Two-loop scale dependence of the static QCD potential including quark masses

Stanley J. Brodsky, Michael Melles, Johan Rathsman
1999 Physical Review D, Particles and fields  
The interaction potential V(Q^2) between static test charges can be used to define an effective charge α_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 α_V scheme is
more » ... e α_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 α_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 M̅S̅ scheme.
doi:10.1103/physrevd.60.096006 fatcat:msd2vhvg35hzth5iqmxdh3a4wa