PERTURBATIVE QCD POTENTIAL AND THE T(T)OVER-BAR THRESHOLD - ART. NO. 014006

We include the full second-order corrections to the static QCD potenti al in the analysis of the t (t) over bar threshold cross section. Ther e is an unexpectedly large difference between the QCD potential improv ed by the renormalization-group equation in momentum space and the pot ential improved by the renormalization-group equation in coordinate sp ace. This difference remains even at a fairly shea distance 1/r simila r or equal to 100 GeV and its origin can be understood within perturba tive QCD. We scrutinize the theoretical uncertainties of the QCD poten tial in relation to the t (t) over bar threshold cross section. In par ticular there exists a theoretical uncertainty which limits our presen t theoretical accuracy of the t (t) over bar threshold cross section a t the peak to be delta sigma(peak)/sigma(peak) greater than or equal t o 6% within perturbative QCD. [S0556-2821(98)05013-9].