Hidden-bottom hadronic transitions of $\Upsilon(10753)$

Assuming that the $\Upsilon(10753)$ is a $4S$-$3D$ mixed state, we investigated the hidden-bottom hadronic decays of the $\Upsilon(10753) \to \eta_b(1S)\omega(\eta^{(\prime)})$ via the intermediate meson loops. In a commonly accepted range of the model parameter $\alpha$ in the form factor, the predicted branching ratios may reach to the order of $10^{-3}$--$10^{-2}$. The relative ratio of the partial decay widths of the $\Upsilon(10753)\to\eta_b\eta^{(\prime)}$ to $\Upsilon(10753)\to \eta_b\omega$ is found to be dependent on the $\eta$-$\eta'$ mixing angle. In addition, we also calculated the ratios of the partial decays widths of the $\Upsilon(10753) \to \eta_b \omega$ to $\Upsilon(10753)\to \Upsilon(nS)\pi^+\pi^-$ ($n=1\,,2$), which are found to be around 0.4 and 0.2 for $n=1$ and $n=2$, respectively. These values are in accordance with the preliminary experimental results. The calculations presented here tend to favor the $\Upsilon(10753)$ as the $4S$-$3D$ mixture. We hope these predictions could be verified by the future BelleII experiments.