N$^3$LO approximate results for top-quark differential cross sections and forward-backward asymmetry

Abstract: I present a calculation of approximate N$^3$LO corrections from NNLL soft-gluon resummation for differential distributions in top-antitop pair production in hadronic collisions. Soft-gluon corrections are the dominant contribution to top-quark production and closely approximate exact results through NNLO. I show aN$^3$LO results for the total $t{\bar t}$ cross section, the top-quark $p_T$ and rapidity distributions, and the top-quark forward-backward asymmetry. The higher-order corrections are significant and they reduce theoretical uncertainties.