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Title: Quark pseudodistributions at short distances

We perform a one-loop study of the small-$$z_3^2$$ behavior of the Ioffe-time distribution (ITD) $${\cal M} (\nu, z_3^2)$$, the basic function that may be converted into parton pseudo- and quasi-distributions. We calculate the corrections at the operator level, so that our results may be later used for pseudo-distribution amplitudes and generalized parton pseudo-distributions. We separate two sources of the $$z_3^2$$-dependence at small $$z_3^2$$. One is related to the ultraviolet (UV) singularities generated by the gauge link, and another to short-distance logarithms generating perturbative evolution of parton densities. Our calculation explicitly shows that, for a finite UV cut-off, the UV-singular terms vanish when $$z_3^2=0$$. The UV divergences are absent in the ratio $${\cal M} (\nu, z_3^2)/{\cal M} (0, z_3^2)$$ ("reduced" ITD). Still, it has a non-trivial short-distance behavior due to $$\ln z_3^2 \Lambda^2$$ terms generating perturbative evolution of the parton densities. We give an explicit expression, up to constant terms, for the reduced ITD at one loop. It may be used in extraction of PDFs from the lattice QCD simulations. We also use our results to get new insights concerning the structure of parton quasi-distributions at one-loop level.
Authors:
ORCiD logo [1]
  1. Old Dominion Univ., Norfolk, VA (United States). Physics Dept.; Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Publication Date:
Report Number(s):
JLAB-THY-17-2579; DOE/OR/-23177-4247; arXiv:1710.08813
Journal ID: ISSN 0370-2693; PII: S0370269318303071
Grant/Contract Number:
AC05-06OR23177; FG02-97ER41028
Type:
Published Article
Journal Name:
Physics Letters. Section B
Additional Journal Information:
Journal Volume: 781; Journal Issue: C; Journal ID: ISSN 0370-2693
Publisher:
Elsevier
Research Org:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
OSTI Identifier:
1454289
Alternate Identifier(s):
OSTI ID: 1454730

Radyushkin, Anatoly V. Quark pseudodistributions at short distances. United States: N. p., Web. doi:10.1016/j.physletb.2018.04.023.
Radyushkin, Anatoly V. Quark pseudodistributions at short distances. United States. doi:10.1016/j.physletb.2018.04.023.
Radyushkin, Anatoly V. 2018. "Quark pseudodistributions at short distances". United States. doi:10.1016/j.physletb.2018.04.023.
@article{osti_1454289,
title = {Quark pseudodistributions at short distances},
author = {Radyushkin, Anatoly V.},
abstractNote = {We perform a one-loop study of the small-$z_3^2$ behavior of the Ioffe-time distribution (ITD) ${\cal M} (\nu, z_3^2)$, the basic function that may be converted into parton pseudo- and quasi-distributions. We calculate the corrections at the operator level, so that our results may be later used for pseudo-distribution amplitudes and generalized parton pseudo-distributions. We separate two sources of the $z_3^2$-dependence at small $z_3^2$. One is related to the ultraviolet (UV) singularities generated by the gauge link, and another to short-distance logarithms generating perturbative evolution of parton densities. Our calculation explicitly shows that, for a finite UV cut-off, the UV-singular terms vanish when $z_3^2=0$. The UV divergences are absent in the ratio ${\cal M} (\nu, z_3^2)/{\cal M} (0, z_3^2)$ ("reduced" ITD). Still, it has a non-trivial short-distance behavior due to $\ln z_3^2 \Lambda^2$ terms generating perturbative evolution of the parton densities. We give an explicit expression, up to constant terms, for the reduced ITD at one loop. It may be used in extraction of PDFs from the lattice QCD simulations. We also use our results to get new insights concerning the structure of parton quasi-distributions at one-loop level.},
doi = {10.1016/j.physletb.2018.04.023},
journal = {Physics Letters. Section B},
number = C,
volume = 781,
place = {United States},
year = {2018},
month = {6}
}