χ b ( 3 P ) multiplet revisited: Hyperfine mass splitting and radiative transitions

Invoked by the recent CMS observation regarding candidates of the χb(3P) multiplet, we analyze the hyperfine and mass splittings among the 3P multiplet in our unquenched quark model studies. The mass difference of χb2 and χb1 in the 3P multiplet measured by the CMS Collaboration (10.6±0.64±0.17 MeV) is very close to our theoretical prediction (12 MeV). Our corresponding mass splitting of χb1 and χb0 enables us to predict more precisely the mass of χb0(3P) to be (10490±3) MeV. Moreover, we predict ratios of the radiative decays of χbJ(nP) candidates, both in the unquenched quark model and quark potential model. Our predicted relative branching fraction of χb0(3P)→Υ(3S)γ is one order of magnitude smaller than χb2(3P); this naturally explains the nonobservation of χb0(3P) in the recent CMS search. We hope these results provide useful references for forthcoming experimental searches.