Exact mass dependent two--loop $\barα_s(Q^2)$ in the background MOM renormalization scheme
F. Jegerlehner, O. V. Tarasov
TL;DR
The paper addresses how quark masses affect the QCD running coupling and heavy-quark decoupling by computing the exact mass-dependent two-loop beta function in a BF-MOM renormalization scheme. It uses the background field method to obtain a gauge-invariant, decoupling-friendly framework, delivering compact analytic expressions for the BF-MOM self-energy and the resulting beta functions. It also derives the relation between BF-MOM and MSbar couplings and demonstrates, via numerical studies and a scale-rescaling approach, how scheme dependence can be mitigated at high energies while preserving physical thresholds. The results highlight non-negligible mass effects and provide a practical, mass-aware alternative to MSbar for precision QCD analyses.
Abstract
A two-loop calculation of the renormalization group $β$--function in a momentum subtraction scheme with massive quarks is presented using the background field formalism. The results have been obtained by using a set of new generalized recurrence relations proposed recently by one of the authors (O.V.T.). The behavior of the mass dependent effective coupling constant is investigated in detail. Compact analytic results are presented.