O(alpha_s^2) Corrections to e+e- to ttbar Total and Differential Cross Sections Near Threshold

Recently full O(alpha_s^2, alpha_s*beta, beta^2) corrections to the threshold total cross section for e+e- to ttbar have been calculated, and the reported corrections turned out to be unexpectedly large. We study how to reduce theoretical uncertainties of the cross section. We adopt a new mass definition proposed by Beneke, which incorporates a renormalon-pole cancellation in the total energy of a static quark-antiquark pair. This improves the convergence of the 1S resonance mass, while the normalization of the cross section scarcely changes. We argue that resummations of logarithms are indispensable, since two largely separated scales dictate the shape of the cross section. As a first step, we resum logarithms in the Coulombic part of the t-tbar potential and observe a considerable improvement in the convergence of corresponding corrections. There still remain, however, large corrections, which arise from a 1/r^2 term in the ttbar potential. We also calculate full O(alpha_s^2, alpha_s*beta, beta^2) corrections to the momentum distributions of top quarks in the threshold region. Corrections to the distribution shape are small on the 1S resonance. At higher energies, corrections become larger.