skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Quasi parton distributions and the gradient flow

Abstract

We propose a new approach to determining quasi parton distribution functions (PDFs) from lattice quantum chromodynamics. By incorporating the gradient flow, this method guarantees that the lattice quasi PDFs are finite in the continuum limit and evades the thorny, and as yet unresolved, issue of the renormalization of quasi PDFs on the lattice. In the limit that the flow time is much smaller than the length scale set by the nucleon momentum, the moments of the smeared quasi PDF are proportional to those of the lightfront PDF. Finally, we use this relation to derive evolution equations for the matching kernel that relates the smeared quasi PDF and the light-front PDF.

Authors:
 [1];  [2]
  1. Rutgers, the State Univ. of New Jersey, Piscataway, NJ (United States)
  2. College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1350963
Report Number(s):
JLAB-THY-16-2402; DOE/OR/23177-4026; arXiv:1612.01584
Journal ID: ISSN 1029-8479; PII: 5728; TRN: US1700589
Grant/Contract Number:
AC05-06OR23177
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 3; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice QCD; Lattice Quantum Field Theory

Citation Formats

Monahan, Christopher, and Orginos, Kostas. Quasi parton distributions and the gradient flow. United States: N. p., 2017. Web. doi:10.1007/JHEP03(2017)116.
Monahan, Christopher, & Orginos, Kostas. Quasi parton distributions and the gradient flow. United States. doi:10.1007/JHEP03(2017)116.
Monahan, Christopher, and Orginos, Kostas. Wed . "Quasi parton distributions and the gradient flow". United States. doi:10.1007/JHEP03(2017)116. https://www.osti.gov/servlets/purl/1350963.
@article{osti_1350963,
title = {Quasi parton distributions and the gradient flow},
author = {Monahan, Christopher and Orginos, Kostas},
abstractNote = {We propose a new approach to determining quasi parton distribution functions (PDFs) from lattice quantum chromodynamics. By incorporating the gradient flow, this method guarantees that the lattice quasi PDFs are finite in the continuum limit and evades the thorny, and as yet unresolved, issue of the renormalization of quasi PDFs on the lattice. In the limit that the flow time is much smaller than the length scale set by the nucleon momentum, the moments of the smeared quasi PDF are proportional to those of the lightfront PDF. Finally, we use this relation to derive evolution equations for the matching kernel that relates the smeared quasi PDF and the light-front PDF.},
doi = {10.1007/JHEP03(2017)116},
journal = {Journal of High Energy Physics (Online)},
number = 3,
volume = 2017,
place = {United States},
year = {Wed Mar 22 00:00:00 EDT 2017},
month = {Wed Mar 22 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 7works
Citation information provided by
Web of Science

Save / Share:
  • Here, we show that quasi-PDFs may be treated as hybrids of PDFs and primordial rest-frame momentum distributions of partons. This results in a complicated convolution nature of quasi-PDFs that necessitates using large p 3≳ 3 GeV momenta to get reasonably close to the PDF limit. Furthemore, as an alternative approach, we propose to use pseudo-PDFs P(x, zmore » $$2\atop{3}$$) that generalize the light-front PDFs onto spacelike intervals and are related to Ioffe-time distributions M (v, z$$2\atop{3}$$), the functions of the Ioffe time v = p 3 z 3 and the distance parameter z$$2\atop{3}$$ with respect to which it displays perturbative evolution for small z 3. In this form, one may divide out the z$$2\atop{3}$$ dependence coming from the primordial rest-frame distribution and from the problematic factor due to lattice renormalization of the gauge link. The v-dependence remains intact and determines the shape of PDFs.« less
    Cited by 5
  • We study the impact of non-zero (and apparently large) value of the nucleon mass M on the shape of parton quasi-distributions Q(y,p 3), in particular on its change with the change of the nucleon momentum p 3. We observe that the usual target-mass corrections induced by the M-dependence of the twist-2 operators are rather small. Moreover, we show that within the framework based on parametrizations by transverse momentum dependent distribution functions (TMDs) these corrections are canceled by higher-twist contributions. Lastly, we identify a novel source of kinematic target-mass dependence of TMDs and build models corrected for such dependence. We findmore » that resulting changes may be safely neglected for p 3≳2M.« less
  • We study the impact of non-zero (and apparently large) value of the nucleon mass M on the shape of parton quasi-distributions Q(y,p 3), in particular on its change with the change of the nucleon momentum p 3. We observe that the usual target-mass corrections induced by the M-dependence of the twist-2 operators are rather small. Moreover, we show that within the framework based on parametrizations by transverse momentum dependent distribution functions (TMDs) these corrections are canceled by higher-twist contributions. Lastly, we identify a novel source of kinematic target-mass dependence of TMDs and build models corrected for such dependence. We findmore » that resulting changes may be safely neglected for p 3≳2M.« less
  • Using the formalism of parton virtuality distribution functions (VDFs) we establish a connection between the transverse momentum dependent distributions (TMDs) F(x,k 2) and quasi-distributions (PQDs) Q(y,p 3) introduced recently by X. Ji for lattice QCD extraction of parton distributions f(x). We build models for PQDs from the VDF-based models for soft TMDs, and analyze the p 3 dependence of the resulting PQDs. We observe a strong nonperturbative evolution of PQDs for small and moderately large values of p 3 reflecting the transverse momentum dependence of TMDs. Furthermore, the study of PQDs on the lattice in the domain of strongmore » nonperturbative effects opens a new perspective for investigation of the 3-dimensional hadron structure.« less