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.

18 pages, no figures, 8 tables

References in corpus (2)

• The ${\eta }_c(3654)$ and hyperfine splitting in charmonium
• Phenomenology from lattice QCD

Cited by in corpus (9)

• Decay constants of the heavy-light mesons from the field correlator method
• Di-Pion Decays of Heavy Quarkonium in the Field Correlator Method
• Leptonic widths of high excitations in heavy quarkonia
• Dynamics of confined gluons
• Higher ${\eta }_c(nS)$ and ${\eta }_b(nS)$ mesons
• Masses of the η_c(nS) and η_b(nS) mesons
• The running mass $m_s$ at low scalefrom the heavy-light meson decay constants
• The gluonic condensate from the hyperfine splitting $M_{\mathrm{cog}}({\chi }_{cJ})-M(h_c)$ in charmonium
• Phenomenology of Strong Interactions -- Towards an Effective Theory for Low Energy QCD