We compute the QCD corrections to the production of a top quark pair in association with one hard jet at the Tevatron and the LHC, using the method of generalized D-dimensional unitarity. Top quark decays are included at leading order in perturbative QCD. We present kinematic distributions of top quark decay products in lepton plus jets and dilepton final states at the Tevatron and the LHC, using realistic selection cuts. We confirm a strong reduction of the top quark forward-backward asymmetry for the process ttbar+jet at the Tevatron at next-to-leading order, first observed by Dittmaier, Uwer and Weinzierl. We argue that there is a natural way to understand this reduction and that it does not imply a breakdown of the perturbative expansion for the asymmetry.
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