Testing the Quasi-temporal Gauge on the Lattice

TL;DR

This paper assesses the quasi-temporal gauge on the lattice, demonstrating its low computational cost and evaluating its effectiveness through renormalization constants, while noting issues like lattice Gribov copies and finite volume effects.

Contribution

It introduces the quasi-temporal gauge as a practical lattice gauge fixing method and evaluates its performance using the Clover action and Ward identities.

Findings

Reasonable agreement with previous Ward identity results

Large fluctuations due to lattice Gribov copies observed

Finite volume effects likely influence results

Abstract

We investigate the viability of the quasi-temporal gauge on the lattice. This is a complete gauge fixing condition that can be implemented on the lattice at a very low computational cost. As a test case, using the Clover action, we have evaluated the (gauge invariant) renormalisation constant of the non-singlet axial current, using Ward identities extracted from quark states. Our result is in reasonable but not complete agreement with previous values obtained from Ward identities both on hadronic states and on quark states in the Landau gauge. We observe large fluctuations due to lattice Gribov copies. The influence of finite volume effects is expected to be non-negligible in the case we are considering.