Hyperfine spin splittings in heavy quarkonia

The hyperfine spin splittings in heavy quarkonia are studied using the recently developed renormalization-group-improved spin-spin potential which is independent of the scale parameter μ. The calculated energy difference between the J/ψ and the ηc fits the experimental data well, while the predicted energy difference ΔMP between the center of gravity of the 13P0,1,2 states and the 11P1 state of charmonium has the correct sign but is somewhat larger than the experimental data. This is not surprising since there are several other contributions to ΔMP, which we discuss, that are of comparable size (∼1 MeV) that should be included, before precise agreement with the data can be expected. The mass differences of the ψ'-ηc', Υ(1S)-ηb, Υ(2S)-ηb', and Bc*-Bc are also predicted. copyright 1996 The American Physical Society