Determination of $\alpha_S$ in the $SU(3)$ Yang-Mills theory

TL;DR

This paper presents a novel strategy to determine the strong coupling constant in $SU(3)$ Yang-Mills theory using a finite-volume scheme with twisted boundary conditions and gradient-flow coupling, aiming for reduced errors.

Contribution

The authors introduce a new approach employing twisted boundary conditions and step-scaling to accurately compute the running of the coupling in pure gauge theory.

Findings

Preliminary continuum extrapolation results for the step-scaling function.

Expected reduction in statistical errors compared to other finite-volume methods.

Absence of linear cutoff effects due to translational invariance.

Abstract

The decoupling strategy allows one to obtain the value of the strong coupling in QCD from the running in pure gauge. Here we present our strategy to determine the running in the $SU(3)$ Yang-Mills theory. We use a finite-volume scheme with twisted boundary conditions and a step-scaling approach based on a gradient-flow coupling. We show preliminary results for the continuum extrapolation of the step-scaling function. Compared with other finite-volume approaches, we expect a reduced statistical error and absence of linear cutoff effects due to the translational invariance of the boundary conditions.