Nonperturbative renormalization of nonlocal quark bilinears for quasi-PDFs on the lattice using an auxiliary field

TL;DR

This paper introduces a nonperturbative renormalization method for nonlocal operators in quasi-PDF calculations on the lattice, using an auxiliary field approach to improve the accuracy of nucleon matrix element computations.

Contribution

It develops a novel auxiliary field technique to renormalize nonlocal operators nonperturbatively, providing a master formula and parameter determination method for lattice QCD quasi-PDFs.

Findings

Renormalization parameters obtained for two lattice spacings.

Consistent renormalized matrix elements across discretizations.

Improved nucleon matrix element calculations at different lattice spacings.

Abstract

Quasi-PDFs provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking, and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the MS-bar scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters we show the effect of renormalization on nucleon matrix elements with pion mass approximately 370 MeV, and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.