# 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:

- Old Dominion Univ., Norfolk, VA (United States). Physics Dept.; Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

- Publication Date:

- Research Org.:
- Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- 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; PII: S0370269318303071

- Grant/Contract Number:
- AC05-06OR23177; FG02-97ER41028

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Physics Letters. Section B

- Additional Journal Information:
- Journal Volume: 781; Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Radyushkin, Anatoly V.
```*Quark pseudodistributions at short distances*. United States: N. p., 2018.
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. Thu .
"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 = {Thu Jun 14 00:00:00 EDT 2018},

month = {Thu Jun 14 00:00:00 EDT 2018}

}