PERTURBATIVE O(ALPHA(2)(S)) CORRECTIONS TO THE HADRONIC CROSS-SECTIONNEAR HEAVY QUARK-ANTIQUARK THRESHOLDS IN E(-) ANNIHILATION()E()

It is demonstrated how perturbative O(alpha(s)(2)) relativistic correc tions to the nonrelativistic stable heavy quark-antiquark production c ross section in e(+)e(-) annihilation based on a Coulombic QCD potenti al can be systematically calculated using the concept of effective fie ld theories. The O(alpha(s)(2)) corrections from the relativistic ener gy-momentum relation, the relativistic phase space corrections and the O(alpha(s)(2)) corrections involving the group theoretical factors C- F(2) and CFT are determined explicitly. For the case of <t(t)over bar> production the sum of these corrections amounts to 3%-7% over the who le threshold regime and is insensitive to variations in the top width. Perturbative O(alpha(s)(2)) corrections to the leptonic decay width o f heavy quark-antiquark S-3(1) vector resonances are extracted.