# Gluon pseudo-distributions at short distances: Forward case

## Abstract

We present the results that are necessary in the ongoing lattice calculations of the gluon parton distribution functions (PDFs) within the pseudo-PDF approach. We give a classification of possible two-gluon correlator functions and identify those that contain the invariant amplitude determining the gluon PDF in the light-cone $z^2$ -> 0 limit. One-loop calculations have been performed in the coordinate representation and in an explicitly gauge-invariant form. We made an effort to separate ultraviolet (UV) and infrared (IR) sources of the ln ($-z^2$)-dependence at short distances $z^2$. The UV terms cancel in the reduced Ioffe-time distribution (ITD), and we obtain the matching relation between the reduced ITD and the light-cone ITD. Using a kernel form, we get a direct connection between lattice data for the reduced ITD and the normalized gluon PDF. We also show that our results may be used for a rather straightforward calculation of the one-loop matching relations for quasi-PDFs.

- 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:
- 1638534

- Alternate Identifier(s):
- OSTI ID: 1644311

- Report Number(s):
- JLAB-THY-19-3087; DOE-OR-23177-4803; arXiv:1910.13963

Journal ID: ISSN 0370-2693; S037026932030424X; 135621; PII: S037026932030424X

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

- Resource Type:
- Published Article

- Journal Name:
- Physics Letters B

- Additional Journal Information:
- Journal Name: Physics Letters B Journal Volume: 808 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

```
Balitsky, Ian, Morris, Wayne, and Radyushkin, Anatoly. Gluon pseudo-distributions at short distances: Forward case. Netherlands: N. p., 2020.
Web. https://doi.org/10.1016/j.physletb.2020.135621.
```

```
Balitsky, Ian, Morris, Wayne, & Radyushkin, Anatoly. Gluon pseudo-distributions at short distances: Forward case. Netherlands. https://doi.org/10.1016/j.physletb.2020.135621
```

```
Balitsky, Ian, Morris, Wayne, and Radyushkin, Anatoly. Tue .
"Gluon pseudo-distributions at short distances: Forward case". Netherlands. https://doi.org/10.1016/j.physletb.2020.135621.
```

```
@article{osti_1638534,
```

title = {Gluon pseudo-distributions at short distances: Forward case},

author = {Balitsky, Ian and Morris, Wayne and Radyushkin, Anatoly},

abstractNote = {We present the results that are necessary in the ongoing lattice calculations of the gluon parton distribution functions (PDFs) within the pseudo-PDF approach. We give a classification of possible two-gluon correlator functions and identify those that contain the invariant amplitude determining the gluon PDF in the light-cone $z^2$ -> 0 limit. One-loop calculations have been performed in the coordinate representation and in an explicitly gauge-invariant form. We made an effort to separate ultraviolet (UV) and infrared (IR) sources of the ln ($-z^2$)-dependence at short distances $z^2$. The UV terms cancel in the reduced Ioffe-time distribution (ITD), and we obtain the matching relation between the reduced ITD and the light-cone ITD. Using a kernel form, we get a direct connection between lattice data for the reduced ITD and the normalized gluon PDF. We also show that our results may be used for a rather straightforward calculation of the one-loop matching relations for quasi-PDFs.},

doi = {10.1016/j.physletb.2020.135621},

journal = {Physics Letters B},

number = C,

volume = 808,

place = {Netherlands},

year = {2020},

month = {9}

}

https://doi.org/10.1016/j.physletb.2020.135621