Perturbative investigation of Wilson-line operators in Parton Physics

TL;DR

This paper studies the renormalization of Wilson-line operators relevant for lattice QCD calculations of parton distributions, providing one-loop conversion factors and initial results for staple-shaped operators in various regularizations.

Contribution

It offers the first one-loop conversion factors for straight-line Wilson-line operators and preliminary renormalization results for staple-shaped operators in continuum and lattice regularizations.

Findings

Derived one-loop conversion factors between RI' and MSbar schemes.

Identified operator mixing patterns for staple-shaped operators.

Presented initial renormalization results in continuum and lattice frameworks.

Abstract

We investigate the renormalization of a class of gauge-invariant nonlocal quark bilinear operators, including a finite-length Wilson-line (called Wilson-line operators). The matrix elements of these operators are involved in the recent "quasi-distribution" approach for computing light-cone distributions of Hadronic Physics on the lattice. We consider two classes of Wilson-line operators: straight-line and staple-shaped operators, which are related to the parton distribution functions (PDFs) and transverse momentum-dependent distributions (TMDs), respectively. We present our one-loop results for the conversion factors of straight-line operators between the RI' (appropriate for nonperturbative renormalization on the lattice) and MSbar (typically used in phenomenology) renormalization schemes in the presence of nonzero quark masses. In addition, we present the first results of our preliminary work for the renormalization of staple-shaped operators both in continuum (Dimensional Regularization) and lattice (Wilson/clover fermions and Symanzik improved gluons) regularizations. We identify the observed mixing pairs among these operators, which must be disentangled in the nonperturbative investigations of heavy-quark quasi-PDFs and of light-quark quasi-TMDs.