Perturbative QCD potential, renormalon cancellation, and phenomenological potentials

We examine the total energy E_tot(r) = 2m_pole+ V _QCD(r) of the b̄ system within perturbative QCD up to script O sign(α_S³). 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^-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.