One-Loop Hybrid Renormalization Matching Kernels for Quasi-Parton Distributions

TL;DR

This paper derives one-loop matching kernels for quasi-parton distributions in a hybrid renormalization scheme, enabling more accurate lattice QCD calculations of hadron structure functions.

Contribution

It introduces a hybrid-RI/MOM renormalization scheme for quasi-PDFs, unifying different schemes and addressing scheme subtleties in lattice QCD calculations.

Findings

Derived matching kernels for unpolarized, helicity, and transversity PDFs.

Established the connection between hybrid-RI/MOM and other renormalization schemes.

Discussed the impact of scheme parameters on the matching kernels.

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.