On the possibility to observe higher $n^3{D}_1$ bottomonium states in the $e^{+}{e}^{-}$ processes

Abstract

The possibility to observe new bottomonium states with $J^{PC}=1^{--}$ in the region $10.7-11.1$ GeV is discussed. The analysis of the di-electron widths shows that the $(n+1{)}^3{S}_1$ and $n^3{D}_1$ states ($n\ge 3$) may be mixed with a rather large mixing angle, $\theta \sim 30^{\circ }$ and this effect provides the correct values of ${\Gamma }_{ee}({\rm Y}(10580))$ and ${\Gamma }_{ee}({\rm Y}(11020))$. On the other hand, the $S-D$ mixing gives rise to an increase by two orders of magnitude of the di-electron widths of the mixed $\widetilde{{\rm Y}}(n^3{D}_1$) resonances ($n=3,4,5$), which originate from pure $D-$wave states. The value ${\Gamma }_{ee}(\widetilde{{\rm Y}}(3D))=0.095_{-0.025}^{+0.028}$ keV is obtained, being only $\sim 3$ times smaller than the di-electron width of ${\rm Y}(10580)$, while ${\Gamma }_{ee}(\widetilde{{\rm Y}}(5D))\sim 135$ eV appears to be close to ${\Gamma }_{ee}({\rm Y}(11020))$ and therefore this resonance may become manifest in the $e^{+}{e}^{-}$ experiments. The mass differences between $M(nD)$ and $M((n+1)S)(n=4,5)$ are shown to be rather small, $50\pm 10$ MeV.

Comments: 5 pages, no figures