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Title: Theory and applications of parton pseudodistributions

Abstract

We review the basic theory of the parton pseudodistributions approach and its applications to lattice extractions of parton distribution functions. The crucial idea of the approach is the realization that the correlator $M(z,p)$ of the parton fields is a function $M(ν,-z^2)$ of Lorentz invariants $ν=-(zp)$, the Ioffe time, and the invariant interval $z^2$. This observation allows to extract the Ioffe-time distribution $M(ν,-z^2)$ from Euclidean separations z accessible on the lattice. Another basic feature is the use of the ratio $M(ν,-z^2)≡M(ν,-z^2)/M(0,-z^2)$, that allows to eliminate artificial ultraviolet divergence generated by the gauge link for spacelike intervals. The remaining $z^2$-dependence of the reduced Ioffe-time distribution $M(ν,-z^2)$ corresponds to perturbative evolution, and can be converted into the scale-dependence of parton distributions $f(x,μ^2)$ using matching relations. The ν-dependence of $M(ν,-z^2)$ governs the x-dependence of parton densities $f(x,μ^2)$. The perturbative evolution was successfully observed in exploratory quenched lattice calculation. The analysis of its precise data provides a framework for extraction of parton densities using the pseudodistributions approach. It was used in the recently performed calculations of the nucleon and pion valence quark distributions. We also discuss matching conditions for the pion distribution amplitude and generalized parton distributions, the lattice studies of which are now inmore » progress.« less

Authors:
ORCiD logo [1]
  1. Old Dominion Univ., Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP)
OSTI Identifier:
1604344
Report Number(s):
JLAB-THY-19-3118; DOE/OR-23177-4856; arXiv:1912.04244
Journal ID: ISSN 0217-751X
Grant/Contract Number:  
FG02-97ER41028; AC05-06OR23177
Resource Type:
Accepted Manuscript
Journal Name:
International Journal of Modern Physics A
Additional Journal Information:
Journal Volume: 35; Journal Issue: 05; Journal ID: ISSN 0217-751X
Publisher:
World Scientific
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Parton distributions; lattice; quantum chromodynamics

Citation Formats

Radyushkin, A. V. Theory and applications of parton pseudodistributions. United States: N. p., 2020. Web. doi:10.1142/S0217751X20300021.
Radyushkin, A. V. Theory and applications of parton pseudodistributions. United States. doi:https://doi.org/10.1142/S0217751X20300021
Radyushkin, A. V. Thu . "Theory and applications of parton pseudodistributions". United States. doi:https://doi.org/10.1142/S0217751X20300021. https://www.osti.gov/servlets/purl/1604344.
@article{osti_1604344,
title = {Theory and applications of parton pseudodistributions},
author = {Radyushkin, A. V.},
abstractNote = {We review the basic theory of the parton pseudodistributions approach and its applications to lattice extractions of parton distribution functions. The crucial idea of the approach is the realization that the correlator $M(z,p)$ of the parton fields is a function $M(ν,-z^2)$ of Lorentz invariants $ν=-(zp)$, the Ioffe time, and the invariant interval $z^2$. This observation allows to extract the Ioffe-time distribution $M(ν,-z^2)$ from Euclidean separations z accessible on the lattice. Another basic feature is the use of the ratio $M(ν,-z^2)≡M(ν,-z^2)/M(0,-z^2)$, that allows to eliminate artificial ultraviolet divergence generated by the gauge link for spacelike intervals. The remaining $z^2$-dependence of the reduced Ioffe-time distribution $M(ν,-z^2)$ corresponds to perturbative evolution, and can be converted into the scale-dependence of parton distributions $f(x,μ^2)$ using matching relations. The ν-dependence of $M(ν,-z^2)$ governs the x-dependence of parton densities $f(x,μ^2)$. The perturbative evolution was successfully observed in exploratory quenched lattice calculation. The analysis of its precise data provides a framework for extraction of parton densities using the pseudodistributions approach. It was used in the recently performed calculations of the nucleon and pion valence quark distributions. We also discuss matching conditions for the pion distribution amplitude and generalized parton distributions, the lattice studies of which are now in progress.},
doi = {10.1142/S0217751X20300021},
journal = {International Journal of Modern Physics A},
number = 05,
volume = 35,
place = {United States},
year = {2020},
month = {2}
}

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