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

TL;DR

This paper explores the potential observation of higher bottomonium states with specific quantum numbers in electron-positron collisions, highlighting the effects of S-D mixing on their di-electron widths and the likelihood of detecting these states experimentally.

Contribution

It introduces the possibility of observing higher $n^3D_1$ bottomonium states in $e^+e^-$ processes and analyzes the impact of S-D mixing on their di-electron widths and experimental signatures.

Findings

S-D mixing significantly increases di-electron widths of certain bottomonium states.

Predicted di-electron width of $ ildeD_1(3)$ is about 0.095 keV.

Mass differences between $nD$ and $(n+1)S$ states are approximately 50 MeV.

Abstract

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. The mass differences between $M(nD)$ and $M((n+1)S) (n=4,5)$ are shown to be rather small, $50\pm 10$ MeV.