Corrections to the Hadronic Cross Section Near Heavy Quark-Antiquark Thresholds in e+e− Annihilation

It is demonstrated how perturbative O(α2 s ) relativistic corrections to the non-relativistic stable heavy quark-antiquark production cross section in ee annihilation based on a Coulombic QCD potential can be systematically calculated using the concept of effective field theories. The O(αs) corrections from the relativistic energy-momentum relation, the relativistic phase space corrections and the O(α2 s ) corrections involving the group theoretical factors C F and CFT are determined explicitly. For the case of tt̄ 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(αs) corrections to the leptonic decay width of heavy quark-antiquark S1 vector resonances are extracted. In the kinematic regime where the c.m. energy is much larger than the quark masses the total hadronic cross section in e+e− collisions Rhad = σ(e +e− → Hadrons)/σpt, where σpt is the point cross section, belongs to the theoretically best known and understood quantities in electroweak physics. Inspired by the asthonishing precision of the LEP experiments Rhad has been calculated up to O(αs) accuracy for LEP energies based on sophisticated multi-loop techniques [1]. In the kinematic regime near quark-antiquark thresholds, however, which is characterized by the relation