Origin and resummation of threshold logarithms in the lattice QCD calculations of PDFs

Gao, Xiang; Lee, Kyle; Mukherjee, Swagato; Shugert, Charles; Zhao, Yong

doi:10.1103/physrevd.103.094504

Title: Origin and resummation of threshold logarithms in the lattice QCD calculations of PDFs

Journal Article · Tue May 11 00:00:00 EDT 2021 · Physical Review. D.

DOI:https://doi.org/10.1103/physrevd.103.094504· OSTI ID:1784489

Gao, Xiang ^[1]; Lee, Kyle ^[2];

^[3]; Shugert, Charles ^[4]; Zhao, Yong ^[5]

Brookhaven National Lab. (BNL), Upton, NY (United States); Tsinghua Univ., Beijing (China)
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
Brookhaven National Lab. (BNL), Upton, NY (United States)
Brookhaven National Lab. (BNL), Upton, NY (United States); Stony Brook Univ., NY (United States)
Brookhaven National Lab. (BNL), Upton, NY (United States); Argonne National Lab. (ANL), Argonne, IL (United States)

Many present lattice QCD approaches to calculate the parton distribution functions (PDFs) rely on a factorization formula or effective theory expansion of certain Euclidean matrix elements in boosted hadron states. In the quasi- and pseudo-PDF methods, the matching coefficient in the factorization or expansion formula includes large logarithms near the threshold, which arise from the subtle interplay of collinear and soft divergences of an underlying 3D momentum distribution. We use the standard prescription to resum such logarithms in the Mellin-moment space at next-to-leading logarithmic accuracy, which also accounts for the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution, and we show that it can suppress the PDF at large x . Unlike the deep inelastic scattering and Drell-Yan cross sections, the resummation formula is away from the Landau pole. We then apply our formulation to reanalyze the recent lattice results for the pion valence PDF, and find that within the current data sensitivity, the effect of threshold resummation is marginal for the accessible moments and the PDF at large x.

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0012704

OSTI ID:: 1784489

Report Number(s):: BNL-221451-2021-JAAM; TRN: US2210196

Journal Information:: Physical Review. D., Vol. 103, Issue 9; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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