Exact gauge invariant mass dependence of \alpha_s through two loops

TL;DR

This paper presents a two-loop calculation of the gauge invariant, mass-dependent QCD coupling , providing a comprehensive understanding of quark mass effects on the coupling relevant for various high-energy physics applications.

Contribution

It offers the first complete two-loop gauge invariant, mass-dependent  calculation, including analytical fitting and limits, advancing precision in QCD coupling analysis.

Findings

Finite-mass fermionic corrections to the heavy quark potential are summarized.

The gauge invariant mass dependence of  is now known through two loops.

The results include decoupling, massless, and Abelian limits.

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.