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

We show analytically that the QCD potential can be expressed, up to an O(ΛQCD3r2) 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 αS and the renormalon dominance picture. The expansion of VQCD(r) is truncated at O(αSN) (N=6π/(β0αS)), 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