Perturbative Renormalisation of the Second Moment of Generalised Parton Distributions

TL;DR

This paper computes the one-loop renormalisation factors for the second moment of generalized parton distributions in lattice QCD, accounting for operator mixing and non-forward matrix elements using Wilson fermions.

Contribution

It provides the first detailed calculation of mixing matrices for non-forward matrix elements relevant to GPD moments with Wilson fermions in lattice QCD.

Findings

Determined mixing matrices for key operator representations.

Identified additional operators contributing due to non-forward kinematics.

Enhanced understanding of operator mixing in lattice GPD calculations.

Abstract

We calculate the non-forward quark matrix elements of operators with two covariant derivatives needed for the renormalisation of the second moment of generalised parton distributions in one-loop lattice perturbation theory using Wilson fermions. For some representations of the hypercubic group commonly used in simulations we determine the sets of all possible mixing operators. For those representations the one-loop mixing matrices of renormalisation factors are found. Due to non-vanishing contributions of operators with external ordinary derivatives the number of contributing operators increases compared to forward matrix elements.