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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:
 [1];  [2];  [1];  [1]
  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:
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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Virtuality distributions in application to <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi>γ</mml:mi><mml:msup><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mrow><mml:mo>⁎</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:math> transition form factor at handbag level
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