Perturbative QCD potential, renormalon cancellation, and phenomenological potentials

We examine the total energy E-tot(r)=2m(pole)+V-QCD(r) of the b (b) over bar system within perturbative QCD up to O(alpha(S)(3)). We extend a previous analysis by incorporating effects of the nonzero 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-1less than or similar torless than or similar to3 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.