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

Abstract

The dielectron widths of $Υ(nS) (n=1,...,7)$ and vector decay constants are calculated using the Relativistic String Hamiltonian with a universal interaction. For $Υ(nS) (n=1,2,3)$ the dielectron widths and their ratios are obtained in full agreement with the latest CLEO data. For $Υ(10580)$ and $Υ(11020)$ a good agreement with experiment is reached only if the 4S--3D mixing (with a mixing angle $θ=27^\circ\pm 4^\circ$) and 6S--5D mixing (with $θ=40^\circ\pm 5^\circ$) are taken into account. The possibility to observe higher "mixed $D$-wave" resonances, $\tildeΥ(n {}^3D_1)$ with $n=3,4,5$ is discussed. In particular, $\tildeΥ(\approx 11120)$, originating from the pure $5 {}^3D_1$ 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, $Γ_{ee}(n{}^3 D_1) \leq 2$ eV.