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. $O(v^2)$, $O(v{\alpha }_s)$ and $O({\alpha }_s^2)$) relativistic corrections to the total photon mediated $t\bar{t}$ production cross section at threshold are presented in the framework of nonrelativistic quantum chromodynamics. The results are obtained using semi-analytic 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.