One-Loop Hybrid Renormalization Matching Kernels for Quasi-Parton Distributions
Journal
PHYSICAL REVIEW D
Journal Volume
106
Journal Issue
1
Date Issued
2022-04-18
Author(s)
Chien-Yu Chou
Abstract
Large momentum effective theory allows extraction of hadron parton
distribution functions in lattice QCD by matching them to quark bilinear matrix
elements of hadrons with large momenta. We calculate the matching kernels for
the unpolarized, helicity, and transversity isovector parton distribution
functions and skewless generalized parton distributions of all hadrons in the
hybrid-RI/MOM scheme. This renormalization scheme uses RI/MOM when the Wilson
line length is less then $z_s$, otherwise a mass subtraction scheme is used. By
design, the non-hybrid scheme is recovered as $z_s \to \infty$. In the opposite
limit, $z \to 0$, the self renormalization scheme is obtained. When the
parameters $p_z^R=0$ and $\mu^R z_s \ll 1$, the hybrid-RI/MOM scheme coincides
with the hybrid-ratio scheme times the charge of the PDF. We also discuss the
subtlety related to the commutativity of Fourier transform and $\epsilon$
expansion in the $\bar{\text{MS}}$ scheme.
Subjects
SPACE; High Energy Physics - Lattice; High Energy Physics - Lattice
Publisher
AMER PHYSICAL SOC
Type
journal article