Masses of the \eta_c(nS) and \eta_b(nS) mesons

Abstract

The hyperfine splittings in heavy quarkonia are studied using new experimental data on the di-electron widths. The smearing of the spin-spin interaction is taken into account, while 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, $r_{ss}\approx 0.06$ 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 $(n=1,2,...6)$ the values we predict (in MeV) are 28, 12, 10, 6, 6, and 3, respectively. In single-channel approximation for the $3S$ and $4S$ charmonium states the splittings 16(2) MeV and 12(4) MeV are obtained.

Comments: 13 pages, no figures