Bilinear quark operator renormalization at generalized symmetric point

TL;DR

This paper calculates two-loop Green's functions for bilinear quark operators at a generalized symmetric point, aiding lattice gauge theory in matching high-energy behaviors for various operators relevant to nucleon structure studies.

Contribution

It provides the first two-loop computations of Green's functions for bilinear quark operators at a generalized symmetric momentum configuration, supporting lattice QCD analyses.

Findings

Two-loop Green's functions computed for scalar, vector, and tensor currents.

Results facilitate improved matching between lattice QCD and continuum theories.

Supports analysis of nucleon structure functions in deep inelastic scattering.

Abstract

We compute Green's functions with a bilinear quark operator inserted at non-zero momentum for a generalized momentum configuration to two loops. These are required to assist lattice gauge theory measurements of the same quantity in matching to the high energy behaviour. The flavour non-singlet operators considered are the scalar, vector and tensor currents as well as the second moment of the twist-2 Wilson operator used in deep inelastic scattering for the measurement of nucleon structure functions.