# Quasi-parton distribution functions: A study in the diquark spectator model

## Abstract

A set of quasi-parton distribution functions (quasi-PDFs) have been recently proposed by Ji. Defined as the matrix elements of equal-time spatial correlations, they can be computed on the lattice and should reduce to the standard PDFs when the proton momentum P _{z} is very large. Since taking the P _{z} → ∞ limit is not feasible in lattice simulations, it is essential to provide guidance for which values of P _{z} the quasi-PDFs are good approximations of standard PDFs. Within the framework of the spectator diquark model, we evaluate both the up and down quarks' quasi-PDFs and standard PDFs for all leading-twist distributions (unpolarized distribution f₁, helicity distribution g₁, and transversity distribution h₁). We find that, for intermediate parton momentum fractions x , quasi-PDFs are good approximations to standard PDFs (within 20–30%) when P _{z} ≳ 1.5–2 GeV. On the other hand, for large x~1 much larger P _{z} > 4 GeV is necessary to obtain a satisfactory agreement between the two sets. We further test the Soffer positivity bound, and find that it does not hold in general for quasi-PDFs.

- Authors:

- Penn State Berks, Reading, PA (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1198586

- Alternate Identifier(s):
- OSTI ID: 1200902

- Grant/Contract Number:
- FG02-07ER41460; AC02-05CH11231; 20130783PRD2; 20130019DR

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Physics Letters. Section B

- Additional Journal Information:
- Journal Volume: 743; 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

```
Gamberg, Leonard, Kang, Zhong -Bo, Vitev, Ivan, and Xing, Hongxi.
```*Quasi-parton distribution functions: A study in the diquark spectator model*. United States: N. p., 2015.
Web. doi:10.1016/j.physletb.2015.02.021.

```
Gamberg, Leonard, Kang, Zhong -Bo, Vitev, Ivan, & Xing, Hongxi.
```*Quasi-parton distribution functions: A study in the diquark spectator model*. United States. doi:10.1016/j.physletb.2015.02.021.

```
Gamberg, Leonard, Kang, Zhong -Bo, Vitev, Ivan, and Xing, Hongxi. Thu .
"Quasi-parton distribution functions: A study in the diquark spectator model". United States.
doi:10.1016/j.physletb.2015.02.021.
```

```
@article{osti_1198586,
```

title = {Quasi-parton distribution functions: A study in the diquark spectator model},

author = {Gamberg, Leonard and Kang, Zhong -Bo and Vitev, Ivan and Xing, Hongxi},

abstractNote = {A set of quasi-parton distribution functions (quasi-PDFs) have been recently proposed by Ji. Defined as the matrix elements of equal-time spatial correlations, they can be computed on the lattice and should reduce to the standard PDFs when the proton momentum Pz is very large. Since taking the Pz → ∞ limit is not feasible in lattice simulations, it is essential to provide guidance for which values of Pz the quasi-PDFs are good approximations of standard PDFs. Within the framework of the spectator diquark model, we evaluate both the up and down quarks' quasi-PDFs and standard PDFs for all leading-twist distributions (unpolarized distribution f₁, helicity distribution g₁, and transversity distribution h₁). We find that, for intermediate parton momentum fractions x , quasi-PDFs are good approximations to standard PDFs (within 20–30%) when Pz ≳ 1.5–2 GeV. On the other hand, for large x~1 much larger Pz > 4 GeV is necessary to obtain a satisfactory agreement between the two sets. We further test the Soffer positivity bound, and find that it does not hold in general for quasi-PDFs.},

doi = {10.1016/j.physletb.2015.02.021},

journal = {Physics Letters. Section B},

number = C,

volume = 743,

place = {United States},

year = {Thu Feb 12 00:00:00 EST 2015},

month = {Thu Feb 12 00:00:00 EST 2015}

}

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