Explaining the anomalous $\Upsilon(5S)\to \chi_{bJ}\omega$ decays through the hadronic loop effect

In this work, we carry out the study on $\Upsilon(5S)\to \chi_{bJ}\omega$ ($J=0,1,2$) by considering the hadronic loop mechanism. Our results show that the Belle's preliminary data of the branching ratios for $\Upsilon(5S)\to \chi_{bJ}\omega$ can be well reproduced in our calculation with a common parameter range, which reflects the similarity among these $\Upsilon(5S)\to \chi_{bJ}\omega$ decays of concern.