Fe b 19 98 The Perturbative QCD Potential and the tt̄ Threshold

The Perturbative QCD Potential and the t ¯ t Threshold Abstract We include the full second-order corrections to the static QCD potential in the analysis of the t ¯ t threshold cross section. There is an unexpectedly large difference between the QCD potential improved by the renormalization-group equation in momentum space and the potential improved by the renormalization-group equation in coordinate space. This difference remains even at a fairly short distance 1/r ≃ 100 GeV and its origin can be understood within perturbative QCD. We scrutinize the theoretical uncertainties of the QCD potential in relation to the t ¯ t threshold cross section. In particular there exists a theoretical uncertainty which limits our present theoretical accuracy of the t ¯ t threshold cross section at the peak to be δσ peak /σ peak > ∼ 6% within perturbative QCD.