Threshold production of heavy top quarks: QCD and the Higgs boson

We calculate the threshold cross section for ${\mathit{e}}^{+}$ ${\mathit{e}}^{\mathrm{-}}$→tt¯ to leading-logarithmic order in QCD, using a nonrelativistic approximation suggested by Fadin and Khoze. We study the mass range 100≤${\mathit{m}}_{\mathit{t}}$≤250 GeV, and show that the cross section is an excellent measure of ${\mathrm{\alpha }}_{\mathit{s}}$ for the lower portion of the mass range, while for a heavier top quark it is sensitive to the mass and couplings of the Higgs boson. We argue that a precise determination of ${\mathit{m}}_{\mathit{t}}$ and a measurement of ${\mathrm{\Gamma }}_{\mathit{t}}$ are possible. We also show that nonperturbative effects are small, confirming that the tt¯ threshold is a detailed perturbative test of the standard model.