The Two-Loop Scale Dependence of the Static QCD Potential including Quark Masses

TL;DR

This paper derives the two-loop scale dependence of the static QCD potential including finite quark masses, providing a gauge-invariant, analytic, and decoupling-compatible effective coupling scheme with implications for precise QCD calculations.

Contribution

It introduces a next-to-leading order correction to the Gell Mann-Low function in the V-scheme that incorporates finite quark masses and ensures automatic decoupling of heavy quarks.

Findings

Effective number of flavors as a gauge-independent function of Q^2/m^2

Automatic decoupling of heavy quarks in the running coupling

Scale-invariant connection between observables via the alpha_V scheme

Abstract

The interaction potential V(Q^2) between static test charges can be used to define an effective charge $\alpha_V(Q^2)$ and a physically-based renormalization scheme for quantum chromodynamics and other gauge theories. In this paper we use recent results for the finite-mass fermionic corrections to the heavy-quark potential at two-loops to derive the next-to-leading order term for the Gell Mann-Low function of the V-scheme. The resulting effective number of flavors $N_F(Q^2/m^2)$ in the $\alpha_V$ scheme is determined as a gauge-independent and analytic function of the ratio of the momentum transfer to the quark pole mass. The results give automatic decoupling of heavy quarks and are independent of the renormalization procedure. Commensurate scale relations then provide the next-to-leading order connection between all perturbatively calculable observables to the analytic and gauge-invariant $\alpha_V$ scheme without any scale ambiguity and a well defined number of active flavors. The inclusion of the finite quark mass effects in the running of the coupling is compared with the standard treatment of finite quark mass effects in the $\bar{MS}$ scheme.