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

TL;DR

This paper calculates how charm quark effects influence the strong coupling constant in lattice QCD, providing a way to correct lattice artifacts and understand charm loop impacts on the coupling in the continuum limit.

Contribution

It introduces a perturbative calculation of fermionic contributions to the strong coupling, enabling subtraction of lattice artifacts and assessment of charm effects in the continuum.

Findings

Fermionic contributions to $eta_{qq}$ computed up to order $g^4$.

Leading lattice artifacts from charm quarks subtracted from existing data.

Charm loop effects on $eta_{qq}$ evaluated in the continuum limit.

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.