Singular gauge dependence of the QCD coupling constant

Renormalization-group equations for the QCD coupling constant alpha-bar(t) and running gauge parameter a(t) in the two-loop approximation are discussed. It is pointed out that in momentum subtraction schemes the evolution of alpha-bar(t) may be different than in the minimal subtraction scheme because of the dependence of β2 on the gauge parameter. In the concrete case of the asymmmetric momentum subtraction scheme it is found that, for the negative initial gauge parameters, alpha-bar(t) does not tend to zero for t→∞. This indicates that the ultraviolet behavior of alpha-bar(t) may strongly depend on the renormalization scheme and on the gauge parameter