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

TL;DR

This paper calculates dielectron widths of bottomonium states using a relativistic model, achieving good agreement with experimental data and exploring the potential observation of mixed D-wave resonances in electron-positron experiments.

Contribution

It provides a comprehensive calculation of dielectron widths for bottomonium states, including mixing effects, and predicts the observability of higher D-wave resonances.

Findings

Good agreement with experimental widths for the first three Upsilon states.

Significant mixing angles are needed to match data for higher states.

Potential observation of higher D-wave resonances with sizable dielectron widths.

Abstract

The dielectron widths of $\Upsilon(nS) (n=1,...,7)$ and vector decay constants are calculated using the Relativistic String Hamiltonian with a universal interaction. For $\Upsilon(nS) (n=1,2,3)$ the dielectron widths and their ratios are obtained in full agreement with the latest CLEO data. For $\Upsilon(10580)$ and $\Upsilon(11020)$ 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, $\tilde\Upsilon(n {}^3D_1)$ with $n=3,4,5$ is discussed. In particular, $\tilde\Upsilon(\approx 11120)$, 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, $\Gamma_{ee}(n{}^3 D_1) \leq 2$ eV.