# Lattice QCD exploration of parton pseudo-distribution functions

## Abstract

Here, we demonstrate a new method of extracting parton distributions from lattice calculations. The starting idea is to treat the generic equal-time matrix element $${\cal M} (Pz_3, z_3^2)$$ as a function of the Ioffe time $$\nu = Pz_3$$ and the distance $$z_3$$. The next step is to divide $${\cal M} (Pz_3, z_3^2)$$ by the rest-frame density $${\cal M} (0, z_3^2)$$. Our lattice calculation shows a linear exponential $$z_3$$-dependence in the rest-frame function, expected from the $$Z(z_3^2)$$ factor generated by the gauge link. Still, we observe that the ratio $${\cal M} (Pz_3 , z_3^2)/{\cal M} (0, z_3^2)$$ has a Gaussian-type behavior with respect to $$z_3$$ for 6 values of $P$ used in the calculation. This means that $$Z(z_3^2)$$ factor was canceled in the ratio. When plotted as a function of $$\nu$$ and $$z_3$$, the data are very close to $$z_3$$-independent functions. This phenomenon corresponds to factorization of the $x$- and $$k_\perp$$-dependence for the TMD $${\cal F} (x, k_\perp^2)$$. For small $$z_3 \leq 4a$$, the residual $$z_3$$-dependence is explained by perturbative evolution, with $$\alpha_s/\pi =0.1$$.

- Authors:

- The College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Old Dominion Univ., Norfolk, VA (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1408203

- Alternate Identifier(s):
- OSTI ID: 1408063

- Report Number(s):
- JLAB-THY-17-2494; DOE/OR/23177-4189; arXiv:1706.05373

Journal ID: ISSN 2470-0010; PRVDAQ; TRN: US1703290

- Grant/Contract Number:
- AC05-06OR23177; AC02-05CH11231; FG02-04ER41302; FG02-97ER41028; PHY-1516509; PHY-1626177

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 9; 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

```
Orginos, Kostas, Radyushkin, Anatoly, Karpie, Joseph, and Zafeiropoulos, Savvas. Lattice QCD exploration of parton pseudo-distribution functions. United States: N. p., 2017.
Web. doi:10.1103/PhysRevD.96.094503.
```

```
Orginos, Kostas, Radyushkin, Anatoly, Karpie, Joseph, & Zafeiropoulos, Savvas. Lattice QCD exploration of parton pseudo-distribution functions. United States. doi:10.1103/PhysRevD.96.094503.
```

```
Orginos, Kostas, Radyushkin, Anatoly, Karpie, Joseph, and Zafeiropoulos, Savvas. Wed .
"Lattice QCD exploration of parton pseudo-distribution functions". United States. doi:10.1103/PhysRevD.96.094503. https://www.osti.gov/servlets/purl/1408203.
```

```
@article{osti_1408203,
```

title = {Lattice QCD exploration of parton pseudo-distribution functions},

author = {Orginos, Kostas and Radyushkin, Anatoly and Karpie, Joseph and Zafeiropoulos, Savvas},

abstractNote = {Here, we demonstrate a new method of extracting parton distributions from lattice calculations. The starting idea is to treat the generic equal-time matrix element ${\cal M} (Pz_3, z_3^2)$ as a function of the Ioffe time $\nu = Pz_3$ and the distance $z_3$. The next step is to divide ${\cal M} (Pz_3, z_3^2)$ by the rest-frame density ${\cal M} (0, z_3^2)$. Our lattice calculation shows a linear exponential $z_3$-dependence in the rest-frame function, expected from the $Z(z_3^2)$ factor generated by the gauge link. Still, we observe that the ratio ${\cal M} (Pz_3 , z_3^2)/{\cal M} (0, z_3^2)$ has a Gaussian-type behavior with respect to $z_3$ for 6 values of $P$ used in the calculation. This means that $Z(z_3^2)$ factor was canceled in the ratio. When plotted as a function of $\nu$ and $z_3$, the data are very close to $z_3$-independent functions. This phenomenon corresponds to factorization of the $x$- and $k_\perp$-dependence for the TMD ${\cal F} (x, k_\perp^2)$. For small $z_3 \leq 4a$, the residual $z_3$-dependence is explained by perturbative evolution, with $\alpha_s/\pi =0.1$.},

doi = {10.1103/PhysRevD.96.094503},

journal = {Physical Review D},

number = 9,

volume = 96,

place = {United States},

year = {2017},

month = {11}

}

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