Masses of the ηc(nS) and ηb(nS) mesons

AbstractThe 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/ψ−ηc(1S) and ψ(2S)−ηc′(2S) splittings and appears to be small, rss≈0.06 fm. Nevertheless, even with such a small radius an essential suppression of the hyperfine splittings (∼50%) is observed in bottomonium. For the nS bb¯ 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) and 12(4) MeV are obtained