Lattice QCD exploration of parton pseudo-distribution functions
- 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)
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 $$\alpha_s/\pi =0.1$$.
- Research Organization:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- AC05-06OR23177; AC02-05CH11231; FG02-04ER41302; FG02-97ER41028; PHY-1516509; PHY-1626177
- OSTI ID:
- 1408203
- Alternate ID(s):
- OSTI ID: 1408063
- Report Number(s):
- JLAB-THY-17-2494; DOE/OR/23177-4189; arXiv:1706.05373; PRVDAQ; TRN: US1703290
- Journal Information:
- Physical Review D, Vol. 96, Issue 9; ISSN 2470-0010
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
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