the most recent and relevant computer algebra and special function algorithms are presented that are currently used or that may play an important role to perform such challenging precision calculations in the future. They are discussed in the context of analytic zero, single and double scale calculations in the Quantum Field Theories of the Standard Model and effective field theories, also with classical applications. These calculations play a central role in the analysis of precision measurements at present and future colliders to obtain ultimate information for fundamental physics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.13015v3-abstract-full').style.display = 'none'; document.getElementById('2203.13015v3-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> 10 January, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 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">42 pages, see also the overview article arXiv:2203.13011.v3: journal version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> SAGEX-22-05, DESY 22--032, DO--TH 22/07, RISC Report number 22--03 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Phys. A: Math. Theor. 55 443005 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2203.13011">arXiv:2203.13011</a> <span> [<a href="https://arxiv.org/pdf/2203.13011">pdf</a>, <a href="https://arxiv.org/format/2203.13011">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 - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</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/10.1088/1751-8121/ac8380">10.1088/1751-8121/ac8380 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The SAGEX Review on Scattering Amplitudes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Travaglini%2C+G">Gabriele Travaglini</a>, <a href="/search/hep-ph?searchtype=author&query=Brandhuber%2C+A">Andreas Brandhuber</a>, <a href="/search/hep-ph?searchtype=author&query=Dorey%2C+P">Patrick Dorey</a>, <a href="/search/hep-ph?searchtype=author&query=McLoughlin%2C+T">Tristan McLoughlin</a>, <a href="/search/hep-ph?searchtype=author&query=Abreu%2C+S">Samuel Abreu</a>, <a href="/search/hep-ph?searchtype=author&query=Bern%2C+Z">Zvi Bern</a>, <a href="/search/hep-ph?searchtype=author&query=Bjerrum-Bohr%2C+N+E+J">N. Emil J. Bjerrum-Bohr</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">Johannes Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Britto%2C+R">Ruth Britto</a>, <a href="/search/hep-ph?searchtype=author&query=Carrasco%2C+J+J+M">John Joseph M. Carrasco</a>, <a href="/search/hep-ph?searchtype=author&query=Chicherin%2C+D">Dmitry Chicherin</a>, <a href="/search/hep-ph?searchtype=author&query=Chiodaroli%2C+M">Marco Chiodaroli</a>, <a href="/search/hep-ph?searchtype=author&query=Damgaard%2C+P+H">Poul H. Damgaard</a>, <a href="/search/hep-ph?searchtype=author&query=Del+Duca%2C+V">Vittorio Del Duca</a>, <a href="/search/hep-ph?searchtype=author&query=Dixon%2C+L+J">Lance J. Dixon</a>, <a href="/search/hep-ph?searchtype=author&query=Dorigoni%2C+D">Daniele Dorigoni</a>, <a href="/search/hep-ph?searchtype=author&query=Duhr%2C+C">Claude Duhr</a>, <a href="/search/hep-ph?searchtype=author&query=Geyer%2C+Y">Yvonne Geyer</a>, <a href="/search/hep-ph?searchtype=author&query=Green%2C+M+B">Michael B. Green</a>, <a href="/search/hep-ph?searchtype=author&query=Herrmann%2C+E">Enrico Herrmann</a>, <a href="/search/hep-ph?searchtype=author&query=Heslop%2C+P">Paul Heslop</a>, <a href="/search/hep-ph?searchtype=author&query=Johansson%2C+H">Henrik Johansson</a>, <a href="/search/hep-ph?searchtype=author&query=Korchemsky%2C+G+P">Gregory P. Korchemsky</a>, <a href="/search/hep-ph?searchtype=author&query=Kosower%2C+D+A">David A. Kosower</a>, <a href="/search/hep-ph?searchtype=author&query=Mason%2C+L">Lionel Mason</a> , et al. (13 additional authors not shown) </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="2203.13011v3-abstract-short" style="display: inline;"> This is an introduction to, and invitation to read, a series of review articles on scattering amplitudes in gauge theory, gravity, and superstring theory. Our aim is to provide an overview of the field, from basic aspects to a selection of current (2022) research and developments. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2203.13011v3-abstract-full" style="display: none;"> This is an introduction to, and invitation to read, a series of review articles on scattering amplitudes in gauge theory, gravity, and superstring theory. Our aim is to provide an overview of the field, from basic aspects to a selection of current (2022) research and developments. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.13011v3-abstract-full').style.display = 'none'; document.getElementById('2203.13011v3-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> 8 January, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 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">15 pages, overview article. v3: journal version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> SAGEX-22-01 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2203.08271">arXiv:2203.08271</a> <span> [<a href="https://arxiv.org/pdf/2203.08271">pdf</a>, <a href="https://arxiv.org/format/2203.08271">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 - Phenomenology">hep-ph</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 - 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/10.1088/1361-6471/ad1a78">10.1088/1361-6471/ad1a78 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The strong coupling constant: State of the art and the decade ahead </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=d%27Enterria%2C+D">D. d'Enterria</a>, <a href="/search/hep-ph?searchtype=author&query=Kluth%2C+S">S. Kluth</a>, <a href="/search/hep-ph?searchtype=author&query=Zanderighi%2C+G">G. Zanderighi</a>, <a href="/search/hep-ph?searchtype=author&query=Ayala%2C+C">C. Ayala</a>, <a href="/search/hep-ph?searchtype=author&query=Benitez-Rathgeb%2C+M+A">M. A. Benitez-Rathgeb</a>, <a href="/search/hep-ph?searchtype=author&query=Bluemlein%2C+J">J. Bluemlein</a>, <a href="/search/hep-ph?searchtype=author&query=Boito%2C+D">D. Boito</a>, <a href="/search/hep-ph?searchtype=author&query=Brambilla%2C+N">N. Brambilla</a>, <a href="/search/hep-ph?searchtype=author&query=Britzger%2C+D">D. Britzger</a>, <a href="/search/hep-ph?searchtype=author&query=Camarda%2C+S">S. Camarda</a>, <a href="/search/hep-ph?searchtype=author&query=Cooper-Sarkar%2C+A+M">A. M. Cooper-Sarkar</a>, <a href="/search/hep-ph?searchtype=author&query=Cridge%2C+T">T. Cridge</a>, <a href="/search/hep-ph?searchtype=author&query=Cvetic%2C+G">G. Cvetic</a>, <a href="/search/hep-ph?searchtype=author&query=Brida%2C+M+D">M. Dalla Brida</a>, <a href="/search/hep-ph?searchtype=author&query=Deur%2C+A">A. Deur</a>, <a href="/search/hep-ph?searchtype=author&query=Giuli%2C+F">F. Giuli</a>, <a href="/search/hep-ph?searchtype=author&query=Golterman%2C+M">M. Golterman</a>, <a href="/search/hep-ph?searchtype=author&query=Hoang%2C+A+H">A. H. Hoang</a>, <a href="/search/hep-ph?searchtype=author&query=Huston%2C+J">J. Huston</a>, <a href="/search/hep-ph?searchtype=author&query=Jamin%2C+M">M. Jamin</a>, <a href="/search/hep-ph?searchtype=author&query=Kotikov%2C+A+V">A. V. Kotikov</a>, <a href="/search/hep-ph?searchtype=author&query=Krivokhizhin%2C+V+G">V. G. Krivokhizhin</a>, <a href="/search/hep-ph?searchtype=author&query=Kronfeld%2C+A+S">A. S. Kronfeld</a>, <a href="/search/hep-ph?searchtype=author&query=Leino%2C+V">V. Leino</a>, <a href="/search/hep-ph?searchtype=author&query=Lipka%2C+K">K. Lipka</a> , et al. (33 additional authors not shown) </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="2203.08271v2-abstract-short" style="display: inline;"> Theoretical predictions for particle production cross sections and decays at colliders rely heavily on perturbative Quantum Chromodynamics (QCD) calculations, expressed as an expansion in powers of the strong coupling constant $伪_s$. The current $\mathcal{O}(1\%)$ uncertainty of the QCD coupling evaluated at the reference Z boson mass, $伪_s(m_Z) = 0.1179 \pm 0.0009$, is one of the limiting factors… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.08271v2-abstract-full').style.display = 'inline'; document.getElementById('2203.08271v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2203.08271v2-abstract-full" style="display: none;"> Theoretical predictions for particle production cross sections and decays at colliders rely heavily on perturbative Quantum Chromodynamics (QCD) calculations, expressed as an expansion in powers of the strong coupling constant $伪_s$. The current $\mathcal{O}(1\%)$ uncertainty of the QCD coupling evaluated at the reference Z boson mass, $伪_s(m_Z) = 0.1179 \pm 0.0009$, is one of the limiting factors to more precisely describe multiple processes at current and future colliders. A reduction of this uncertainty is thus a prerequisite to perform precision tests of the Standard Model as well as searches for new physics. This report provides a comprehensive summary of the state-of-the-art, challenges, and prospects in the experimental and theoretical study of the strong coupling. The current $伪_s(m_Z)$ world average is derived from a combination of seven categories of observables: (i) lattice QCD, (ii) hadronic $蟿$ decays, (iii) deep-inelastic scattering and parton distribution functions fits, (iv) electroweak boson decays, hadronic final-states in (v) $e^+e^-$, (vi) e-p, and (vii) p-p collisions, and (viii) quarkonia decays and masses. We review the current status of each of these seven $伪_s(m_Z)$ extraction methods, discuss novel $伪_s$ determinations, and examine the averaging method used to obtain the world-average value. Each of the methods discussed provides a ``wish list'' of experimental and theoretical developments required in order to achieve the goal of a per-mille precision on $伪_s(m_Z)$ within the next decade. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.08271v2-abstract-full').style.display = 'none'; document.getElementById('2203.08271v2-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> 29 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 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">135 pages, 45 figures. White paper for the "Energy Frontier Proceedings of the US Community Study on the Future of Particle Physics" (Snowmass 2021). Matches JPG published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J.Phys.G 51 (2024) 9, 090501 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2202.08476">arXiv:2202.08476</a> <span> [<a href="https://arxiv.org/pdf/2202.08476">pdf</a>, <a href="https://arxiv.org/format/2202.08476">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 - 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/10.1142/S021773232230004X">10.1142/S021773232230004X <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> High Precision QED Initial State Corrections for $e^+ e^- \rightarrow 纬^*/Z^*$ Annihilation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2202.08476v1-abstract-short" style="display: inline;"> The precise knowledge of the QED initial state corrections is of instrumental importance in studying high luminosity measurements in $e^+e^-$ annihilation at facilities like LEP, the International Linear Collider ILC, CLIC, a Giga-$Z$ facility, and the planned FCC\_ee. Logarithmic corrections of up to $O(伪^6 L^5)$ are necessary with various subleading terms taken into account. This applies to both… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2202.08476v1-abstract-full').style.display = 'inline'; document.getElementById('2202.08476v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2202.08476v1-abstract-full" style="display: none;"> The precise knowledge of the QED initial state corrections is of instrumental importance in studying high luminosity measurements in $e^+e^-$ annihilation at facilities like LEP, the International Linear Collider ILC, CLIC, a Giga-$Z$ facility, and the planned FCC\_ee. Logarithmic corrections of up to $O(伪^6 L^5)$ are necessary with various subleading terms taken into account. This applies to both the inclusive measurement of processes like $e^+ e^- \rightarrow 纬^*/Z^*$ and also the forward-backward asymmetry. As has been shown recently, techniques from massive QCD, such as the computation of massive on-shell operator matrix elements, can be used for these calculations. We give an introduction to this topic and present both the calculation methods and the numerical corrections having been reached so far. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2202.08476v1-abstract-full').style.display = 'none'; document.getElementById('2202.08476v1-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> 17 February, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 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 LATEX, 5 Figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 22--024, DO-TH 22/04, TTP 22--011, SAGEX 22--19 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2202.03216">arXiv:2202.03216</a> <span> [<a href="https://arxiv.org/pdf/2202.03216">pdf</a>, <a href="https://arxiv.org/ps/2202.03216">ps</a>, <a href="https://arxiv.org/format/2202.03216">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-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/10.1016/j.nuclphysb.2022.115794">10.1016/j.nuclphysb.2022.115794 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Two-Loop Massless Off-Shell QCD Operator Matrix Elements to Finite Terms </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Marquard%2C+P">P. Marquard</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2202.03216v1-abstract-short" style="display: inline;"> We calculate the unpolarized and polarized two--loop massless off--shell operator matrix elements in QCD to $O(\varepsilon)$ in the dimensional parameter in an automated way. Here we use the method of arbitrary high Mellin moments and difference ring theory, based on integration-by-parts relations. This method also constitutes one way to compute the QCD anomalous dimensions. The presented higher o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2202.03216v1-abstract-full').style.display = 'inline'; document.getElementById('2202.03216v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2202.03216v1-abstract-full" style="display: none;"> We calculate the unpolarized and polarized two--loop massless off--shell operator matrix elements in QCD to $O(\varepsilon)$ in the dimensional parameter in an automated way. Here we use the method of arbitrary high Mellin moments and difference ring theory, based on integration-by-parts relations. This method also constitutes one way to compute the QCD anomalous dimensions. The presented higher order contributions to these operator matrix elements occur as building blocks in the corresponding higher order calculations up to four--loop order. All contributing quantities can be expressed in terms of harmonic sums in Mellin--$N$ space or by harmonic polylogarithms in $z$--space. We also perform comparisons to the literature. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2202.03216v1-abstract-full').style.display = 'none'; document.getElementById('2202.03216v1-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> 7 February, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 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">101 pages Latex</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 21--028, DO--TH 21/33, TTP 21--007, RISC Report Series 22--01, SAGEX--21--39 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2111.15501">arXiv:2111.15501</a> <span> [<a href="https://arxiv.org/pdf/2111.15501">pdf</a>, <a href="https://arxiv.org/ps/2111.15501">ps</a>, <a href="https://arxiv.org/format/2111.15501">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Symbolic Computation">cs.SC</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="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> Hypergeometric Structures in Feynman Integrals </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Saragnese%2C+M">M. Saragnese</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</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="2111.15501v1-abstract-short" style="display: inline;"> Hypergeometric structures in single and multiscale Feynman integrals emerge in a wide class of topologies. Using integration-by-parts relations, associated master or scalar integrals have to be calculated. For this purpose it appears useful to devise an automated method which recognizes the respective (partial) differential equations related to the corresponding higher transcendental functions. We… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.15501v1-abstract-full').style.display = 'inline'; document.getElementById('2111.15501v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2111.15501v1-abstract-full" style="display: none;"> Hypergeometric structures in single and multiscale Feynman integrals emerge in a wide class of topologies. Using integration-by-parts relations, associated master or scalar integrals have to be calculated. For this purpose it appears useful to devise an automated method which recognizes the respective (partial) differential equations related to the corresponding higher transcendental functions. We solve these equations through associated recursions of the expansion coefficient of the multivalued formal Taylor series. The expansion coefficients can be determined using either the package {\tt Sigma} in the case of linear difference equations or by applying heuristic methods in the case of partial linear difference equations. In the present context a new type of sums occurs, the Hurwitz harmonic sums, and generalized versions of them. The code {\tt HypSeries} transforming classes of differential equations into analytic series expansions is described. Also partial difference equations having rational solutions and rational function solutions of Pochhammer symbols are considered, for which the code {\tt solvePartialLDE} is designed. Generalized hypergeometric functions, Appell-,~Kamp茅 de F茅riet-, Horn-, Lauricella-Saran-, Srivasta-, and Exton--type functions are considered. We illustrate the algorithms by examples. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.15501v1-abstract-full').style.display = 'none'; document.getElementById('2111.15501v1-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 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 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">55 pages, several anc. files</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 21--071, DO--TH 21/16, RISC Report Series 21--17, SAGEX-21-10-E </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2111.12401">arXiv:2111.12401</a> <span> [<a href="https://arxiv.org/pdf/2111.12401">pdf</a>, <a href="https://arxiv.org/format/2111.12401">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 - Phenomenology">hep-ph</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 - Theory">hep-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/10.1007/JHEP01(2022)193">10.1007/JHEP01(2022)193 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Marquard%2C+P">P. Marquard</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2111.12401v2-abstract-short" style="display: inline;"> Future high luminosity polarized deep--inelastic scattering experiments will improve both the knowledge of the spin sub--structure of the nucleons and contribute further to the precision determination of the strong coupling constant, as well as, reveal currently yet unknown higher twist contributions in the polarized sector. For all these tasks to be performed, it is necessary to know the QCD lead… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.12401v2-abstract-full').style.display = 'inline'; document.getElementById('2111.12401v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2111.12401v2-abstract-full" style="display: none;"> Future high luminosity polarized deep--inelastic scattering experiments will improve both the knowledge of the spin sub--structure of the nucleons and contribute further to the precision determination of the strong coupling constant, as well as, reveal currently yet unknown higher twist contributions in the polarized sector. For all these tasks to be performed, it is necessary to know the QCD leading twist scaling violations of the measured structure functions. Here an important ingredient consists in the polarized singlet anomalous dimensions and splitting functions in QCD. We recalculate these quantities to three--loop order in the M--scheme by using the traditional method of space--like off--shell massless operator matrix elements, being a gauge--dependent framework. Here one obtains the anomalous dimensions without referring to gravitational currents, needed when calculating them using the forward Compton amplitude. We also calculate the non--singlet splitting function $螖P_{\rm qq}^{(2), \rm s, NS}$ and compare the final results to the literature, also including predictions for the region of small values of Bjorken $x$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.12401v2-abstract-full').style.display = 'none'; document.getElementById('2111.12401v2-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> 28 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 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">28 pages Latex, 1 figure</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 21--192, DO--TH 21/31, TTP 21--052, RISC Report Series 21--19, SAGEX--21--36 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2107.09350">arXiv:2107.09350</a> <span> [<a href="https://arxiv.org/pdf/2107.09350">pdf</a>, <a href="https://arxiv.org/format/2107.09350">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> </div> </div> <p class="title is-5 mathjax"> New 2- and 3-loop heavy flavor corrections to unpolarized and polarized deep-inelastic scattering </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Ablinger%2C+J">J. Ablinger</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=Saragnese%2C+M">M. Saragnese</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2107.09350v1-abstract-short" style="display: inline;"> A survey is given on the new 2- and 3-loop results for the heavy flavor contributions to deep-inelastic scattering in the unpolarized and the polarized case. We also discuss related new mathematical aspects applied in these calculations. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2107.09350v1-abstract-full" style="display: none;"> A survey is given on the new 2- and 3-loop results for the heavy flavor contributions to deep-inelastic scattering in the unpolarized and the polarized case. We also discuss related new mathematical aspects applied in these calculations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.09350v1-abstract-full').style.display = 'none'; document.getElementById('2107.09350v1-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> 20 July, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 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">14 pages Latex, 4 Figures, Contribution to the Proceedings of DIS 2021 and RADCOR 2021</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 21--092, DO--TH 21/20, TTP 21--023, SAGEX--21--11, RISC Report Series 21--14 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2107.06267">arXiv:2107.06267</a> <span> [<a href="https://arxiv.org/pdf/2107.06267">pdf</a>, <a href="https://arxiv.org/ps/2107.06267">ps</a>, <a href="https://arxiv.org/format/2107.06267">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey 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 - Theory">hep-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/10.1016/j.nuclphysb.2021.115542">10.1016/j.nuclphysb.2021.115542 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Marquard%2C+P">P. Marquard</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2107.06267v1-abstract-short" style="display: inline;"> We calculate the unpolarized and polarized three--loop anomalous dimensions and splitting functions $P_{\rm NS}^+, P_{\rm NS}^-$ and $P_{\rm NS}^{\rm s}$ in QCD in the $\overline{\sf MS}$ scheme by using the traditional method of space--like off shell massless operator matrix elements. This is a gauge--dependent framework. For the first time we also calculate the three--loop anomalous dimensions… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.06267v1-abstract-full').style.display = 'inline'; document.getElementById('2107.06267v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2107.06267v1-abstract-full" style="display: none;"> We calculate the unpolarized and polarized three--loop anomalous dimensions and splitting functions $P_{\rm NS}^+, P_{\rm NS}^-$ and $P_{\rm NS}^{\rm s}$ in QCD in the $\overline{\sf MS}$ scheme by using the traditional method of space--like off shell massless operator matrix elements. This is a gauge--dependent framework. For the first time we also calculate the three--loop anomalous dimensions $P_{\rm NS}^{\rm \pm tr}$ for transversity directly. We compare our results to the literature. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.06267v1-abstract-full').style.display = 'none'; document.getElementById('2107.06267v1-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 July, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 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">40 pages Latex</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 21--104,DO--TH 21/23,TTP 21--024,RISC Report Series 21--13,SAGEX--21--15 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2107.01293">arXiv:2107.01293</a> <span> [<a href="https://arxiv.org/pdf/2107.01293">pdf</a>, <a href="https://arxiv.org/format/2107.01293">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</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/10.1016/j.physletb.2021.136589">10.1016/j.physletb.2021.136589 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The N$^3$LO Scheme-invariant QCD Evolution of the Non-singlet Structure Functions \boldmath $F^{\rm NS}_2(x,Q^2)$ and $g_1^{\rm NS}(x,Q^2)$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Saragnese%2C+M">M. Saragnese</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="2107.01293v1-abstract-short" style="display: inline;"> We present the scheme-invariant unpolarized and polarized flavor non-singlet evolution equation to N$^3$LO for the structure functions $F_2(x,Q^2)$ and $g_1(x,Q^2)$ including the charm- and bottom quark effects in the asymptotic representation. The corresponding evolution is based on the experimental measurement of the non-singlet structure functions at a starting scale $Q_0^2$. In this way the ev… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.01293v1-abstract-full').style.display = 'inline'; document.getElementById('2107.01293v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2107.01293v1-abstract-full" style="display: none;"> We present the scheme-invariant unpolarized and polarized flavor non-singlet evolution equation to N$^3$LO for the structure functions $F_2(x,Q^2)$ and $g_1(x,Q^2)$ including the charm- and bottom quark effects in the asymptotic representation. The corresponding evolution is based on the experimental measurement of the non-singlet structure functions at a starting scale $Q_0^2$. In this way the evolution does only depend on the strong coupling constant $伪_s(M_Z)$ or the QCD scale $螞_{\rm QCD}$ and the charm and bottom quark masses $m_c$ and $m_b$ and provides one of the cleanest ways to measure the strong coupling constant in future high luminosity deep-inelastic scattering experiments. The yet unknown parts of the 4-loop anomalous dimensions introduce only a marginal error in this analysis. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.01293v1-abstract-full').style.display = 'none'; document.getElementById('2107.01293v1-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> 2 July, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 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">14 pages Latex, 12 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 21--096, DO--TH 21/21, SAGEX--21--13--E </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2105.09572">arXiv:2105.09572</a> <span> [<a href="https://arxiv.org/pdf/2105.09572">pdf</a>, <a href="https://arxiv.org/ps/2105.09572">ps</a>, <a href="https://arxiv.org/format/2105.09572">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-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.104.034030">10.1103/PhysRevD.104.034030 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Logarithmic Contributions to the Polarized and Operator Matrix Elements in Deeply Inelastic Scattering </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=Saragnese%2C+M">M. Saragnese</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2105.09572v1-abstract-short" style="display: inline;"> We compute the logarithmic contributions to the polarized massive Wilson coefficients for deep-inelastic scattering in the asymptotic region $Q^2 \gg m^2$ to 3-loop order in the fixed-flavor number scheme and present the corresponding expressions for the polarized massive operator matrix elements needed in the variable flavor number scheme. The calculation is performed in the Larin scheme. For the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2105.09572v1-abstract-full').style.display = 'inline'; document.getElementById('2105.09572v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2105.09572v1-abstract-full" style="display: none;"> We compute the logarithmic contributions to the polarized massive Wilson coefficients for deep-inelastic scattering in the asymptotic region $Q^2 \gg m^2$ to 3-loop order in the fixed-flavor number scheme and present the corresponding expressions for the polarized massive operator matrix elements needed in the variable flavor number scheme. The calculation is performed in the Larin scheme. For the massive operator matrix elements $A_{qq,Q}^{(3),\rm PS}$ and $A_{qg,Q}^{(3),\rm S}$ the complete results are presented. The expressions are given in Mellin-$N$ space and in momentum fraction $z$-space. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2105.09572v1-abstract-full').style.display = 'none'; document.getElementById('2105.09572v1-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> 20 May, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 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">86 pages Latex</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 21--008, DO--TH 21/03, TTP 21--008, RISC Report Series 21-06, SAGEX 21--02--E </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 104, 034030 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2103.10652">arXiv:2103.10652</a> <span> [<a href="https://arxiv.org/pdf/2103.10652">pdf</a>, <a href="https://arxiv.org/ps/2103.10652">ps</a>, <a href="https://arxiv.org/format/2103.10652">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 - Theory">hep-th</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="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> Analytic integration methods in quantum field theory: an Introduction </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</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="2103.10652v1-abstract-short" style="display: inline;"> A survey is given on the present status of analytic calculation methods and the mathematical structures of zero- and single scale Feynman amplitudes which emerge in higher order perturbative calculations in the Standard Model of elementary particles, its extensions and associated model field theories, including effective field theories of different kind. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2103.10652v1-abstract-full" style="display: none;"> A survey is given on the present status of analytic calculation methods and the mathematical structures of zero- and single scale Feynman amplitudes which emerge in higher order perturbative calculations in the Standard Model of elementary particles, its extensions and associated model field theories, including effective field theories of different kind. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.10652v1-abstract-full').style.display = 'none'; document.getElementById('2103.10652v1-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, 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">34 pages Latex, 1 style file. arXiv admin note: text overlap with arXiv:1905.02148</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 21--038, DO-TH 21/09, SAGEX-21-06 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2103.08330">arXiv:2103.08330</a> <span> [<a href="https://arxiv.org/pdf/2103.08330">pdf</a>, <a href="https://arxiv.org/ps/2103.08330">ps</a>, <a href="https://arxiv.org/format/2103.08330">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 - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Symbolic Computation">cs.SC</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="Mathematical Physics">math-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.103.096025">10.1103/PhysRevD.103.096025 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Iterated integrals over letters induced by quadratic forms </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Ablinger%2C+J">J. Ablinger</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</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="2103.08330v1-abstract-short" style="display: inline;"> An automated treatment of iterated integrals based on letters induced by real-valued quadratic forms and Kummer--Poincar茅 letters is presented. These quantities emerge in analytic single and multi--scale Feynman diagram calculations. To compactify representations, one wishes to apply general properties of these quantities in computer-algebraic implementations. We provide the reduction to basis rep… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.08330v1-abstract-full').style.display = 'inline'; document.getElementById('2103.08330v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2103.08330v1-abstract-full" style="display: none;"> An automated treatment of iterated integrals based on letters induced by real-valued quadratic forms and Kummer--Poincar茅 letters is presented. These quantities emerge in analytic single and multi--scale Feynman diagram calculations. To compactify representations, one wishes to apply general properties of these quantities in computer-algebraic implementations. We provide the reduction to basis representations, expansions, analytic continuation and numerical evaluation of these quantities. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.08330v1-abstract-full').style.display = 'none'; document.getElementById('2103.08330v1-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 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">14 pages LATEX, 1 anc. file</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 21--031, DO--TH 21/05 RISC-Linz Report Series No. 21-05, SAGEX-21-05 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 103, 096025 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2102.12237">arXiv:2102.12237</a> <span> [<a href="https://arxiv.org/pdf/2102.12237">pdf</a>, <a href="https://arxiv.org/format/2102.12237">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</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/10.1016/j.physletb.2021.136250">10.1016/j.physletb.2021.136250 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The QED Initial State Corrections to the Forward-Backward Asymmetry of $e^+e^- \to 纬^*/Z^{0*}$ to Higher Orders </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2102.12237v1-abstract-short" style="display: inline;"> The QED initial state corrections are calculated to the forward-backward asymmetry for $e^+e^- \rightarrow 纬^*/{Z^{0}}^*$ in the leading logarithmic approximation to $O(伪^6 L^6)$ extending the known corrections up to $O(伪^2 L^2)$ in analytic form. We use the method of massive on-shell operator matrix elements and present the radiators both in Mellin-$N$ and momentum fraction $z$-space. Numerical r… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.12237v1-abstract-full').style.display = 'inline'; document.getElementById('2102.12237v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2102.12237v1-abstract-full" style="display: none;"> The QED initial state corrections are calculated to the forward-backward asymmetry for $e^+e^- \rightarrow 纬^*/{Z^{0}}^*$ in the leading logarithmic approximation to $O(伪^6 L^6)$ extending the known corrections up to $O(伪^2 L^2)$ in analytic form. We use the method of massive on-shell operator matrix elements and present the radiators both in Mellin-$N$ and momentum fraction $z$-space. Numerical results are presented for various energies around the $Z$-peak by also including energy cuts. These corrections are of relevance for the precision measurements at the FCC$\_$ee. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.12237v1-abstract-full').style.display = 'none'; document.getElementById('2102.12237v1-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> 24 February, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 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">Dedicated to the Memory of Tini Veltman, who made it possible to probe the Standard Model at high precision</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 21--013, DO--TH 21/04, TTP21--004, SAGEX--21--03 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2101.05733">arXiv:2101.05733</a> <span> [<a href="https://arxiv.org/pdf/2101.05733">pdf</a>, <a href="https://arxiv.org/ps/2101.05733">ps</a>, <a href="https://arxiv.org/format/2101.05733">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-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/10.1016/j.nuclphysb.2021.115331">10.1016/j.nuclphysb.2021.115331 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Polarized Transition Matrix Element $A_{gq}(N)$ of the Variable Flavor Number Scheme at $O(伪_s^3)$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Behring%2C+A">A. Behring</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=von+Manteuffel%2C+A">A. von Manteuffel</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</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="2101.05733v1-abstract-short" style="display: inline;"> We calculate the polarized massive operator matrix element $A_{gq}^{(3)}(N)$ to 3-loop order in Quantum Chromodynamics analytically at general values of the Mellin variable $N$ both in the single- and double-mass case in the Larin scheme. It is a transition function required in the variable flavor number scheme at $O(伪_s^3)$. We also present the results in momentum fraction space. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2101.05733v1-abstract-full" style="display: none;"> We calculate the polarized massive operator matrix element $A_{gq}^{(3)}(N)$ to 3-loop order in Quantum Chromodynamics analytically at general values of the Mellin variable $N$ both in the single- and double-mass case in the Larin scheme. It is a transition function required in the variable flavor number scheme at $O(伪_s^3)$. We also present the results in momentum fraction space. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2101.05733v1-abstract-full').style.display = 'none'; document.getElementById('2101.05733v1-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> 14 January, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 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">26 pages Latex</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 21-003, DO-TH 21/01, TTP 21-001, RISC Report Series 21-01, MSUHEP-21-002, SAGEX-21-01 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2007.14491">arXiv:2007.14491</a> <span> [<a href="https://arxiv.org/pdf/2007.14491">pdf</a>, <a href="https://arxiv.org/format/2007.14491">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 - Experiment">hep-ex</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 Experiment">nucl-ex</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/10.1088/1361-6471/abf3ba">10.1088/1361-6471/abf3ba <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Large Hadron-Electron Collider at the HL-LHC </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Agostini%2C+P">P. Agostini</a>, <a href="/search/hep-ph?searchtype=author&query=Aksakal%2C+H">H. Aksakal</a>, <a href="/search/hep-ph?searchtype=author&query=Alekhin%2C+S">S. Alekhin</a>, <a href="/search/hep-ph?searchtype=author&query=Allport%2C+P+P">P. P. Allport</a>, <a href="/search/hep-ph?searchtype=author&query=Andari%2C+N">N. Andari</a>, <a href="/search/hep-ph?searchtype=author&query=Andre%2C+K+D+J">K. D. J. Andre</a>, <a href="/search/hep-ph?searchtype=author&query=Angal-Kalinin%2C+D">D. Angal-Kalinin</a>, <a href="/search/hep-ph?searchtype=author&query=Antusch%2C+S">S. Antusch</a>, <a href="/search/hep-ph?searchtype=author&query=Bella%2C+L+A">L. Aperio Bella</a>, <a href="/search/hep-ph?searchtype=author&query=Apolinario%2C+L">L. Apolinario</a>, <a href="/search/hep-ph?searchtype=author&query=Apsimon%2C+R">R. Apsimon</a>, <a href="/search/hep-ph?searchtype=author&query=Apyan%2C+A">A. Apyan</a>, <a href="/search/hep-ph?searchtype=author&query=Arduini%2C+G">G. Arduini</a>, <a href="/search/hep-ph?searchtype=author&query=Ari%2C+V">V. Ari</a>, <a href="/search/hep-ph?searchtype=author&query=Armbruster%2C+A">A. Armbruster</a>, <a href="/search/hep-ph?searchtype=author&query=Armesto%2C+N">N. Armesto</a>, <a href="/search/hep-ph?searchtype=author&query=Auchmann%2C+B">B. Auchmann</a>, <a href="/search/hep-ph?searchtype=author&query=Aulenbacher%2C+K">K. Aulenbacher</a>, <a href="/search/hep-ph?searchtype=author&query=Azuelos%2C+G">G. Azuelos</a>, <a href="/search/hep-ph?searchtype=author&query=Backovic%2C+S">S. Backovic</a>, <a href="/search/hep-ph?searchtype=author&query=Bailey%2C+I">I. Bailey</a>, <a href="/search/hep-ph?searchtype=author&query=Bailey%2C+S">S. Bailey</a>, <a href="/search/hep-ph?searchtype=author&query=Balli%2C+F">F. Balli</a>, <a href="/search/hep-ph?searchtype=author&query=Behera%2C+S">S. Behera</a>, <a href="/search/hep-ph?searchtype=author&query=Behnke%2C+O">O. Behnke</a> , et al. (312 additional authors not shown) </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="2007.14491v2-abstract-short" style="display: inline;"> The Large Hadron electron Collider (LHeC) is designed to move the field of deep inelastic scattering (DIS) to the energy and intensity frontier of particle physics. Exploiting energy recovery technology, it collides a novel, intense electron beam with a proton or ion beam from the High Luminosity--Large Hadron Collider (HL-LHC). The accelerator and interaction region are designed for concurrent el… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2007.14491v2-abstract-full').style.display = 'inline'; document.getElementById('2007.14491v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2007.14491v2-abstract-full" style="display: none;"> The Large Hadron electron Collider (LHeC) is designed to move the field of deep inelastic scattering (DIS) to the energy and intensity frontier of particle physics. Exploiting energy recovery technology, it collides a novel, intense electron beam with a proton or ion beam from the High Luminosity--Large Hadron Collider (HL-LHC). The accelerator and interaction region are designed for concurrent electron-proton and proton-proton operation. This report represents an update of the Conceptual Design Report (CDR) of the LHeC, published in 2012. It comprises new results on parton structure of the proton and heavier nuclei, QCD dynamics, electroweak and top-quark physics. It is shown how the LHeC will open a new chapter of nuclear particle physics in extending the accessible kinematic range in lepton-nucleus scattering by several orders of magnitude. Due to enhanced luminosity, large energy and the cleanliness of the hadronic final states, the LHeC has a strong Higgs physics programme and its own discovery potential for new physics. Building on the 2012 CDR, the report represents a detailed updated design of the energy recovery electron linac (ERL) including new lattice, magnet, superconducting radio frequency technology and further components. Challenges of energy recovery are described and the lower energy, high current, 3-turn ERL facility, PERLE at Orsay, is presented which uses the LHeC characteristics serving as a development facility for the design and operation of the LHeC. An updated detector design is presented corresponding to the acceptance, resolution and calibration goals which arise from the Higgs and parton density function physics programmes. The paper also presents novel results on the Future Circular Collider in electron-hadron mode, FCC-eh, which utilises the same ERL technology to further extend the reach of DIS to even higher centre-of-mass energies. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2007.14491v2-abstract-full').style.display = 'none'; document.getElementById('2007.14491v2-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> 12 April, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 July, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 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">373 pages, many figures, to be published by J. Phys. G</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CERN-ACC-Note-2020-0002 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J.Phys.G 48 (2021) 11, 110501 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2006.07032">arXiv:2006.07032</a> <span> [<a href="https://arxiv.org/pdf/2006.07032">pdf</a>, <a href="https://arxiv.org/format/2006.07032">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 - 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.102.054014">10.1103/PhysRevD.102.054014 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Heavy-flavor PDF evolution and variable-flavor number scheme uncertainties in deep-inelastic scattering </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Alekhin%2C+S">S. Alekhin</a>, <a href="/search/hep-ph?searchtype=author&query=Bluemlein%2C+J">J. Bluemlein</a>, <a href="/search/hep-ph?searchtype=author&query=Moch%2C+S">S. Moch</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="2006.07032v1-abstract-short" style="display: inline;"> We consider a detailed account on the construction of the heavy-quark parton distribution functions for charm and bottom, starting from $n_f=3$ light flavors in the fixed-flavor number (FFN) scheme and by using the standard decoupling relations for heavy quarks in QCD. We also account for two-mass effects. Furthermore, different implementations of the variable-flavor-number (VFN) scheme in deep-in… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2006.07032v1-abstract-full').style.display = 'inline'; document.getElementById('2006.07032v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2006.07032v1-abstract-full" style="display: none;"> We consider a detailed account on the construction of the heavy-quark parton distribution functions for charm and bottom, starting from $n_f=3$ light flavors in the fixed-flavor number (FFN) scheme and by using the standard decoupling relations for heavy quarks in QCD. We also account for two-mass effects. Furthermore, different implementations of the variable-flavor-number (VFN) scheme in deep-inelastic scattering (DIS) are studied, with the particular focus on the resummation of large logarithms in $Q^2/m_h^2$, the ratio the virtuality of the exchanged gauge-boson $Q^2$ to the heavy-quark mass squared $m_h^2$. A little impact of resummation effects if found in the kinematic range of the existing data on the DIS charm-quark production so that they can be described very well within the FFN scheme. Finally, we study the theoretical uncertainties associated to the VFN scheme, which manifest predominantly at small $Q^2$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2006.07032v1-abstract-full').style.display = 'none'; document.getElementById('2006.07032v1-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> 12 June, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 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">20 pages, 12 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 20-061, DO-TH 20/05, SAGEX-20-09 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 102, 054014 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2004.08916">arXiv:2004.08916</a> <span> [<a href="https://arxiv.org/pdf/2004.08916">pdf</a>, <a href="https://arxiv.org/format/2004.08916">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 - Phenomenology">hep-ph</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 - Theory">hep-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/10.1016/j.nuclphysb.2020.115059">10.1016/j.nuclphysb.2020.115059 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Two-mass Contribution to the Three-Loop Polarized Operator Matrix Element $A_{gg,Q}^{(3)}$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Ablinger%2C+J">J. Ablinger</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=Goedicke%2C+A">A. Goedicke</a>, <a href="/search/hep-ph?searchtype=author&query=Saragnese%2C+M">M. Saragnese</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2004.08916v1-abstract-short" style="display: inline;"> We compute the two-mass contributions to the polarized massive operator matrix element $A_{gg,Q}^{(3)}$ at third order in the strong coupling constant $伪_s$ in Quantum Chromodynamics analytically. These corrections are important ingredients for the matching relations in the variable flavor number scheme and for the calculation of Wilson coefficients in deep--inelastic scattering in the asymptotic… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.08916v1-abstract-full').style.display = 'inline'; document.getElementById('2004.08916v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2004.08916v1-abstract-full" style="display: none;"> We compute the two-mass contributions to the polarized massive operator matrix element $A_{gg,Q}^{(3)}$ at third order in the strong coupling constant $伪_s$ in Quantum Chromodynamics analytically. These corrections are important ingredients for the matching relations in the variable flavor number scheme and for the calculation of Wilson coefficients in deep--inelastic scattering in the asymptotic regime $Q^2 \gg m_c^2, m_b^2$. The analytic result is expressed in terms of nested harmonic, generalized harmonic, cyclotomic and binomial sums in $N$-space and by iterated integrals involving square-root valued arguments in $z$ space, as functions of the mass ratio. Numerical results are presented. New two--scale iterative integrals are calculated. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.08916v1-abstract-full').style.display = 'none'; document.getElementById('2004.08916v1-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 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">59 Latex, 2 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 20--051, DO--TH 20/03, TTP 20--013, SAGEX--20--07--E </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2004.04287">arXiv:2004.04287</a> <span> [<a href="https://arxiv.org/pdf/2004.04287">pdf</a>, <a href="https://arxiv.org/format/2004.04287">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-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/10.1016/j.nuclphysb.2020.115045">10.1016/j.nuclphysb.2020.115045 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Subleading Logarithmic QED Initial State Corrections to $e^+e^- \rightarrow 纬^*/{Z^{0}}^*$ to $O(伪^6 L^5)$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Ablinger%2C+J">J. Ablinger</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2004.04287v1-abstract-short" style="display: inline;"> Using the method of massive operator matrix elements, we calculate the subleading QED initial state radiative corrections to the process $e^+e^- \rightarrow 纬^*/Z^*$ for the first three logarithmic contributions from $O(伪^3 L^3), O(伪^3 L^2), O(伪^3 L)$ to $O(伪^5 L^5), O(伪^5 L^4), O(伪^5 L^3)$ and compare their effects to the leading contribution $O(伪^6 L^6)$ and one more subleading term… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.04287v1-abstract-full').style.display = 'inline'; document.getElementById('2004.04287v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2004.04287v1-abstract-full" style="display: none;"> Using the method of massive operator matrix elements, we calculate the subleading QED initial state radiative corrections to the process $e^+e^- \rightarrow 纬^*/Z^*$ for the first three logarithmic contributions from $O(伪^3 L^3), O(伪^3 L^2), O(伪^3 L)$ to $O(伪^5 L^5), O(伪^5 L^4), O(伪^5 L^3)$ and compare their effects to the leading contribution $O(伪^6 L^6)$ and one more subleading term $O(伪^6 L^5)$. The calculation is performed in the limit of large center of mass energies squared $s \gg m_e^2$. These terms supplement the known corrections to $O(伪^2)$, which were completed recently. Given the high precision at future colliders operating at very large luminosity, these corrections are important for concise theoretical predictions. The present calculation needs the calculation of one more two--loop massive operator matrix element in QED. The radiators are obtained as solutions of the associated Callen--Symanzik equations in the massive case. The radiators can be expressed in terms of harmonic polylogarithms to weight {\sf w = 6} of argument $z$ and $(1-z)$ and in Mellin $N$ space by generalized harmonic sums. Numerical results are presented on the position of the $Z$ peak and corrections to the $Z$ width, $螕_Z$. The corrections calculated result into a final theoretical accuracy for $未M_Z$ and $未螕_Z$ which is estimated to be of O(30 keV) at an anticipated systematic accuracy at the FCC\_ee of \sim 100 keV. This precision cannot be reached, however, by including only the corrections up to $O(伪^3)$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.04287v1-abstract-full').style.display = 'none'; document.getElementById('2004.04287v1-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> 8 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">58 pages, 3 Figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 19--231, DO-TH 19/32, TTP20--012, SAGEX 19--36 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2003.14289">arXiv:2003.14289</a> <span> [<a href="https://arxiv.org/pdf/2003.14289">pdf</a>, <a href="https://arxiv.org/format/2003.14289">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-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/10.1016/j.nuclphysb.2020.115055">10.1016/j.nuclphysb.2020.115055 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The $O(伪^2)$ Initial State QED Corrections to $e^+e^- \rightarrow 纬^*/Z_0^*$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=Raab%2C+C">C. Raab</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="2003.14289v1-abstract-short" style="display: inline;"> We calculate the complete $O(伪^2)$ initial state radiation corrections to $e^+ e^-$ annihilation into a neutral vector boson in a direct analytic computation without any approximation. The corrections are represented in terms of iterated incomplete (elliptic) integrals over alphabets of square--root valued letters. Performing the limit $s \gg m_e^2$, we find discrepancies with the earlier results… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.14289v1-abstract-full').style.display = 'inline'; document.getElementById('2003.14289v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2003.14289v1-abstract-full" style="display: none;"> We calculate the complete $O(伪^2)$ initial state radiation corrections to $e^+ e^-$ annihilation into a neutral vector boson in a direct analytic computation without any approximation. The corrections are represented in terms of iterated incomplete (elliptic) integrals over alphabets of square--root valued letters. Performing the limit $s \gg m_e^2$, we find discrepancies with the earlier results of Ref.~\cite{Berends:1987ab} and confirm results obtained in Ref.~\cite{Blumlein:2011mi} where the effective method of massive operator matrix elements has been used, which works for all but the power corrections in $m^2_e/s$. In this way, we also confirm the validity of the factorization of massive partons in the Drell--Yan process. We add non--logarithmic terms at $O(伪^2)$ which have not been considered in previous calculations. The final results in the limit $s \gg m_e^2$ can be given in terms of Nielsen integrals. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.14289v1-abstract-full').style.display = 'none'; document.getElementById('2003.14289v1-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> 31 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">32 pages Latex, several figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 18--196, DO--TH 19/31, TTP 19--045, SAGEX 19--34 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1912.04390">arXiv:1912.04390</a> <span> [<a href="https://arxiv.org/pdf/1912.04390">pdf</a>, <a href="https://arxiv.org/ps/1912.04390">ps</a>, <a href="https://arxiv.org/format/1912.04390">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Symbolic Computation">cs.SC</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="Computational Physics">physics.comp-ph</span> </div> </div> <p class="title is-5 mathjax"> A refined machinery to calculate large moments from coupled systems of linear differential equations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">Johannes Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Marquard%2C+P">Peter Marquard</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">Carsten Schneider</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="1912.04390v1-abstract-short" style="display: inline;"> The large moment method can be used to compute a large number of moments of physical quantities that are described by coupled systems of linear differential equations. Besides these systems the algorithm requires a certain number of initial values as input, that are often hard to derive in a preprocessing step.Thus a major challenge is to keep the number of initial values as small as possible. We… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.04390v1-abstract-full').style.display = 'inline'; document.getElementById('1912.04390v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1912.04390v1-abstract-full" style="display: none;"> The large moment method can be used to compute a large number of moments of physical quantities that are described by coupled systems of linear differential equations. Besides these systems the algorithm requires a certain number of initial values as input, that are often hard to derive in a preprocessing step.Thus a major challenge is to keep the number of initial values as small as possible. We present the basic ideas of the underlying large moment method and present refined versions that reduce significantly the number of required initial values. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.04390v1-abstract-full').style.display = 'none'; document.getElementById('1912.04390v1-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> 9 December, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 19-225, DO-TH 19/13, SAGEX--19-35 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1912.03089">arXiv:1912.03089</a> <span> [<a href="https://arxiv.org/pdf/1912.03089">pdf</a>, <a href="https://arxiv.org/format/1912.03089">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</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"> The Gravitational Potential of Two Point Masses at Five Loops </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">Johannes Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Maier%2C+A">Andreas Maier</a>, <a href="/search/hep-ph?searchtype=author&query=Marquard%2C+P">Peter Marquard</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="1912.03089v1-abstract-short" style="display: inline;"> Corrections to the Newtonian gravitational potential from general relativity can be derived in a combined expansion around flat spacetime and a small velocity of the interacting bodies. We present the calculation of the static five-loop corrections in an effective field theory framework using techniques from multi-loop computations in particle physics. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1912.03089v1-abstract-full" style="display: none;"> Corrections to the Newtonian gravitational potential from general relativity can be derived in a combined expansion around flat spacetime and a small velocity of the interacting bodies. We present the calculation of the static five-loop corrections in an effective field theory framework using techniques from multi-loop computations in particle physics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.03089v1-abstract-full').style.display = 'none'; document.getElementById('1912.03089v1-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> 6 December, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 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">7 pages, no figures. Contribution to 14th International Symposium on Radiative Corrections (RADCOR2019)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 19-218, DO-TH 19/05, SAGEX-19-31 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1912.02536">arXiv:1912.02536</a> <span> [<a href="https://arxiv.org/pdf/1912.02536">pdf</a>, <a href="https://arxiv.org/format/1912.02536">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-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/10.1016/j.nuclphysb.2020.114945">10.1016/j.nuclphysb.2020.114945 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The three-loop single mass polarized pure singlet operator matrix element </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Ablinger%2C+J">J. Ablinger</a>, <a href="/search/hep-ph?searchtype=author&query=Behring%2C+A">A. Behring</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=von+Manteuffel%2C+A">A. von Manteuffel</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="1912.02536v1-abstract-short" style="display: inline;"> We calculate the massive polarized three-loop pure singlet operator matrix element $A_{Qq}^{(3), \rm PS}$ in the single mass case in the Larin scheme. This operator matrix element contributes to the massive polarized three-loop Wilson coefficient $H_{Qq}^{(3),\rm PS}$ in deep-inelastic scattering and constitutes a three-loop transition matrix element in the variable flavor number scheme. We provid… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.02536v1-abstract-full').style.display = 'inline'; document.getElementById('1912.02536v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1912.02536v1-abstract-full" style="display: none;"> We calculate the massive polarized three-loop pure singlet operator matrix element $A_{Qq}^{(3), \rm PS}$ in the single mass case in the Larin scheme. This operator matrix element contributes to the massive polarized three-loop Wilson coefficient $H_{Qq}^{(3),\rm PS}$ in deep-inelastic scattering and constitutes a three-loop transition matrix element in the variable flavor number scheme. We provide analytic results in Mellin $N$ and in $x$ space and study the behaviour of this operator matrix element in the region of small and large values of the Bjorken variable $x$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.02536v1-abstract-full').style.display = 'none'; document.getElementById('1912.02536v1-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 December, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 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">25 pages Latex, 2 Figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 19--216, DO--TH 19/02, TTP 19--043, MSUHEP-19-026, SAGEX 19-30 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1911.11630">arXiv:1911.11630</a> <span> [<a href="https://arxiv.org/pdf/1911.11630">pdf</a>, <a href="https://arxiv.org/format/1911.11630">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-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/10.1016/j.nuclphysb.2020.114916">10.1016/j.nuclphysb.2020.114916 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The three-loop polarized pure singlet operator matrix element with two different masses </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Ablinger%2C+J">J. Ablinger</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=Saragnese%2C+M">M. Saragnese</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="1911.11630v1-abstract-short" style="display: inline;"> We present the two-mass QCD contributions to the polarized pure singlet operator matrix element at three loop order in $x$-space. These terms are relevant for calculating the polarized structure function $g_1(x,Q^2)$ at $O(伪_s^3)$ as well as for the matching relations in the variable flavor number scheme and the polarized heavy quark distribution functions at the same order. The result for the ope… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.11630v1-abstract-full').style.display = 'inline'; document.getElementById('1911.11630v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1911.11630v1-abstract-full" style="display: none;"> We present the two-mass QCD contributions to the polarized pure singlet operator matrix element at three loop order in $x$-space. These terms are relevant for calculating the polarized structure function $g_1(x,Q^2)$ at $O(伪_s^3)$ as well as for the matching relations in the variable flavor number scheme and the polarized heavy quark distribution functions at the same order. The result for the operator matrix element is given in terms of generalized iterated integrals. These integrals depend on the mass ratio through the main argument, and the alphabet includes square--root valued letters. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.11630v1-abstract-full').style.display = 'none'; document.getElementById('1911.11630v1-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> 25 November, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 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">21 pages LATEX, 3 Figures. arXiv admin note: substantial text overlap with arXiv:1711.06717</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 19-163, DO-TH 19/19, TTP 19-038, SAGEX-19-23-E </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1911.06189">arXiv:1911.06189</a> <span> [<a href="https://arxiv.org/pdf/1911.06189">pdf</a>, <a href="https://arxiv.org/ps/1911.06189">ps</a>, <a href="https://arxiv.org/format/1911.06189">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 - Phenomenology">hep-ph</span> </div> </div> <p class="title is-5 mathjax"> The Polarized Three-Loop Anomalous Dimensions from a Massive Calculation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Behring%2C+A">Arnd Behring</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">Johannes Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">Abilio De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=Goedicke%2C+A">Alexander Goedicke</a>, <a href="/search/hep-ph?searchtype=author&query=Klein%2C+S">Sebastian Klein</a>, <a href="/search/hep-ph?searchtype=author&query=van+Manteuffel%2C+A">Andreas van Manteuffel</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">Carsten Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">Kay Sch枚nwald</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="1911.06189v1-abstract-short" style="display: inline;"> We present results on the calculation of the polarized 2- and 3-loop anomalous dimensions in a massive computation of the associated operator matrix element. We also discuss the treatment of $纬_5$ and derive results in the M-scheme.10 </span> <span class="abstract-full has-text-grey-dark mathjax" id="1911.06189v1-abstract-full" style="display: none;"> We present results on the calculation of the polarized 2- and 3-loop anomalous dimensions in a massive computation of the associated operator matrix element. We also discuss the treatment of $纬_5$ and derive results in the M-scheme.10 <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.06189v1-abstract-full').style.display = 'none'; document.getElementById('1911.06189v1-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, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 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">10 pages LATEX. arXiv admin note: substantial text overlap with arXiv:1908.03779</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 19--187, DO-TH 19/26, SAGEX-19-27, PoS(RADCOR19)047 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1911.05029">arXiv:1911.05029</a> <span> [<a href="https://arxiv.org/pdf/1911.05029">pdf</a>, <a href="https://arxiv.org/format/1911.05029">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</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/10.22323/1.375.0046">10.22323/1.375.0046 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Revisiting the $O(伪^2)$ Initial State QED Corrections to $e^+e^-$ Annihilation into a Neutral Boson </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=Raab%2C+C+G">C. G. Raab</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="1911.05029v1-abstract-short" style="display: inline;"> At $e^+ \, e^-$ colliders the QED--initial state radiation forms a large part of the radiative corrections. Their precise and fast evaluation is an essential asset for the experiments at LEP, the ILC and the FCC-ee, operating at high luminosity. A long standing problem in the analytic calculation of the $O(伪^2)$ initial state corrections concerns a discrepancy which has been observed between the r… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.05029v1-abstract-full').style.display = 'inline'; document.getElementById('1911.05029v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1911.05029v1-abstract-full" style="display: none;"> At $e^+ \, e^-$ colliders the QED--initial state radiation forms a large part of the radiative corrections. Their precise and fast evaluation is an essential asset for the experiments at LEP, the ILC and the FCC-ee, operating at high luminosity. A long standing problem in the analytic calculation of the $O(伪^2)$ initial state corrections concerns a discrepancy which has been observed between the result of Berends et al. (1988) \cite{Berends:1987ab} in the limit $m_e^2 \ll s$ and the result by Bl{眉}mlein et al. (2011) \cite{Blumlein:2011mi} using massive operator matrix elements deriving this limit directly. In order to resolve this important issue we recalculated this process by integrating directly over the phase space without any approximation. For parts of the corrections we find exact solutions of the cross section in terms of iterated integrals over square root valued letters representing incomplete elliptic integrals and iterations over them. The expansion in the limit $m_e^2 \ll s$ reveals errors in the constant $O(伪^2)$ term of the former calculation and yields agreement with the calculation based on massive operator matrix elements, which has impact on the experimental analysis programs. This finding also explicitly proofs the factorization of massive initial state particles in the high energy limit including the terms of $O(伪^2)$ for this process. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.05029v1-abstract-full').style.display = 'none'; document.getElementById('1911.05029v1-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> 12 November, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 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">9 pages LAEX</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 19--186, DO-TH 19/25, SAGEX-19-26 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1910.11165">arXiv:1910.11165</a> <span> [<a href="https://arxiv.org/pdf/1910.11165">pdf</a>, <a href="https://arxiv.org/format/1910.11165">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> </div> </div> <p class="title is-5 mathjax"> Resummation of large logarithms in the VFN scheme for DIS heavy-quark production </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Alekhin%2C+S">S. Alekhin</a>, <a href="/search/hep-ph?searchtype=author&query=Bluemlein%2C+J">J. Bluemlein</a>, <a href="/search/hep-ph?searchtype=author&query=Moch%2C+S">S. Moch</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="1910.11165v1-abstract-short" style="display: inline;"> We consider the impact of the resummation of large logarithms, which appear in the QCD evolution of the heavy-quark distributions, on the phenomenology of deep-inelastic heavy-quark production. The heavy-quark PDFs are derived using the fixed-order matching conditions as a boundary for the QCD evolution and the result obtained is compared to the distributions defined by the matching conditions at… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1910.11165v1-abstract-full').style.display = 'inline'; document.getElementById('1910.11165v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1910.11165v1-abstract-full" style="display: none;"> We consider the impact of the resummation of large logarithms, which appear in the QCD evolution of the heavy-quark distributions, on the phenomenology of deep-inelastic heavy-quark production. The heavy-quark PDFs are derived using the fixed-order matching conditions as a boundary for the QCD evolution and the result obtained is compared to the distributions defined by the matching conditions at all scales. With such an approach, the effect of heavy-quark PDF evolution is found to be sizable at LO and dramatically reduces at NLO. The NNLO evolved distributions are not very different from the NLO ones at large scales, however, show substantial differences at low virtualities, i.e. where the additional large logarithms are numerically not important, while a mismatch between the NLO accuracy of the matching conditions and the NNLO accuracy in the evolution kernels causes a substantial excess in the heavy-quark distributions. This excess propagates into the variable flavor number (VFN) scheme predictions for the deep-inelastic structure functions and has to be compensated by a decrease in the small-$x$ gluon distribution determined from PDF fits based on the VFN scheme, which should be considered as a theoretical uncertainty in VFN PDF fits and reaches $\sim 30\%$ for the small-$x$ gluon distribution extracted from the data on deep-inelastic charm-quark production. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1910.11165v1-abstract-full').style.display = 'none'; document.getElementById('1910.11165v1-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> 24 October, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 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">6 pages, 3 figures, proceedings of XXVII International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2018), 8-12 Apr, Torino (Italy)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 19-178, DO-TH 19/20 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1910.05759">arXiv:1910.05759</a> <span> [<a href="https://arxiv.org/pdf/1910.05759">pdf</a>, <a href="https://arxiv.org/format/1910.05759">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</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/10.1016/j.physletb.2019.135196">10.1016/j.physletb.2019.135196 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The effects of $O(伪^2)$ initial state QED corrections to $e^+e^- \rightarrow 纬^*/Z^*$ at very high luminosity colliders </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=Raab%2C+C+G">C. G. Raab</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="1910.05759v1-abstract-short" style="display: inline;"> We present numerical results on the recently completed $O(伪^2)$ initial state corrections to the process $e^+e^- \rightarrow 纬^*/Z^*$, which is a central process at past and future high energy and high luminsoity colliders for precision measurements of the properties of the $Z$-boson, the Higgs boson, and the top quark. We observe differences to an earlier result \cite{Berends:1987ab} in the non-l… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1910.05759v1-abstract-full').style.display = 'inline'; document.getElementById('1910.05759v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1910.05759v1-abstract-full" style="display: none;"> We present numerical results on the recently completed $O(伪^2)$ initial state corrections to the process $e^+e^- \rightarrow 纬^*/Z^*$, which is a central process at past and future high energy and high luminsoity colliders for precision measurements of the properties of the $Z$-boson, the Higgs boson, and the top quark. We observe differences to an earlier result \cite{Berends:1987ab} in the non-logarithmic contributions at $O(伪^2)$. The new result leads to a 4 MeV shift in the $Z$ width considering the lower end $s_0 = 4 m_蟿^2$ of the radiation region, which is larger than the present accuracy. We present predictions on the radiative corrections to the central processes $e^+e^- \rightarrow 纬^*/Z^*$, $e^+e^- \rightarrow Z H$ and $e^+e^- \rightarrow t \overline{t}$ planned at future colliders like the ILC, CLIC, Fcc\_ee and CEPC to measure the mass and the width of the $Z$ boson, the Higgs boson and the top quark, for which the present corrections are significant. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1910.05759v1-abstract-full').style.display = 'none'; document.getElementById('1910.05759v1-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 October, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 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">4 pages LATEX, 6 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 19--162, DO--TH 19/18, SAGEX-19-22 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1909.03533">arXiv:1909.03533</a> <span> [<a href="https://arxiv.org/pdf/1909.03533">pdf</a>, <a href="https://arxiv.org/format/1909.03533">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> </div> </div> <p class="title is-5 mathjax"> An Update of the ABMP16 PDF Fit </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Alekhin%2C+S">S. Alekhin</a>, <a href="/search/hep-ph?searchtype=author&query=Bluemlein%2C+J">J. Bluemlein</a>, <a href="/search/hep-ph?searchtype=author&query=Moch%2C+S">S. Moch</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="1909.03533v1-abstract-short" style="display: inline;"> We present an updated version of the ABMP16 nucleon PDFs, which is tuned by using recent precise data on $W$- and $Z/纬^*$-production at the LHC and the final HERA data on DIS $c$- and $b$-quark production and by imposing a stringent $Q^2$-cut on the inclusive DIS data in order to avoid the impact of higher twist terms at small $x$ at HERA. The new $W$- and $Z$-boson production data, in particular… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1909.03533v1-abstract-full').style.display = 'inline'; document.getElementById('1909.03533v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1909.03533v1-abstract-full" style="display: none;"> We present an updated version of the ABMP16 nucleon PDFs, which is tuned by using recent precise data on $W$- and $Z/纬^*$-production at the LHC and the final HERA data on DIS $c$- and $b$-quark production and by imposing a stringent $Q^2$-cut on the inclusive DIS data in order to avoid the impact of higher twist terms at small $x$ at HERA. The new $W$- and $Z$-boson production data, in particular the updated version of the ATLAS data at the c.m.s. energy 7 TeV, are well accommodated into the present fit. The strange sea distribution obtained is consistent with the average of the up and down quark ones at small $x$. However, it is still suppressed with respect to the non-strange one by a factor of $\sim 0.5$ at moderate $x$. The small-$x$ gluon distribution is enhanced as compared to the previous ABMP16 fit, in line with updated data on the DIS $c$-quark production. Finally, a good description of the non-resonant $纬^*/Z$-production data, which are included into the ABM analysis for the first time, is achieved provided the photon-initiated lepton pair production is taken into account. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1909.03533v1-abstract-full').style.display = 'none'; document.getElementById('1909.03533v1-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> 8 September, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 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">6 pages, 5 figures, proceedings of XXVII International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2018), 8-12 Apr, Torino (Italy)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 19--152, DO-TH 19/16, SAGEX-19-21 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1908.03779">arXiv:1908.03779</a> <span> [<a href="https://arxiv.org/pdf/1908.03779">pdf</a>, <a href="https://arxiv.org/format/1908.03779">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-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/10.1016/j.nuclphysb.2019.114753">10.1016/j.nuclphysb.2019.114753 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Polarized Three-Loop Anomalous Dimensions from On-Shell Massive Operator Matrix Elements </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Behring%2C+A">A. Behring</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=De+Freitas%2C+A">A. De Freitas</a>, <a href="/search/hep-ph?searchtype=author&query=Goedicke%2C+A">A. Goedicke</a>, <a href="/search/hep-ph?searchtype=author&query=Klein%2C+S">S. Klein</a>, <a href="/search/hep-ph?searchtype=author&query=von+Manteuffel%2C+A">A. von Manteuffel</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</a>, <a href="/search/hep-ph?searchtype=author&query=Sch%C3%B6nwald%2C+K">K. Sch枚nwald</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="1908.03779v1-abstract-short" style="display: inline;"> We calculate all contributions $\propto T_F$ to the polarized three-loop anomalous dimensions in the M-scheme using massive operator matrix elements and compare to results in the literature. This includes the complete anomalous dimensions $纬_{qq}^{(2),\rm PS}$ and $纬_{qg}^{(2)}$. We also obtain the complete two-loop polarized anomalous dimensions in an independent calculation. While for most of th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.03779v1-abstract-full').style.display = 'inline'; document.getElementById('1908.03779v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1908.03779v1-abstract-full" style="display: none;"> We calculate all contributions $\propto T_F$ to the polarized three-loop anomalous dimensions in the M-scheme using massive operator matrix elements and compare to results in the literature. This includes the complete anomalous dimensions $纬_{qq}^{(2),\rm PS}$ and $纬_{qg}^{(2)}$. We also obtain the complete two-loop polarized anomalous dimensions in an independent calculation. While for most of the anomalous dimensions the usual direct computation methods in Mellin $N$-space can be applied since all recurrences factorize at first order, this is not the case for $纬_{qg}^{(2)}$. Due to the necessity of deeper expansions of the master integrals in the dimensional parameter $\varepsilon = D-4$, we had to use the method of arbitrary high moments to eliminate elliptic contributions in intermediate steps. 4000 moments were generated to determine this anomalous dimension and 2640 moments turned out to be sufficient. As an aside, we also recalculate the contributions $\propto T_F$ to the three-loop QCD $尾$-function. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.03779v1-abstract-full').style.display = 'none'; document.getElementById('1908.03779v1-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> 10 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">40 pages Latex, 2 Figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 19-118,DO-TH 19/12, MSUHEP-19-013 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1908.00357">arXiv:1908.00357</a> <span> [<a href="https://arxiv.org/pdf/1908.00357">pdf</a>, <a href="https://arxiv.org/format/1908.00357">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 - 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/10.1016/j.nuclphysb.2019.114751">10.1016/j.nuclphysb.2019.114751 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Heavy Fermion Contributions to the Massive Three Loop Form Factors </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Marquard%2C+P">P. Marquard</a>, <a href="/search/hep-ph?searchtype=author&query=Rana%2C+N">N. Rana</a>, <a href="/search/hep-ph?searchtype=author&query=Schneider%2C+C">C. Schneider</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="1908.00357v1-abstract-short" style="display: inline;"> We compute the $n_h$ terms to the massive three loop vector-, axialvector-, scalar- and pseudoscalar form factors in a direct analytic calculation using the method of large moments. This method has the advantage, that the master integrals have to be dealt with only in their moment representation, allowing to also consider quantities which obey differential equations, which are not first order fact… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.00357v1-abstract-full').style.display = 'inline'; document.getElementById('1908.00357v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1908.00357v1-abstract-full" style="display: none;"> We compute the $n_h$ terms to the massive three loop vector-, axialvector-, scalar- and pseudoscalar form factors in a direct analytic calculation using the method of large moments. This method has the advantage, that the master integrals have to be dealt with only in their moment representation, allowing to also consider quantities which obey differential equations, which are not first order factorizable (elliptic and higher), already at this level. To obtain all the associated recursions, up to 8000 moments had to be calculated. A new technique has been applied to solve the associated differential equation systems. Here the decoupling is performed such, that only minimal depth $蔚$--expansions had to be performed for non--first-order factorizing systems, minimizing the calculation of initial values. The pole terms in the dimensional parameter $蔚$ can be completely predicted using renormalization group methods, as confirmed by the present results. A series of contributions at $O(蔚^0)$ have first order factorizable representations. For a smaller number of color--zeta projections this is not the case. All first order factorizing terms can be represented by harmonic polylogarithms. We also obtain analytic results for the non--first-order factorizing terms by Taylor series in a variable $x$, for which we have calculated at least 2000 expansion coefficients, in an approximation. Based on this representation the form factors can be given in the Euclidean region and in the region $q^2 \approx 0$. Numerical results are presented. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.00357v1-abstract-full').style.display = 'none'; document.getElementById('1908.00357v1-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> 1 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">88 pages, 13 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 19--095, DO--TH 19/08, SAGEX-19-10, TIF-UNIMI-2019-13 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1907.01435">arXiv:1907.01435</a> <span> [<a href="https://arxiv.org/pdf/1907.01435">pdf</a>, <a href="https://arxiv.org/format/1907.01435">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 - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> </div> </div> <p class="title is-5 mathjax"> $伪_s$(2019): Precision measurements of the QCD coupling </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-ph?searchtype=author&query=d%27Enterria%2C+D">David d'Enterria</a>, <a href="/search/hep-ph?searchtype=author&query=Kluth%2C+S">Stefan Kluth</a>, <a href="/search/hep-ph?searchtype=author&query=Alekhin%2C+S">S. Alekhin</a>, <a href="/search/hep-ph?searchtype=author&query=Baikov%2C+P+A">P. A. Baikov</a>, <a href="/search/hep-ph?searchtype=author&query=Banfi%2C+A">A. Banfi</a>, <a href="/search/hep-ph?searchtype=author&query=Barreiro%2C+F">F. Barreiro</a>, <a href="/search/hep-ph?searchtype=author&query=Bazavov%2C+A">A. Bazavov</a>, <a href="/search/hep-ph?searchtype=author&query=Bethke%2C+S">S. Bethke</a>, <a href="/search/hep-ph?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/hep-ph?searchtype=author&query=Boito%2C+D">D. Boito</a>, <a href="/search/hep-ph?searchtype=author&query=Brambilla%2C+N">N. Brambilla</a>, <a href="/search/hep-ph?searchtype=author&query=Britzger%2C+D">D. Britzger</a>, <a href="/search/hep-ph?searchtype=author&query=Brodsky%2C+S+J">S. J. Brodsky</a>, <a href="/search/hep-ph?searchtype=author&query=Camarda%2C+S">S. Camarda</a>, <a href="/search/hep-ph?searchtype=author&query=Chetyrkin%2C+K+G">K. G. Chetyrkin</a>, <a href="/search/hep-ph?searchtype=author&query=d%27Enterria%2C+D">D. d'Enterria</a>, <a href="/search/hep-ph?searchtype=author&query=Brida%2C+M+D">M. Dalla Brida</a>, <a href="/search/hep-ph?searchtype=author&query=Tormo%2C+X+G+i">X. Garcia i Tormo</a>, <a href="/search/hep-ph?searchtype=author&query=Golterman%2C+M">M. Golterman</a>, <a href="/search/hep-ph?searchtype=author&query=Horsley%2C+R">R. Horsley</a>, <a href="/search/hep-ph?searchtype=author&query=Huston%2C+J">J. Huston</a>, <a href="/search/hep-ph?searchtype=author&query=Jamin%2C+M">M. Jamin</a>, <a href="/search/hep-ph?searchtype=author&query=Kardos%2C+A">A. Kardos</a>, <a href="/search/hep-ph?searchtype=author&query=Keshavarzi%2C+A">A. Keshavarzi</a>, <a href="/search/hep-ph?searchtype=author&query=Kluth%2C+S">S. Kluth</a> , et al. (28 additional authors not shown) </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="1907.01435v1-abstract-short" style="display: inline;"> This document collects a written summary of all contributions presented at the workshop "$伪_s$(2019): Precision measurements of the strong coupling" held at ECT* (Trento) in Feb. 11--15, 2019. The workshop explored in depth the latest developments on the determination of the QCD coupling $伪_s$ from the key categories where high precision measurements are available: (i) lattice QCD, (ii) hadronic… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1907.01435v1-abstract-full').style.display = 'inline'; document.getElementById('1907.01435v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1907.01435v1-abstract-full" style="display: none;"> This document collects a written summary of all contributions presented at the workshop "$伪_s$(2019): Precision measurements of the strong coupling" held at ECT* (Trento) in Feb. 11--15, 2019. The workshop explored in depth the latest developments on the determination of the QCD coupling $伪_s$ from the key categories where high precision measurements are available: (i) lattice QCD, (ii) hadronic $蟿$ decays, (iii) deep-inelastic scattering and parton distribution functions, (iv) event shapes, jet cross sections, and other hadronic final-states in $e^+e^-$ collisions, (v) Z boson and W boson hadronic decays, and (vi) hadronic final states in p-p collisions. The status of the current theoretical and experimental uncertainties associated to each extraction method, and future perspectives were thoroughly reviewed. Novel $伪_s$ determination approaches were discussed, as well as the combination method used to obtain a world-average value of the QCD coupling at the Z mass pole. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1907.01435v1-abstract-full').style.display = 'none'; document.getElementById('1907.01435v1-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> 2 July, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 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">154 pages, 125 figures. Workshop Proceedings, ECT*, Trento, 11--15 February 2019</span> </p> </li> </ol> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Blumlein%2C+J&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Blumlein%2C+J&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Blumlein%2C+J&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> <li> <a href="/search/?searchtype=author&query=Blumlein%2C+J&start=100" class="pagination-link " aria-label="Page 3" aria-current="page">3 </a> </li> <li> <a href="/search/?searchtype=author&query=Blumlein%2C+J&start=150" class="pagination-link " aria-label="Page 4" aria-current="page">4 </a> </li> <li> <a 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