Top Quark Production and Decay at Next-to-leading Order in $e^+e^-$ Annihilation

We study the effects of QCD corrections to the process $e^+e^-\rightarrow t\bar t+X\rightarrow b\ell^+\nu \bar b\ell^-\bar \nu+X$ above threshold. We show how to treat consistently to ${\cal O}(\alpha_s)$ the gluon radiation in both the production and the decay of the top quarks, while maintaining all angular correlations in the event. At this order there is an ambiguity in the event reconstruction whenever a real gluon occurs in the final state. We study the effects of this ambiguity on the top mass and helicity angle distributions. For a top mass of 175 GeV and collider energy of 400 GeV the gluon radiation is emitted predominantly in the decay of the top quarks.