Analytic O(alpha_s) Results for Bottom and Top Quark Production in e+ e- Collisions

We present a new derivation of the O(alpha_s) angular distribution of the outgoing $q$-quark in the production process $e^+ e^- \to\gamma,Z\to q\,\bar{q}(g)$. In our calculation, we express the three-particle phase-space integration of the gluon-bremsstrahlung process in terms of a general set of analytic integral solutions. A consistent treatment of the QCD one-loop corrections to the axial-vector current deserves special attention. This is relevant in the derivation of the forward-backward asymmetry predicted by the standard model. Finally, we provide the full analytical solutions for the differential rates in closed form and conclude with numerical estimates for bottom and top quark production.