Title: 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:

Orginos, Kostas ^[1]; Radyushkin, Anatoly ^[2]; Karpie, Joseph ^[1]; Zafeiropoulos, Savvas ^[1]

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+ Show Author Affiliations

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

Publication Date:

Wed Nov 08 00:00:00 EST 2017

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