NNNLO soft-gluon corrections for the top-quark pT and rapidity distributions

We present a calculation of next-to-next-to-next-to-leading-order (NNNLO) soft-gluon corrections for differential distributions in top-antitop pair production in hadronic collisions. Approximate NNNLO (aNNNLO) results are obtained from soft-gluon resummation. Theoretical predictions are shown for the top-quark aNNNLO transverse momentum (p(T)) and rapidity distributions at LHC and Tevatron energies. The aNNNLO corrections enhance previous results for the distributions but have smaller theoretical uncertainties.