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 ${\mathrm{\eta }}_{\mathit{c}}$ fits the experimental data well, while the predicted energy difference Δ${\mathit{M}}_{\mathit{P}}$ between the center of gravity of the $1^3$${\mathit{P}}_{0,1,2}$ states and the $1^1$${\mathit{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 Δ${\mathit{M}}_{\mathit{P}}$, 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 ${\mathrm{\psi }}^{\prime }$-${\mathrm{\eta }}_{\mathit{c}}^{\prime }$, Υ(1S)-${\mathrm{\eta }}_{\mathit{b}}$, Υ(2S)-${\mathrm{\eta }}_{\mathit{b}}^{\prime }$, and ${\mathit{B}}_{\mathit{c}}^{\mathrm{*}}$-${\mathit{B}}_{\mathit{c}}$ are also predicted. © 1996 The American Physical Society.

• Received 16 June 1995

DOI:https://doi.org/10.1103/PhysRevD.53.5051