The Hyperfine Spin Splittings In Heavy Quarkonia

Abstract

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 the gravity of $1^3{P}_{0,1,2}$ 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 ($\sim 1$ MeV) that should be included, before precise agreement with the data can be expected. The mass differences of the ${\psi }^{\prime }-{\eta }_c^{\prime }$, ${\rm Y}(1S)-{\eta }_b$, ${\rm Y}(2S)-{\eta }_b^{\prime }$, and $B_c^{\ast }-B_c$ are also predicted.

17 pages

References in corpus (7)

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Cited by in corpus (6)

• S-D Mixing and Searching for the psi(1P1) State at the Beijing Electron-Positron Coolider
• Non-perturbative dynamics of the heavy-light quark system in the non-recoil limit
• Search of 1^P_1 charmonium in B decay
• Measurement of hybrid content of heavy quarkonia using lattice NRQCD
• Non-relativistic quark-antiquark potential: spectroscopy of heavy-quarkonia and exotic SUSY quarkonia
• Hybrid configuration content of heavy S-wave mesons