Lattice QCD exploration of parton pseudodistribution functions
Here, we demonstrate a new method of extracting parton distributions from lattice calculations. The starting idea is to treat the generic equaltime 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 restframe density $${\cal M} (0, z_3^2)$$. Our lattice calculation shows a linear exponential $$z_3$$dependence in the restframe 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 Gaussiantype 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]}
 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:
 Report Number(s):
 JLABTHY172494; DOE/OR/231774189; arXiv:1706.05373
Journal ID: ISSN 24700010; PRVDAQ; TRN: US1703290
 Grant/Contract Number:
 AC0506OR23177; AC0205CH11231; FG0204ER41302; FG0297ER41028; PHY1516509; PHY1626177
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 96; Journal Issue: 9; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Research Org:
 Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
 OSTI Identifier:
 1408203
 Alternate Identifier(s):
 OSTI ID: 1408063
Orginos, Kostas, Radyushkin, Anatoly, Karpie, Joseph, and Zafeiropoulos, Savvas. Lattice QCD exploration of parton pseudodistribution functions. United States: N. p.,
Web. doi:10.1103/PhysRevD.96.094503.
Orginos, Kostas, Radyushkin, Anatoly, Karpie, Joseph, & Zafeiropoulos, Savvas. Lattice QCD exploration of parton pseudodistribution functions. United States. doi:10.1103/PhysRevD.96.094503.
Orginos, Kostas, Radyushkin, Anatoly, Karpie, Joseph, and Zafeiropoulos, Savvas. 2017.
"Lattice QCD exploration of parton pseudodistribution 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 pseudodistribution 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 equaltime 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 restframe density ${\cal M} (0, z_3^2)$. Our lattice calculation shows a linear exponential $z_3$dependence in the restframe 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 Gaussiantype 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}
}