Gribov Noise on the Lattice Axial Current Renormalisation Constant

TL;DR

This paper investigates how Gribov copies in Landau gauge affect the lattice renormalisation constant of the axial current, finding that their impact is within statistical uncertainties and diminishes with increased statistics.

Contribution

It provides a quantitative analysis of Gribov copy effects on axial current renormalisation in lattice QCD, comparing gauge invariant and gauge dependent methods.

Findings

Gribov copies induce observable effects within statistical errors.

Increasing statistics reduces the impact of Gribov ambiguities.

Residual gauge freedom effects are comparable to statistical uncertainties.

Abstract

We study the influence of Gribov copies, in the Landau gauge, on the lattice renormalisation constant of the axial current, obtained from a Ward identity on quark state correlation functions, with the Clover action, in quenched SU(3) gauge theory. A comparison between the gauge invariant determination of the renorma= lization constant and the gauge dependent one is discussed. We find that the residual gauge freedom associated to Gribov copies induces observable effects, which, at the level of numerical accuracy of our simulation, are included in the statistical uncertainty inherent in a Monte Carlo simulation. Doubling the statistics suggests that the fluctuation due to the lattice Gribov ambiguity scales down at least as fast as a pure statistical error.