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 effects of non-zero charm-quark mass in loops up to the next-to-leading non-vanishing order epsilon^3. An extensive quantitative analysis is provided. Qualitatively the effect of the charm mass is to widen the level spacings and the effect becomes larger among higher levels. The size of non-perturbative 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 alpha_s(M_Z). For the b-quark MSbar mass we obtain $m_b^{\overline{MS}}(m_b^{\overline{MS}}) = 4190 \pm 20 \pm 25 \pm 4 ~ {MeV}$.