Top quark pair production at threshold: Complete next-to-next-to-leading order relativistic corrections

Abstract

The complete next-to-next-to-leading order [i.e., $\mathcal{O}{(v}^{2}),$ $\mathcal{O}(v{\ensuremath{\alpha}}_{s}),$ and $\mathcal{O}({\ensuremath{\alpha}}_{s}^{2})]$ relativistic corrections to the total photon mediated $t\overline{t}$ production cross section at threshold are presented in the framework of nonrelativistic quantum chromodynamics. The results are obtained using semianalytic methods and ``direct matching.'' The size of the next-to-next-to-leading order relativistic corrections is found to be comparable to the size of the next-to-leading order ones.