# 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. https://doi.org/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 = {2018},

month = {6}

}

https://doi.org/10.1016/j.physletb.2018.04.023

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

Works referencing / citing this record:

##
Unraveling high-energy hadron structures with lattice QCD

journal, December 2018

- Zhao, Yong
- International Journal of Modern Physics A, Vol. 33, Issue 36

##
Unraveling high-energy hadron structures with lattice QCD

journal, December 2018

- Zhao, Yong
- International Journal of Modern Physics A, Vol. 33, Issue 36

##
Moments of Ioffe time parton distribution functions from non-local matrix elements

journal, November 2018

- Karpie, Joseph; Orginos, Kostas; Zafeiropoulos, Savvas
- Journal of High Energy Physics, Vol. 2018, Issue 11

##
Parton distribution functions from Ioffe time pseudo-distributions

journal, December 2019

- Joó, Bálint; Karpie, Joseph; Orginos, Kostas
- Journal of High Energy Physics, Vol. 2019, Issue 12

##
Pion valence structure from Ioffe-time parton pseudodistribution functions

journal, December 2019

- Joó, Bálint; Karpie, Joseph; Orginos, Kostas
- Physical Review D, Vol. 100, Issue 11

##
Generalized parton distributions and pseudodistributions

journal, December 2019

- Radyushkin, A. V.
- Physical Review D, Vol. 100, Issue 11

##
One-loop evolution of parton pseudo-distribution functions on the lattice

journal, July 2018

- Radyushkin, Anatoly
- Physical Review D, Vol. 98, Issue 1

##
Factorization theorem relating Euclidean and light-cone parton distributions

journal, September 2018

- Izubuchi, Taku; Ji, Xiangdong; Jin, Luchang
- Physical Review D, Vol. 98, Issue 5

##
A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results

journal, June 2019

- Cichy, Krzysztof; Constantinou, Martha
- Advances in High Energy Physics, Vol. 2019

##
Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point

text, January 2019

- Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha
- Deutsches Elektronen-Synchrotron, DESY, Hamburg

Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*