Singular gauge dependence of the QCD coupling constant

Renormalization-group equations for the QCD coupling constant α¯(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 α¯(t) may be different than in the minimal subtraction scheme because of the dependence of ${\beta }_2$ on the gauge parameter. In the concrete case of the asymmmetric momentum subtraction scheme it is found that, for the negative initial gauge parameters, α¯(t) does not tend to zero for t→∞. This indicates that the ultraviolet behavior of α¯(t) may strongly depend on the renormalization scheme and on the gauge parameter.