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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 branchingratios 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 upto $(0.5\sim5.1)\times10^{-3}$, $(0.7\sim7.5)\times10^{-3}$ and$(0.9\sim9.6)\times10^{-4}$, respectively. Since these predicted hadronictransitions of $\Upsilon(5S)$ are comparable with these observed$\Upsilon(5S)\to \Upsilon(nS)\pi^+\pi^-$ $(n=1,2,3)$, we suggest futureexperiment like Belle and BelleII to carry out the search for these anomalous$\Upsilon(5S)\to \Upsilon(1^3D_J)\eta$ transitions.

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