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

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

1999-06-10

arxiv.org/abs/hep-ph/9906324v1

Phys.Rev.D60:096006,1999

Physics

High Energy Physics

High Energy Physics - Phenomenology

27 pages, 13 figures

Scientific paper

10.1103/PhysRevD.60.096006

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.

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