Perturbative O(alpha_s^2) Corrections to the Hadronic Cross Section Near Heavy Quark-Antiquark Thresholds in e+e- Annihilation

It is demonstrated how perturbative O(alpha_s^2) relativistic corrections to the non-relativistic stable heavy quark-antiquark production cross section in e^+e^- annihilation based on a Coulombic QCD potential can be systematically calculated using the concept of effective field theories. The O(alpha_s^2) corrections from the relativistic energy-momentum relation, the relativistic phase space corrections and the O(alpha_s^2) corrections involving the group theoretical factors C_F^2 and C_F T are determined explicitly. For the case of $t\bar{t}$ production the sum of these corrections amounts to 3% - 7% over the whole threshold regime and is insensitive to variations in the top width. Perturbative O(alpha_s^2) corrections to the leptonic decay width of heavy quark-antiquark ${}^3{S}_1$ vector resonances are extracted.