The heavy-quark pole masses in the Hamiltonian approach

Abstract

From the fact that the nonperturbative self-energy contribution $C_{\mathrm{SE}}$ to the heavy meson mass is small: $C_{\mathrm{SE}}(b\bar{b})=0$; $C_{\mathrm{SE}}(c\bar{c})\cong -40$ 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 $\overline{\mathrm{MS}}$ running mass ${\bar{m}}_b({\bar{m}}_b)=4.19\pm 0.04$ GeV and ${\bar{m}}_c({\bar{m}}_c)=1.10\pm 0.05$ GeV. The masses ${\omega }_c$ and ${\omega }_b$, which define the heavy quarkonia spin structure, are shown to be by $\sim 200$ MeV larger than the pole ones.

Comments: 18 pages, no figures, 8 tables