The heavy-quark pole masses in the Hamiltonian approach

From the fact that the nonperturbative self-energy contribution $C_{\mathrm{S}\mathrm{E}}$ to the heavy meson mass is small: $C_{\mathrm{S}\mathrm{E}}(b\bar{b})=0$; $C_{\rm SE}(c\bar{c})\cong -40$ MeV \cite{ref.01}, strong restrictions on the pole masses $m_b$ and $m_c$ are obtained. The analysis of the $b\bar{b}$ and the $c\bar{c}$ spectra with the use of relativistic (string) Hamiltonian gives $m_b$(2-loop)$=4.78\pm 0.05$ GeV and $m_c$(2-loop)$=1.39\pm 0.06$ GeV which correspond to the $\overline{\mathrm{M}\mathrm{S}}$ running mass $\bar{m}_b(\bar{m}_b)=4.19\pm 0.04$GeVand$\bar{m}_c(\bar{m}_c)=1.10\pm 0.05$GeV\mathrm{.}Themasses$\omega_c$and$\omega_b$, which define the heavy quarkonia spin structure, are shown to be by $\sim 200$ MeV larger than the pole ones.