Perturbative Renormalisation for Low Moments of Generalised Parton Distributions with Clover Fermions

TL;DR

This paper computes one-loop lattice perturbation theory renormalisation factors for the first two moments of generalised parton distributions using clover fermions, including operator mixing and tadpole improvement.

Contribution

It provides the first detailed calculation of mixing matrices and renormalisation factors for these moments with clover fermions in a non-forward lattice setting.

Findings

Calculated one-loop mixing matrices for relevant operators.

Applied tadpole improvement to enhance accuracy.

Presented numerical examples demonstrating the results.

Abstract

We present the non-forward quark matrix elements of operators with one and two covariant derivatives needed for the renormalisation of the first and second moments of generalised parton distributions in one-loop lattice perturbation theory using clover fermions. For some representations of the hypercubic group commonly used in simulations we define the sets of possible mixing operators and compute the one-loop mixing matrices of renormalisation factors. Tadpole improvement is applied to the results and some numerical examples are presented.