The Perturbative QCD Potential and the ttbar Threshold

We include the full second-order corrections to the static QCD potential in the analysis of the ttbar 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 \simeq 100 GeV and its origin can be understood within perturbative QCD. We scrutinize the theoretical uncertainties of the QCD potential in relation to the ttbar threshold cross section. In particular there exists a theoretical uncertainty which limits our present theoretical accuracy of the ttbar threshold cross section at the peak to be not better than 6% within perturbative QCD.