QCD potential as a "Coulomb-plus-linear" potential

Abstract

We show analytically that the QCD potential can be expressed, up to an O(Lambda_QCD^3 r^2) uncertainty, as the sum of a ``Coulomb'' potential (with log corrections at short distances) and a linear potential, within an approximation based on perturbative expansion in alpha_S and the renormalon dominance picture. The expansion of V_QCD(r) is truncated at O(alpha_S^N) [N = 6 pi/(beta_0 alpha_S)], where the term becomes minimal according to the estimate by NLO renormalon, and is studied for N >> 1. Analytic expressions for the linear potential are obtained in some cases.

Comments: Version to appear in Phys.Lett.B; Explanations on derivation added; Leading ultrasoft logs included in the analysis (Sec.5);12 pages,4 figures