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Explaining the anomalous<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">ϒ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>5</mml:mn><mml:mi>S</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">→</mml:mo><mml:msub><mml:mrow><mml:mi>χ</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:mi>ω</mml:mi></mml:mrow></mml:math>decays through the hadronic loop effect
In this work, we carry out the study on $\mathrm{\ensuremath{\Upsilon}}(5S)\ensuremath{\rightarrow}{\ensuremath{\chi}}_{bJ}\ensuremath{\omega}$ ($J=0,1,2$) by considering the hadronic loop mechanism. Our results show that Belle's preliminary data of the branching ratios for $\mathrm{\ensuremath{\Upsilon}}(5S)\ensuremath{\rightarrow}{\ensuremath{\chi}}_{bJ}\ensuremath{\omega}$ can be well reproduced in our calculation with a common parameter range, which reflects the similarity among these $\mathrm{\ensuremath{\Upsilon}}(5S)\ensuremath{\rightarrow}{\ensuremath{\chi}}_{bJ}\ensuremath{\omega}$ decays …