Predicted $Ξ_b(6087)^0$ and further predictions

Abstract

The methods of QCD sum rules and light-cone sum rules within the framework of heavy quark effective theory have been widely applied to study the singly heavy baryons, and especially, we have applied these methods to predict not only the mass and width of the $Ξ_b(6087)^0$ recently discovered by LHCb, but also its observation channel and its mass difference from the $Ξ_b(6100)^-$. We apply the same approach to perform a complete study on the $P$-wave bottom baryons of the $SU(3)$ flavor $\mathbf{\bar 3}_F$ and investigate their fine structure. Besides the $Λ_b(5912)^0$, $Λ_b(5920)^0$, $Ξ_b(6087)^0$, and $Ξ_b(6100)^-$, our results suggest the existence of the other two $Λ_b$ and two $Ξ_b$ baryons, whose widths are limited. They are the $Λ_b(J^P = 3/2^-)$ with the mass and width about $(5.93^{+0.13}_{-0.13}~{\rm GeV},\,0.0^{+12.0}_{-~0.0}~{\rm MeV})$, the $Λ_b(5/2^-)$ with $(5.94^{+0.13}_{-0.13}~{\rm GeV},\,\approx0~{\rm MeV})$, the $Ξ_b(3/2^-)$ with $(6.10^{+0.15}_{-0.10}~{\rm GeV},\,1.4{^{+11.6}_{-~1.4}}~{\rm MeV})$, and the $Ξ_b(5/2^-)$ with $(6.11^{+0.15}_{-0.10}~{\rm GeV},\,1.0{^{+7.4}_{-1.0}}~{\rm MeV})$. Their mass splittings are calculated to be $M_{Λ_b(5/2^-)} - M_{Λ_b(3/2^-)} = 17\pm7~{\rm MeV}$ and $M_{Ξ_b(5/2^-)} - M_{Ξ_b(3/2^-)} = 14\pm7~{\rm MeV}$. All these baryons are explained as the $P$-wave bottom baryons of the $ρ$-mode, where the orbital excitation is between the two light quarks. However, the existence of this mode is still controversial, so their experimental searches can verify both our approach and the existence of the $ρ$-mode, which can significantly improve our understanding on the internal structure of hadrons.