One-loop renormalisation of quark bilinears for overlap fermions with improved gauge actions

TL;DR

This paper calculates the renormalisation constants for quark bilinear operators in lattice QCD using overlap fermions with various improved gauge actions, providing insights into perturbative effects and mean field improvement.

Contribution

It presents the first comprehensive perturbative calculation of renormalisation constants for overlap fermions with multiple improved gauge actions, including mean field improvement methods.

Findings

Renormalisation constants are computed for various gauge actions.

Gauge dependent parts are shown to be independent of fermion representation.

Mean field (tadpole) improvement can be applied to overlap fermions.

Abstract

We compute lattice renormalisation constants of local bilinear quark operators for overlap fermions and improved gauge actions. Among the actions we consider are the Symanzik, L\"uscher-Weisz, Iwasaki and DBW2 gauge actions. The results are given for a variety of $\rho$ parameters. We show how to apply mean field (tadpole) improvement to overlap fermions. The question, what is a good gauge action, is discussed from the perturbative point of view. Finally, we show analytically that the gauge dependent part of the self-energy and the amputated Green functions are independent of the lattice fermion representation, using either Wilson or overlap fermions.