Renormalization of Wilson-line operators in the presence of nonzero quark masses

TL;DR

This paper investigates how nonzero quark masses influence the renormalization of gauge-invariant nonlocal quark operators with Wilson lines, providing perturbative calculations and conversion factors crucial for lattice QCD studies of parton distributions.

Contribution

It presents the first perturbative calculation of renormalization factors for massive quark Wilson-line operators and their conversion between RI' and MSbar schemes.

Findings

Calculated renormalization factors in RI' and MSbar schemes

Provided conversion factors for lattice to MSbar scheme

Analyzed operator mixing effects due to quark masses

Abstract

In this paper, we examine the effect of nonzero quark masses on the renormalization of gauge-invariant nonlocal quark bilinear operators, including a finite-length Wilson line (called Wilson-line operators). These operators are relevant to the definition of parton quasi-distribution functions, the calculation on the lattice of which allows the direct nonperturbative study of the corresponding physical parton distribution functions. We present our perturbative calculations of the bare Green's functions, the renormalization factors in RI' and MSbar schemes, as well as the conversion factors of these operators between the two renormalization schemes. Our computations have been performed in dimensional regularization at one-loop level, using massive quarks. The conversion factors can be used to convert the corresponding lattice nonperturbative results to the MSbar scheme, which is the most widely used renormalization scheme for the analysis of experimental data in high-energy physics. Also, our study is relevant for disentangling the additional operator mixing which occurs in the presence of nonzero quark masses, both on the lattice and in dimensional regularization.