Quark pseudodistributions at short distances
Abstract
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:
- 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:
- 1454289
- Alternate Identifier(s):
- OSTI ID: 1454730
- Report Number(s):
- JLAB-THY-17-2579; DOE/OR/-23177-4247; arXiv:1710.08813
Journal ID: ISSN 0370-2693; S0370269318303071; PII: S0370269318303071
- Grant/Contract Number:
- FG02-97ER41028; AC05-06OR23177
- Resource Type:
- Published Article
- Journal Name:
- Physics Letters B
- Additional Journal Information:
- Journal Name: Physics Letters B Journal Volume: 781 Journal Issue: C; Journal ID: ISSN 0370-2693
- Publisher:
- Elsevier
- Country of Publication:
- Netherlands
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Radyushkin, A. V. Quark pseudodistributions at short distances. Netherlands: N. p., 2018.
Web. doi:10.1016/j.physletb.2018.04.023.
Radyushkin, A. V. Quark pseudodistributions at short distances. Netherlands. https://doi.org/10.1016/j.physletb.2018.04.023
Radyushkin, A. V. Fri .
"Quark pseudodistributions at short distances". Netherlands. https://doi.org/10.1016/j.physletb.2018.04.023.
@article{osti_1454289,
title = {Quark pseudodistributions at short distances},
author = {Radyushkin, A. 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 B},
number = C,
volume = 781,
place = {Netherlands},
year = {Fri Jun 01 00:00:00 EDT 2018},
month = {Fri Jun 01 00:00:00 EDT 2018}
}
https://doi.org/10.1016/j.physletb.2018.04.023
Web of Science
Figures / Tables:
Works referencing / citing this record:
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journal, December 2018
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Unraveling high-energy hadron structures with lattice QCD
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Moments of Ioffe time parton distribution functions from non-local matrix elements
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Parton distribution functions from Ioffe time pseudo-distributions
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Figures / Tables found in this record: