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

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 previous unquenched quark model (UQM) studies. The mass splitting $\Delta m_{21} = m(\chi_{b2})-m(\chi_{b1})$ 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 $\Delta m_{10}$ value enables us to predict more precisely the mass of $\chi_{b0}(3P)$ to be ($10490\pm 3$) MeV. Moreover, we predict ratios of radiative decays of $\chi_{bJ}(nP)$ candidates both in UQM and quark potential model, which might provide useful references for future experimental searches.