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

Abstract

The dielectron widths of ${\rm Y}(nS)(n=1,...,7)$ and vector decay constants are calculated using the Relativistic String Hamiltonian with a universal interaction. For ${\rm Y}(nS)(n=1,2,3)$ the dielectron widths and their ratios are obtained in full agreement with the latest CLEO data. For ${\rm Y}(10580)$ and ${\rm Y}(11020)$ a good agreement with experiment is reached only if the 4S--3D mixing (with a mixing angle $\theta =27^{\circ }\pm 4^{\circ }$) and 6S--5D mixing (with $\theta =40^{\circ }\pm 5^{\circ }$) are taken into account. The possibility to observe higher "mixed $D$-wave" resonances, $\widetilde{{\rm Y}}(n{}^3{D}_1)$ with $n=3,4,5$ is discussed. In particular, $\widetilde{{\rm Y}}(\approx 11120)$, 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, ${\Gamma }_{ee}(n{}^3{D}_1)\le 2$ eV.

Comments: 13 pages, no figures