A Precise Determination of the Running Coupling in the SU(3) Yang-Mills Theory

TL;DR

This paper employs a non-perturbative finite-size scaling method to accurately determine the running coupling in SU(3) Yang-Mills theory across energy scales, connecting low-energy scales with high-energy perturbative behavior.

Contribution

It introduces a precise non-perturbative technique to measure the running coupling in SU(3) Yang-Mills theory, bridging low-energy scales with perturbative regimes.

Findings

Contact with fundamental scales like string tension at low energies

Coupling evolution matches perturbation theory at high energies

MS-bar scheme coupling determined with a few percent error

Abstract

A non-perturbative finite-size scaling technique is used to study the evolution of the running coupling (in a certain adapted scheme) in the SU(3) Yang-Mills theory. At low energies contact is made with the fundamental dynamical scales, such as the string tension K, while at larger energies the coupling is shown to evolve according to perturbation theory. In that regime the coupling in the MS-bar scheme of dimensional regularization is obtained with an estimated total error of a few percent.