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

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.