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

TL;DR

This paper revisits the $chi_b(3P)$ multiplet using an unquenched quark model, predicting ultrafine mass splittings and radiative decay ratios that align with recent experimental data and guide future searches.

Contribution

It provides new theoretical predictions for mass splittings and decay ratios of the $chi_b(3P)$ multiplet, enhancing understanding of bottomonium states.

Findings

Mass difference between $chi_{b2}$ and $chi_{b1}$ matches CMS measurements.

Predicted mass of $chi_{b0}(3P)$ is ($10490 ext{ MeV}$) with small uncertainty.

Relative branching fraction of $chi_{b0}(3P) o ext{Upsilon}(3S) ext{gamma}$ is much smaller than $chi_{b2}(3P)$.

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 $\chi_{b0}(3P)\to\Upsilon(3S)\gamma$ 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.