Perturbative QCD potential and thett¯threshold

We include the full second-order corrections to the static QCD potential in the analysis of the $t\overline{t}$ 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 $1/r\simeq 100\mathrm{GeV}$ and its origin can be understood within perturbative QCD. We scrutinize the theoretical uncertainties of the QCD potential in relation to the $t\overline{t}$ threshold cross section. In particular there exists a theoretical uncertainty which limits our present theoretical accuracy of the $t\overline{t}$ threshold cross section at the peak to be $\delta {\sigma }_{\mathrm{peak}}/{\sigma }_{\mathrm{peak}}\gtrsim 6\%$ within perturbative QCD.