Quark pseudodistributions at short distances
We perform a oneloop study of the small$$z_3^2$$ behavior of the Ioffetime distribution (ITD) $${\cal M} (\nu, z_3^2)$$, the basic function that may be converted into parton pseudo and quasidistributions. We calculate the corrections at the operator level, so that our results may be later used for pseudodistribution amplitudes and generalized parton pseudodistributions. 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 shortdistance logarithms generating perturbative evolution of parton densities. Our calculation explicitly shows that, for a finite UV cutoff, the UVsingular 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 nontrivial shortdistance 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 quasidistributions at oneloop level.
 Authors:

^{[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):
 JLABTHY172579; DOE/OR/231774247; arXiv:1710.08813
Journal ID: ISSN 03702693; PII: S0370269318303071
 Grant/Contract Number:
 AC0506OR23177; FG0297ER41028
 Type:
 Published Article
 Journal Name:
 Physics Letters. Section B
 Additional Journal Information:
 Journal Volume: 781; Journal Issue: C; Journal ID: ISSN 03702693
 Publisher:
 Elsevier
 Research Org:
 Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Nuclear Physics (NP) (SC26)
 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 oneloop study of the small$z_3^2$ behavior of the Ioffetime distribution (ITD) ${\cal M} (\nu, z_3^2)$, the basic function that may be converted into parton pseudo and quasidistributions. We calculate the corrections at the operator level, so that our results may be later used for pseudodistribution amplitudes and generalized parton pseudodistributions. 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 shortdistance logarithms generating perturbative evolution of parton densities. Our calculation explicitly shows that, for a finite UV cutoff, the UVsingular 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 nontrivial shortdistance 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 quasidistributions at oneloop 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}
}