Quarkonium spectroscopy and perturbative QCD: Massive quark-loop effects

We study the spectra of the bottomonium and B-c states within perturbative QCD up to order alpha(s)(4). The O(Lambda(QCD)) renormalon cancellation between the static potential and the pole mass is- performed in the epsilon-expansion scheme. We extend our previous analysis by including the (dominant) effects of nonzero charm-quark mass in loops up to the next-to-leading nonvanishing order epsilon(3). We fix the b-quark (MS) over bar mass (m) over bar (b) = m(b)((MS) over bar)(m(b)((MS) over bar)) on Y(1S) and compute the higher levels. The effect of the charm mass decreases (m) over bar (b) by about 11 MeV and increases the n = 2 and n = 3 levels by about 70-100 MeV and 240-280 MeV, respectively. We provide an extensive quantitative analysis. The size of nonperturbative and higher order contributions is discussed by comparing the obtained predictions with the experimental data. An agreement of the perturbative predictions and the experimental data depends crucially on the precise value (inside the present error) of alphas(8)(M-Z). We obtain m(b)((MS) over bar)(m(b)((MS) over bar)) = 4190+/-20+/-25+/-3 MeV.