Renormalization-group improved calculation of top-quark production near threshold

The top quark cross section close to threshold in $e^+e^-$ annihilation is computed including the summation of logarithms of the velocity at next-to-next-to-leading-logarithmic order in QCD. The remaining theoretical uncertainty in the normalization of the total cross section is at the few percent level, an order of magnitude smaller than in previous next-to-next-to-leading order calculations. This uncertainty is smaller than the effects of a light standard model Higgs boson.