Perturbative matching of continuum and lattice quasi-distributions

Tomomi Ishikawa

doi:10.1051/epjconf/201817506028

Abstract

Matching of the quasi parton distribution functions between continuum and lattice is addressed using lattice perturbation theory specifically withWilson-type fermions. The matching is done for nonlocal quark bilinear operators with a straightWilson 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.

Highlights

Understanding the internal structure of nucleons through quantum chromodynamics (QCD) gives phenomenological implications to high-energy physics and astrophysics
The scattering cross sections are written in a convolution of the perturbative hard part and nonperturbative parton distribution functions (PDFs), which absorb all collinear divergences of the partonic scattering
The one-loop perturbative continuum-lattice matching for the nonlocal quark bilinear, which appears in the quasi-PDF approach, was demonstrated with Wilson quark formalism

Summary

Introduction

Understanding the internal structure of nucleons through quantum chromodynamics (QCD) gives phenomenological implications to high-energy physics and astrophysics. The nonperturbative subtraction method of the power divergence in the nonlocal bilinear has been proposed in Refs. The nonlocal quark bilinear (3) can mix with different Γ on the lattice, which was found in the oneloop lattice perturbative calculation [21] and later supported by Ref. We investigate the matching factor for the nonlocal quark bilinear (3) between continuum and lattice using one-loop perturbation theory. We set three dimensional UV cutoff in the direction perpendicular to z to regulate the UV divergence, for simplicity The detail of this scheme can be seen in Ref. The smearing on the Wilson line makes the operator mixing negligible in the larger δz region

Symmetry analysis for the operator mixing

Summary