<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>10753</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">→</mml:mo><mml:mi mathvariant="normal">ϒ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">S</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math> decays induced by hadronic loop mechanism
Zi-Yue Bai, Yu-Shuai Li, Qi Huang, Xiang Liu, Takayuki Matsuki
Abstract
In this work, we investigate the $\mathrm{\ensuremath{\Upsilon}}(10753)\ensuremath{\rightarrow}\mathrm{\ensuremath{\Upsilon}}(nS){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ ($n=1$, 2, 3) processes by considering the hadronic loop mechanism, where $\mathrm{\ensuremath{\Upsilon}}(10753)$ is assigned to a conventional bottomonium in the $4S\text{\ensuremath{-}}3D$ mixing scheme. Our results of the concerned processes own considerable branching ratios, which can reach up to the order of magnitude of ${10}^{\ensuremath{-}4}--{10}^{\ensuremath{-}3}$. We indicate that the measured ${\mathrm{\ensuremath{\Gamma}}}_{{e}^{+}{e}^{\ensuremath{-}}}\ifmmode\times\else\texttimes\fi{}\mathcal{B}[\mathrm{\ensuremath{\Upsilon}}(10753)\ensuremath{\rightarrow}\mathrm{\ensuremath{\Upsilon}}(nS){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}]$ values given by Belle can be reproduced well. This fact supports the former bottomonium assignment to the $\mathrm{\ensuremath{\Upsilon}}(10753)$ in the $4S\text{\ensuremath{-}}3D$ mixing scheme. Obviously, it is a good opportunity for the ongoing Belle II experiment if the predicted result in this work can be tested further.