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

The complete next-to-next-to-leading order [i.e., $\mathcal{O}{(v}^2),$ $\mathcal{O}\left(v{\alpha }_s\right),$ and $\mathcal{O}\left({\alpha }_s^2\right)]$ 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.