un 2 00 3 QCD potential as a “ Coulomb – plus – linear ” potential

We show analytically that the QCD potential can be expressed, up to an O(Λ 3 QCD 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 α S and the renormalon dominance picture. The expansion of V QCD (r) is truncated at O(α N S) [N = 6π/(β 0 α 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.