The completion of the third-order QCD corrections to the inclusive top-pair
production cross section near threshold demonstrates that the strong dynamics
is under control at the few percent level. In this paper we consider the
effects of the Higgs boson on the cross section and, for the first time,
combine the third-order QCD result with the third-order P-wave, the leading QED
and the leading non-resonant contributions. We study the size of the different
effects and investigate the sensitivity of the cross section to variations of
the top-quark Yukawa coupling due to possible new physics effects.Comment: LaTeX, 17 page