One-loop renormalisation for the second moment of GPDs with Wilson fermions

TL;DR

This paper computes one-loop lattice perturbation theory corrections for operators relevant to the second moment of generalized parton distributions using Wilson fermions, aiding in their non-perturbative renormalization.

Contribution

It provides the first detailed calculation of mixing and renormalization matrices for these operators with Wilson fermions in lattice QCD.

Findings

Determined mixing operators for various hypercubic group representations.

Calculated renormalization matrices for second moment operators.

Facilitates more accurate lattice QCD measurements of GPDs.

Abstract

We calculate the non-forward quark matrix elements for operators with two covariant derivatives in one-loop lattice perturbation theory using Wilson fermions. These matrix elements are needed in the renormalisation of the second moment of generalised parton distributions measured in lattice QCD. For some commonly used representations of the hypercubic group we determine the sets of all mixing operators and find the matrices of mixing and renormalisation factors.