The SU(3) running coupling from lattice gluons

TL;DR

This paper presents lattice-based numerical results for the SU(3) Yang-Mills running coupling, showing agreement with 2-loop predictions at high momenta and demonstrating minimal lattice artifacts within measurement precision.

Contribution

It introduces a first-principles method to determine the SU(3) running coupling from lattice gluon correlation functions using renormalisation constants.

Findings

Coupling runs according to 2-loop asymptotic formula above 2 GeV

Lattice artifacts are negligible within measurement precision

Method provides a direct non-perturbative determination of the running coupling

Abstract

We provide numerical results for the running coupling in $SU(3)$ Yang-Mills theory as determined from an analysis of lattice two and three-point gluon correlation functions. The coupling is evaluated directly, from first principles, by defining suitable renormalisation constants from the lattice triple gluon vertex and gluon propagator. For momenta larger than 2 GeV, the coupling is found to run according to the 2-loop asymptotic formula. The influence of lattice artifacts on the results appears negligible within the precision of our measurements, although further work on this point is in progress.