Investigating the $\mathbf{Υ(10753)\to Υ(1^3D_J)η}$ transitions

Abstract: In this work, we investigate the $\Upsilon(10753)\to\Upsilon(1<sup>3D_J)\eta$ ($J=1,2,3$) processes, where the $\Upsilon(10753)$ is assigned as a conventional bottomonium under the $4S$-$3D$ mixing scheme. Our result shows that the concerned processes have considerable branching ratios, {\it i.e.}, branching ratios $$\mathcal{B}[\Upsilon(10753)\to\Upsilon(1<sup>3D_{1})\eta]$$ and $$\mathcal{B}[\Upsilon(10753)\to\Upsilon(1<sup>3D_{2})\eta]$$ can reach up to the order of magnitude of $10<sup>{-4}-10<sup>{-3}$, while $$\mathcal{B}[\Upsilon(10753)\to\Upsilon(1<sup>3D_{3})\eta]$$ is around $10<sup>{-6}-10<sup>{-5}$. With the running of Belle II, it is a good opportunity for finding out the concerned hidden-bottom hadronic decays.