Renormalisation of Composite Operators in Lattice Perturbation Theory with Clover Fermions: Non-forward Matrix Elements

TL;DR

This paper calculates the one-loop renormalisation factors for lattice QCD operators with derivatives using clover fermions, focusing on non-forward matrix elements relevant for parton distributions.

Contribution

It provides a detailed one-loop perturbative calculation of operator renormalisation and mixing matrices for non-forward matrix elements with clover fermions, including tadpole improvement.

Findings

Computed renormalisation matrices for relevant operators.

Identified operator mixing patterns for hypercubic group representations.

Applied tadpole improvement to enhance perturbative results.

Abstract

We consider the renormalisation of lattice QCD operators with one and two covariant derivatives related to the first and second moments of generalised parton distributions and meson distribution amplitudes. Employing the clover fermion action we calculate their non-forward quark matrix elements in one-loop lattice perturbation theory. For some representations of the hypercubic group commonly used in simulations we determine the sets of all possible mixing operators and compute the matrices of renormalisation factors in one-loop approximation. We describe how tadpole improvement is applied to the results.