Top-quark spin correlations at hadron colliders: predictions at next-to-leading order QCD.

The collider experiments at the Tevatron and the LHC will allow for detailed investigations of the properties of the top quark. This requires precise predictions of the hadronic production of tt pairs and of their subsequent decays. In this Letter we present for the reactions pp, pp-->tt+X-->l+l'-+X the first calculation of the dilepton angular distribution at next-to-leading order in the QCD coupling, keeping the full dependence on the spins of the intermediate tt state. The angular distribution reflects the degree of correlation of the t and t spins which we determine for different choices of t and t spin bases. In the case of the Tevatron, the QCD corrections are sizable, and the distribution is quite sensitive to the parton content of the proton.