A New Method of Calculating the Running Coupling Constant

TL;DR

This paper introduces a novel lattice-based method to compute the running coupling constant in gauge theories, enabling accurate non-perturbative measurements across various energy scales.

Contribution

The paper presents a new scheme using Wilson loops for calculating the running coupling, with perturbative definitions and benchmark tests in quenched QCD.

Findings

Successfully determined the non-perturbative running coupling over a wide energy range.

Achieved high statistical accuracy with fewer gauge configurations.

Confirmed consistency with perturbative predictions at high energies.

Abstract

We propose a new method to compute the running coupling constant of gauge theories on the lattice. We first give the definition of the running coupling in the new scheme using the Wilson loops in a finite volume, and explain how the running of the coupling constant is extracted from the measurement of the volume dependence. The perturbative calculation of the renormalization constant to define the scheme is also given at the leading order. As a benchmark test of the new scheme we apply the method the case of the quenched QCD. We show the preliminary result from our numerical simulations which are carried out with plaquette gauge action for various lattice sizes and bare lattice couplings. With techniques to improve the statistical accuracy, we show that we can determine the non-perturbative running of the coupling constant in a wide range of the energy scale with relatively small number of gauge configurations in our scheme. We compare our lattice data of the running coupling constant with perturbative renormalization group evolution at one- and two-loop order, and confirm the consistency between them at high energy.