We present the O(alpha_s) corrections to the cross section for the
reaction e+e- –> gamma^* –> Q \bar Q in the energy region close to
the threshold. We assume that the energy of the reaction is such that
both the perturbative expansion in the strong coupling constant and
expansion in the relative velocity of the heavy quarks can be used.
We explicitly obtain terms O(alpha_s^2/beta^2, alpha_s^2/beta,
alpha_s^2) in the relative correction to the threshold cross section.
Using the ideas of asymptotic expansions, we demonstrate how an
expansion of Feynman diagrams in the threshold region is constructed.
From this analysis we obtain a matching relation between the vector
current in full QCD and the quark–antiquark current in NRQCD at
leading order in 1/m and the second order in the strong coupling
constant.
