Mass spectrum of $1^{--}$ heavy quarkonium

Abstract

We calculate the masses and leptonic decay widths of the bottomonium $b\bar{b}$ and charmonium $c\bar{c}$ states in a constituent quark model where the Cornell-like potential and spin-dependent interaction are employed, with all model parameters predetermined by studying ground and first radial excited states of S- and P-wave heavy quarkonium mesons. By comparing the theoretical predictions for $J^{PC}=1^{--}$ quarkonium states with experimental data and considering possible mixtures of $nS$ and $(n-1)D$ states, we provide tentative assignments for all observed $J^{PC}=1^{--}$ heavy quarkonia. The work suggests that the $\hat{I}\yen$(10860) and $\hat{I}\yen$(11020) are $b\bar{b}$ $5S-4D$ mixture states, and the $\ddot{I}ˆ$(4360) and $\ddot{I}ˆ$(4415) are largely $4S$ and $3D$ $c\bar{c}$ states respectively. The $\ddot{I}ˆ$(4260) may not be accommodated with the conventional meson picture in the present work.