Perturbative matching of continuum and lattice quasi-distributions

TL;DR

This paper develops a perturbative method to match continuum and lattice quasi-distribution functions, focusing on Wilson-type fermions and nonlocal operators, addressing operator mixing and lattice artifacts.

Contribution

It introduces a perturbative matching framework for continuum and lattice quasi-distributions with analysis of operator mixing and O(a) effects for Wilson-type fermions.

Findings

Derived matching formulas for nonlocal operators

Analyzed operator mixing and symmetry-based O(a) operators

Provided insights into lattice-continuum correspondence for quasi-distributions

Abstract

Matching of the quasi parton distribution functions between continuum and lattice is addressed using lattice perturbation theory specifically with Wilson-type fermions. The matching is done for nonlocal quark bilinear operators with a straight Wilson line in a spatial direction. We also investigate operator mixing in the renormalization and possible O(a) operators for the nonlocal operators based on a symmetry argument on lattice.