${\chi }_b(3P)$ Multiplet Revisited: Ultrafine Mass Splitting and Radiative Transitions

Abstract

Invoked by the recent CMS observation regarding candidates of the ${\chi }_b(3P)$ multiplet, we analyze the ultrafine and mass splittings among $3P$ multiplet in our unquenched quark model (UQM) studies. The mass difference of ${\chi }_{b2}$ and ${\chi }_{b1}$ in $3P$ multiplet measured by CMS collaboration ($10.6\pm 0.64\pm 0.17$ MeV) is very close to our theoretical prediction ($12$ MeV). Our corresponding mass splitting of ${\chi }_{b1}$ and ${\chi }_{b0}$ enables us to predict more precisely the mass of ${\chi }_{b0}(3P)$ to be ($10490\pm 3$) MeV. Moreover, we predict ratios of the radiative decays of ${\chi }_{bJ}(nP)$ candidates, both in UQM and quark potential model. Our predicted relative branching fraction of ${\chi }_{b0}(3P)\to {\rm Y}(3S)\gamma$ is one order of magnitude smaller than ${\chi }_{b2}(3P)$, this naturally explains the non-observation of ${\chi }_{b0}(3P)$ in recent CMS search. We hope these results might provide useful references for forthcoming experimental searches.

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• Predicting a new resonance as charmed-strange baryonic analog of $D_{s0}^{\ast }(2317)$
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• Bottomonium spectrum with a Dirac potential model in the momentum space
• Heavy quark spin partners of the $Y(4260)$ in coupled-channel formalism
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