Renormalization scheme and gauge dependence of perturbative QCD predictions

The problem of renormalization scheme and gauge dependence of perturbative QCD predictions in the momentum subtraction schemes is considered. A renormalization-group-improved expression for the QCD contribution to the σT(e+e-→hadrons)/σ (e+e-→μ+μ-) ratio is discussed in detail in the next-to-next-to-leading order. A rather strong gauge dependence is found because a nontrivial gauge dependence of the running coupling constant is not compensated by the gauge dependence of the expansion coefficients. The three-loop expression is found to have a stronger gauge dependence than the two-loop expression. Thus an important problem arises: How should the results of perturbative calculations in the momentum subtraction schemes be compared with the experimental data?