Two-Loop QCD Corrections to the Heavy Quark Pair Production Cross Section ine+e−Annihilation near Threshold

We present $O\left({\alpha }_s^2\right)$ corrections to the cross section for $e^{+}{e}^{-}\to {\gamma }^{*}\to Q\overline{Q}$ close to threshold. We assume that the energy of the reaction is such that both the perturbative expansion in the strong coupling constant ${\alpha }_s$ and expansion in the velocity $\beta$ of the heavy quarks can be used. We obtain terms $O({\alpha }_s^2/{\beta }^2,{\alpha }_s^2/\beta ,{\alpha }_s^2)$ in the relative correction. We demonstrate how an expansion of Feynman diagrams in the threshold region is constructed. We obtain a matching relation between the vector current in full QCD and in nonrelativistic QCD.