# Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions

## Abstract

Here, we show that quasi-PDFs may be treated as hybrids of PDFs and primordial rest-frame momentum distributions of partons. This results in a complicated convolution nature of quasi-PDFs that necessitates using large p _{3}≳ 3 GeV momenta to get reasonably close to the PDF limit. Furthemore, as an alternative approach, we propose to use pseudo-PDFs P(x, z$$2\atop{3}$$) that generalize the light-front PDFs onto spacelike intervals and are related to Ioffe-time distributions M (v, z$$2\atop{3}$$), the functions of the Ioffe time v = p _{3} z _{3} and the distance parameter z$$2\atop{3}$$ with respect to which it displays perturbative evolution for small z _{3}. In this form, one may divide out the z$$2\atop{3}$$ dependence coming from the primordial rest-frame distribution and from the problematic factor due to lattice renormalization of the gauge link. The v-dependence remains intact and determines the shape of PDFs.

- Authors:

- Old Dominion Univ., Norfolk, VA (United States); 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:
- 1377014

- Alternate Identifier(s):
- OSTI ID: 1377118

- Report Number(s):
- JLAB-THY-17-2455; DOE/OR/23177-4149; arXiv:1705.01488

Journal ID: ISSN 2470-0010; PRVDAQ

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

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 3; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Radyushkin, Anatoly V.
```*Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevD.96.034025.

```
Radyushkin, Anatoly V.
```*Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions*. United States. doi:10.1103/PhysRevD.96.034025.

```
Radyushkin, Anatoly V. Mon .
"Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions". United States.
doi:10.1103/PhysRevD.96.034025. https://www.osti.gov/servlets/purl/1377014.
```

```
@article{osti_1377014,
```

title = {Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions},

author = {Radyushkin, Anatoly V.},

abstractNote = {Here, we show that quasi-PDFs may be treated as hybrids of PDFs and primordial rest-frame momentum distributions of partons. This results in a complicated convolution nature of quasi-PDFs that necessitates using large p3≳ 3 GeV momenta to get reasonably close to the PDF limit. Furthemore, as an alternative approach, we propose to use pseudo-PDFs P(x, z$2\atop{3}$) that generalize the light-front PDFs onto spacelike intervals and are related to Ioffe-time distributions M (v, z$2\atop{3}$), the functions of the Ioffe time v = p3 z3 and the distance parameter z$2\atop{3}$ with respect to which it displays perturbative evolution for small z3. In this form, one may divide out the z$2\atop{3}$ dependence coming from the primordial rest-frame distribution and from the problematic factor due to lattice renormalization of the gauge link. The v-dependence remains intact and determines the shape of PDFs.},

doi = {10.1103/PhysRevD.96.034025},

journal = {Physical Review D},

number = 3,

volume = 96,

place = {United States},

year = {Mon Aug 28 00:00:00 EDT 2017},

month = {Mon Aug 28 00:00:00 EDT 2017}

}

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