Higher ${\eta }_c(nS)$ and ${\eta }_b(nS)$ mesons

Abstract

The hyperfine splittings in heavy quarkonia are studied in a model-independent way using the experimental data on di-electron widths. Relativistic correlations are taken into account together with the smearing of the spin-spin interaction. The radius of smearing is fixed by the known $J/\psi -{\eta }_c(1S)$ and $\psi (2S)-{\eta }_c^{\prime }(2S)$ splittings and appears to be small, $r_{ss}\cong 0.06$ fm. Nevertheless, even with such a small radius an essential suppression of the hyperfine splittings ($\sim 50$ is observed in bottomonium. For the $nSb\bar{b}$ states $(n=1,2,...,6)$ we predict the values (in MeV) 28, 12, 10, 6, 6, and 3, respectively. For the $3S$ and $4S$ charmonium states the splittings 16(2) MeV and 12(4) MeV are obtained.

23 pages

References in corpus (24)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• Mesons with Beauty and Charm: Spectroscopy
• Charmonium levels near threshold and the narrow state $X(3872) \to π^{+}π^{-}\jpsi$
• Field strength correlators in full QCD
• Charmless Final States and S--D-wave mixing in the ${\psi }^{\prime \prime }$
• Observation of h_c(^1P_1) State of Charmonium
• Observation of eta_c^{prime} Production in gamma gamma Fusion at CLEO
• QCD string in light-light and heavy-light mesons
• Measurements of the mass and width of the eta_c meson and of an eta_c(2S) candidate
• Light meson radial Regge trajectories
• Observation of the ^1P_1 State of Charmonium
• The ${\eta }_c(3654)$ and hyperfine splitting in charmonium
• The restriction on the strong coupling constant in the IR region from the 1D-1P splitting in bottomonium
• Determination of Alpha_s(1 GeV) from the charmonium fine structure
• Production of the ${\eta }_b(nS)$ states
• A Measurement of the Total Width, the Electronic Width, and the Mass of the Upsilon(10580) Resonance
• Leptonic widths of high excitations in heavy quarkonia
• Hyperfine splitting and leptonic decay rates in heavy quarkonia
• Inclusive eta' Production from the Upsilon(1S)
• Search for eta_b in two-photon collisions at LEP II with the DELPHI detector
• etab Decay into Two Photons
• The heavy-quark pole masses in the Hamiltonian approach
• Nonperturbative hyperfine contribution to the $b_1$ and $h_1$ meson masses
• The gluonic condensate from the hyperfine splitting $M_{\mathrm{cog}}({\chi }_{cJ})-M(h_c)$ in charmonium

Cited by in corpus (10)

• Hadron interaction with heavy quarkonia
• Channel coupling in heavy quarkonia: energy levels, mixing, widths and new states
• The $\mathbf{S}-\mathbf{D}$ mixing and di-electron widths of higher charmonium $1^{--}$ states
• Strong decays and dipion transitions of Upsilon(5S)
• Bottomonium dipion transitions
• On the possibility to observe higher $n^3{D}_1$ bottomonium states in the $e^{+}{e}^{-}$ processes
• The Hyperfine Splittings in Bottomonium and the $B_q(q=n,s,c)$ Mesons
• Relativistic theory of string breaking in QCD
• Charmonium states in a coupled-channel model
• Single eta production in heavy quarkonia: breakdown of multipole expansion