Abstract
Lattice QCD offers the possibility of computing parton distributions from first principles, although not in the usual \( \overline{MS} \) factorization scheme. Calculations are therefore matched to \( \overline{MS} \) using a perturbative procedure which is the source of significant uncertainty within the currently accessible kinematics. We present the possibility of computing the z2 evolution of non-singlet pseudo-parton distribution functions within the short factorization scheme in a numerically improvable way. The goal is to have tools to evolve a calculation to a scale where perturbative uncertainties are less pronounced. We compare a numerical extraction of the evolution operator from lattice data to the computation of z2 dependence in perturbation theory. Finally, we discuss how this numerical work may be extended to address the two-scale problem that arises when the Ioffe time range must be made large to extend the reach of the calculation of the pseudo-PDF to smaller values of the momentum fraction.
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Acknowledgments
We thank Jianwei Qiu, Anatoly Radyushkin and Valerio Bertone for stimulating discussions and comments on the manuscript. KO and HD were supported in part by the U.S. DOE Grant #DE-FG02-04ER41302. CJM is supported in part by the U.S. DOE EC Award #DE-SC0023047. KO and JK were supported in part by the US Department of Energy (DOE) Contract No. DE-AC05-06OR23177, under which Jefferson Science Associates, LLC operates Jefferson Lab. SZ acknowledges support by the French Centre national de la recherche scientifique (CNRS) under an Emergence@INP 2023 project. This work has benefited from the collaboration enabled by the Quark-Gluon Tomography (QGT) Topical Collaboration, U.S. DOE Award DE-SC0023646. The authors also acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources, like Frontera computing system [96] that has contributed to the research results reported within this paper.
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Dutrieux, H., Karpie, J., Monahan, C. et al. Evolution of parton distribution functions in the short-distance factorization scheme. J. High Energ. Phys. 2024, 61 (2024). https://doi.org/10.1007/JHEP04(2024)061
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DOI: https://doi.org/10.1007/JHEP04(2024)061