Dielectron widths of the S-, D-vector bottomonium states

The dielectron widths of $\mathrm{{\rm Y}}(nS)(n=1,\mathrm{.}\mathrm{.}\mathrm{.},7)$ and vector decay constants are calculated using the Relativistic String Hamiltonian with a universal interaction. For $\mathrm{{\rm Y}}(nS)(n=1,2,3)$ the dielectron widths and their ratios are obtained in full agreement with the latest CLEO data. For $\mathrm{{\rm Y}}(10580)$ and $\mathrm{{\rm Y}}(11020)$ a good agreement with experiment is reached only if the 4S–3D mixing (with a mixing angle $\theta=27^\circ\pm 4^\circ$)and6S--5Dmixing(with$\theta=40^\circ\pm 5^\circ$) are taken into account. The possibility to observe higher “mixed $D$-wave” resonances, $\widetilde{\mathrm{{\rm Y}}}(n{}^3{D}_1)$ with $n=3,4,5$ is discussed. In particular, $\widetilde{\mathrm{{\rm Y}}}(\approx 11120)$, originating from the pure $5{}^3{D}_1$ state, can acquire a rather large dielectron width, $\sim 130$ eV, so that this resonance may become manifest in the $e^{+}{e}^{-}$ experiments. On the contrary, the widths of pure $D$-wave states are very small, ${\mathrm{\Gamma }}_{ee}(n{}^3{D}_1)\le 2$ eV.