Exact mass dependent two--loop $\bar{\alpha}_s(Q^2)$ in the background   MOM renormalization scheme
  A two-loop calculation of the renormalization group $\beta$--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. 
F. Jegerlehner and O.V. Tarasov