On the possibility to observe higher $n^3D_1$ bottomonium states in the $e^+e^-$ processes

Understand

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 $(n+1)^3S_1$ and $n^3D_1$ states ($n\geq 3$) may be mixed with a rather large mixing angle, $\theta\sim30^\circ$ and this effect provides the correct values of $\Gamma_{ee}(\Upsilon(10580))$ and $\Gamma_{ee}(\Upsilon(11020))$.
• 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 $\tilde\Upsilon(n^3D_1$) resonances ($n=3,4,5$), which originate from pure $D-$wave states.
• The value $\Gamma_{ee}(\tilde\Upsilon(3D))=0.095^{+0.028}_{-0.025}$ keV is obtained, being only $\sim 3$ times smaller than the di-electron width of $\Upsilon(10580)$, while $\Gamma_{ee}(\tilde\Upsilon(5D))\sim 135$ eV appears to be close to $\Gamma_{ee}(\Upsilon(11020))$ and therefore this resonance may become manifest in the $e^+e^-$ experiments.