Origin and resummation of threshold logarithms in the lattice QCD calculations of PDFs
Abstract
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.
- Authors:
-
[3];
- 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)
- Publication Date:
- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- OSTI Identifier:
- 1784489
- Report Number(s):
- BNL-221451-2021-JAAM
Journal ID: ISSN 2470-0010; TRN: US2210196
- Grant/Contract Number:
- SC0012704
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. D.
- Additional Journal Information:
- Journal Volume: 103; Journal Issue: 9; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Deep inelastic scattering; Effective field theory; Lattice QCD; Perturbative QCD; Quantum chromodynamics
Citation Formats
Gao, Xiang, Lee, Kyle, Mukherjee, Swagato, Shugert, Charles, and Zhao, Yong. Origin and resummation of threshold logarithms in the lattice QCD calculations of PDFs. United States: N. p., 2021.
Web. doi:10.1103/physrevd.103.094504.
Gao, Xiang, Lee, Kyle, Mukherjee, Swagato, Shugert, Charles, & Zhao, Yong. Origin and resummation of threshold logarithms in the lattice QCD calculations of PDFs. United States. https://doi.org/10.1103/physrevd.103.094504
Gao, Xiang, Lee, Kyle, Mukherjee, Swagato, Shugert, Charles, and Zhao, Yong. Tue .
"Origin and resummation of threshold logarithms in the lattice QCD calculations of PDFs". United States. https://doi.org/10.1103/physrevd.103.094504. https://www.osti.gov/servlets/purl/1784489.
@article{osti_1784489,
title = {Origin and resummation of threshold logarithms in the lattice QCD calculations of PDFs},
author = {Gao, Xiang and Lee, Kyle and Mukherjee, Swagato and Shugert, Charles and Zhao, Yong},
abstractNote = {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.},
doi = {10.1103/physrevd.103.094504},
journal = {Physical Review. D.},
number = 9,
volume = 103,
place = {United States},
year = {Tue May 11 00:00:00 EDT 2021},
month = {Tue May 11 00:00:00 EDT 2021}
}
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