Perturbative QCD Potential, Renormalon Cancellation and Phenomenological Potentials

Abstract

We examine the total energy E_tot(r) = 2 m_pole + V_QCD(r) of the b\bar b system within perturbative QCD up to O(α_S^3). We extend a previous analysis by incorporating effects of the non-zero charm-quark mass in loops. We find that, once the renormalon cancellation is performed, E_tot(r) agrees well with typical phenomenological potentials for heavy quarkonia at distances 0.5 GeV^-1 ~< r ~< 3 GeV^-1. We also examine the perturbative predictions for E_tot(r) of other heavy quarkonium systems. Whenever stable predictions are obtained, they agree with each other up to an r-independent constant.