Prediction of anomalous $\Upsilon(5S)\to\Upsilon(1^3D_J)\eta$ transitions

TL;DR

This paper predicts the branching ratios of specific anomalous transitions in bottomonium states using hadronic loop contributions, suggesting these could be observed in future experiments like Belle and BelleII.

Contribution

It introduces a theoretical prediction of branching ratios for $S$ transitions to $
3D_J\,eta$ states, highlighting potential observability.

Findings

Predicted branching ratios range from 0.5 to 9.6 times 10^{-3}.

Predictions are comparable to observed $S o
S\,pi^+\,pi^-$ transitions.

Future experiments are encouraged to search for these transitions.

Abstract

In this work, we study the hadronic loop contribution to the $\Upsilon(5S)\to \Upsilon(1^3D_J)\eta$ ($J=1,2,3$) transitions. We predict that the branching ratios of $\Upsilon(5S)\to \Upsilon(1^3D_1)\eta$, $\Upsilon(5S)\to \Upsilon(1^3D_2)\eta$ and $\Upsilon(5S)\to \Upsilon(1^3D_3)\eta$ can reach up to $(0.5\sim5.1)\times10^{-3}$, $(0.7\sim7.5)\times10^{-3}$ and $(0.9\sim9.6)\times10^{-4}$, respectively. Since these predicted hadronic transitions of $\Upsilon(5S)$ are comparable with these observed $\Upsilon(5S)\to \Upsilon(nS)\pi^+\pi^-$ $(n=1,2,3)$, we suggest future experiment like Belle and BelleII to carry out the search for these anomalous $\Upsilon(5S)\to \Upsilon(1^3D_J)\eta$ transitions.