The influence of gauge field smearing on discretisation effects

TL;DR

This paper investigates how gauge field smearing, particularly via Wilson gradient flow, affects discretisation effects and the approach to the continuum limit in lattice gauge theories, using Creutz ratios as key observables.

Contribution

It analyzes the impact of smearing on discretisation effects and demonstrates that fixed physical flow time improves the continuum limit behavior of Creutz ratios.

Findings

Smearing reduces ultraviolet fluctuations and affects the effective lattice spacing.

Creutz ratios based on smeared gauge fields are effective for studying scaling behavior.

Using fixed physical flow time yields smaller corrections at finite lattice spacing.

Abstract

When designing lattice actions, gauge field smearing is frequently used to define the lattice Dirac operator. Since the smearing procedure removes effects of ultraviolet fluctuations, the fermions effectively see a larger lattice spacing than the gauge fields. Creutz ratios, formed from ratios of rectangular Wilson loops, based on smeared gauge fields are adequate observables to investigate the effect of smearing since they do not need renormalisation and provide a measure of the physical forces felt by the fermions. We study their behaviour at various smearing radii (fixed in lattice units) and in particular how the smearing influences the scaling towards the continuum limit. Since we employ the Wilson gradient flow as smearing, the same Creutz ratios have another, well defined continuum limit, when the flow time is fixed in physical units. That continuum limit is reached with smaller corrections at finite $a$.