One-loop Renormalisation of Lattice QCD Operators for Non-forward Matrix Elements: From Clover to Overlap Fermions

TL;DR

This paper calculates one-loop renormalisation factors for lattice QCD operators related to GPDs and DAs, comparing clover and overlap fermions, and highlights the advantages of chiral fermions in avoiding operator mixing.

Contribution

It provides the first detailed one-loop renormalisation matrices for non-forward matrix elements using both clover and overlap fermions, emphasizing the chiral symmetry benefits of overlap fermions.

Findings

Overlap fermions do not mix with lower-dimensional operators of different chirality.

Renormalisation matrices are explicitly computed for non-zero momentum transfer.

Chiral fermions are advantageous for operator renormalisation in lattice QCD.

Abstract

We consider the renormalisation of composite quark-antiquark operators with one and two lattice covariant derivatives related to the lowest moments of generalised parton distributions (GPDs) and meson distribution amplitudes (DAs). Their matrix elements are calculated in one-loop lattice perturbation theory for non-zero momentum transfer. Using clover and overlap fermions we present the resulting matrices of mixing and renormalisation factors. For overlap fermions we explicitly check the absence of mixing with lower-dimensional operators of different chirality in particular representations of the hypercubic group. This feature favours the use of chiral fermions.