A new scheme for the running coupling constant in gauge theories using Wilson loops

TL;DR

This paper introduces a novel renormalization scheme for the running coupling constant in gauge theories using Wilson loops, enabling precise determination across energy scales with fewer configurations.

Contribution

The paper presents a new scheme utilizing Wilson loops and Creutz ratios, combined with zeta-function resummation, for improved accuracy in lattice gauge theory calculations.

Findings

Successfully applied to quenched QCD with plaquette gauge action

Achieved accurate running coupling determination over wide energy range

Reduced statistical errors with multiple improvement methods

Abstract

We propose a new renormalization scheme of the running coupling constant in general gauge theories using the Wilson loops. The renormalized coupling constant is obtained from the Creutz ratio in lattice simulations and the corresponding perturbative coefficient at the leading order. The latter can be calculated by adopting the zeta-function resummation techniques. We perform a benchmark test of our scheme in quenched QCD with the plaquette gauge action. The running of the coupling constant is determined by applying the step-scaling procedure. Using several methods to improve the statistical accuracy, we show that the running coupling constant can be determined in a wide range of energy scales with relatively small number of gauge configurations.