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

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

Figure 1

The necessary diagrams depicting $\mathrm{\Upsilon }(5S)\to {\chi }_{bJ}\omega$ decays under the hadronic loop effect.

Figure 2

The quark level diagram depicting $\mathrm{\Upsilon }(5S)\to {\chi }_{bJ}\omega$ decay under the hadronic loop effect.

Figure 3

The branching ratios of $\mathrm{\Upsilon }(5S)\to {\chi }_{bJ}\omega$ dependent on the parameter ${\alpha }_{\mathrm{\Lambda }}$. The horizontal bands are the experimental data measured by the Belle Collaboration, while the vertical bands indicate the ${\alpha }_{\mathrm{\Lambda }}$ range when our results overlap with the Belle data.