Computation of the Running Coupling in the SU(2) Yang-Mills Theory

TL;DR

This paper uses finite-size scaling to compute the non-perturbative running coupling in SU(2) Yang-Mills theory, finding agreement with 2-loop predictions at low momenta and providing precise coupling values at high momenta.

Contribution

It introduces a non-perturbative method to calculate the running coupling in SU(2) gauge theory using finite-size scaling techniques.

Findings

Running coupling matches 2-loop approximation at low q

Precise value of alpha_MSbar at q=20 sqrt(K)

Demonstrates effectiveness of finite-size scaling in gauge theories

Abstract

A finite-size scaling technique is applied to the SU(2) gauge theory (without matter fields) to compute a non-perturbatively defined running coupling alpha(q) for a range of momenta q given in units of the string tension K. We find that already at rather low q, the evolution of alpha(q) is well described by the 2-loop approximation to the Callan-Symanzik beta-function. At the highest momentum reached, q=20 sqrt(K), we obtain alpha_MSbar(q)=0.187 +/- 0.005 +/- 0.009 for the running coupling in the MSbar scheme of dimensional regularization.