Charm quark effects on the strong coupling extracted from the static force

Abstract

We compute the fermionic contribution to the strong coupling $\alpha_{qq}$ extracted from the static force in Lattice QCD up to order $g^4$ in perturbation theory. This allows us to subtract the leading fermionic lattice artifacts from recent determinations of $\alpha_{qq}$ produced in simulations of two dynamical charm quarks. Moreover, by using a suitable parametrization of the $\beta_{qq}$-function, we can evaluate the charm loop effects on $\alpha_{qq}$ in the continuum limit.