Exact gauge invariant mass dependence of \alpha_s through two loops

Abstract

A physically defined QCD coupling parameter naturally incorporates massive quark flavor thresholds in a gauge invariant, renormalization scale independent and analytical way. In this paper we summarize recent results for the finite-mass fermionic corrections to the heavy quark potential through two loops leading to the numerical solution of the physical and mass dependent Gell-Mann Low function. The decoupling-, massless- and Abelian-limits are reproduced and an analytical fitting function is obtained in the V-scheme. Thus the gauge invariant mass dependence of $\alpha_V$ is now known through two loops. Possible applications in lattice analyses, heavy quark physics and effective charges are briefly discussed.