RG/Padé Estimate of the Three-Loop Contribution to the QCD Static Potential Function

The three renormalization-group-accessible three-loop coefficients of powers of logarithms within the MS series for the QCD static potential are calculated and compared to values obtained via asymptotic Padé-approximant methods. The leading and next-to-leading logarithmic coefficients are both found to be in exact agreement with their asymptotic Padé-predictions. The predicted value for the third RGaccessible coefficient is found to be within 7% relative |error| of its true value for nf ≤ 6, and is shown to be in exact agreement with its true value in the nf → ∞ limit. Asymptotic Padé estimates are also obtained for the remaining (RG-inaccessible) three-loop coefficient. The perturbative portion of the QCD static potential is presently known to two subleading orders of perturbation theory [1]. This potential may be expressed as an integral over an MS perturbative-QCD series in momentum space, Vpert(r) = ∫ dq (2π)3 e q·~r (