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 mu. The calculated energy difference between the J/psi and the eta(c) fits the experimental data well, while the predicted energy difference Delta M(p) between the center of gravity of the 1(3)p(0,1,2) states and the 1(1)P(1) 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 Delta M(p), which we discuss, that are of comparable size (similar to 1 MeV) that should be included, before precise agreement with the data can be expected. The mass differences of the psi'-eta(c)', Y(1S)-eta(b), Y(2S)-eta(b)', and B-c*-B-c are also predicted.