Top quark production near threshold: on resummation of O( (\beta_0\alpha_s)^n) QCD corrections

We discuss the resummation of the potentially large O((\beta_0\alpha_s)^n) QCD corrections to the total cross section of the process e^+e^- \to t \bar t near the threshold. In this approximation, the cross section factorization into the short- and long-distance parts is valid. The short-distance correction is reduced to the production vertex renormalization. It amounts to -9.5% and is well under control. The long distance corrections are accounted for as the effect of the coupling’s running in the QCD potential. We argue that the accuracy of present predictions for the cross section in the scheme with the running QCD coupling is about 10%.