Higher ηc(nS) and ηb(nS) mesons

The hyperfine splittings in heavy quarkonia are studied in a model-independent way using experimental data on dielectron widths. Relativistic correlations are taken into account together with the smearing of spin-spin interaction. The radius of smearing is fixed by known J/psi-eta(c)(1S), psi(2S)-eta(')(c)(2S) splittings, which appears to be small, r(ss) congruent to 0.06 fm. Nevertheless, even with such a small radius, substantial suppression of hyperfine splittings (similar to 50%) is observed in bottomonium. For nS b (b) over bar states (n = 1, 2, ..., 6), our predicted splittings (in MeV) are 28, 12, 10, 5, 6, 3. For the 3S and 4S charmonium states, the splittings 16(2) and 12(4) MeV are obtained.