Predicted $\Xi_b(6087)^0$ and further predictions

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 $\Xi_b(6087)^0$ recently discovered by LHCb, but also its observation channel and its mass difference from the $\Xi_b(6100)^-$. 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 $\Lambda_b(5912)^0$, $\Lambda_b(5920)^0$, $\Xi_b(6087)^0$, and $\Xi_b(6100)^-$, our results suggest the existence of the other two $\Lambda_b$ and two $\Xi_b$ baryons, whose widths are limited. They are the $\Lambda_b(J^P = 3/2^-)$ with the mass and width about $(5.93^{+0.13}_{-0.13}~{\rm GeV},\,0.0^{+12.0}_{-~0.0}~{\rm MeV})$, the $\Lambda_b(5/2^-)$ with $(5.94^{+0.13}_{-0.13}~{\rm GeV},\,\approx0~{\rm MeV})$, the $\Xi_b(3/2^-)$ with $(6.10^{+0.15}_{-0.10}~{\rm GeV},\,1.4{^{+11.6}_{-~1.4}}~{\rm MeV})$, and the $\Xi_b(5/2^-)$ with $(6.11^{+0.15}_{-0.10}~{\rm GeV},\,1.0{^{+7.4}_{-1.0}}~{\rm MeV})$. Their mass splittings are calculated to be $M_{\Lambda_b(5/2^-)} - M_{\Lambda_b(3/2^-)} = 17\pm7~{\rm MeV}$ and $M_{\Xi_b(5/2^-)} - M_{\Xi_b(3/2^-)} = 14\pm7~{\rm MeV}$. All these baryons are explained as the $P$-wave bottom baryons of the $\rho$-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 $\rho$-mode, which can significantly improve our understanding on the internal structure of hadrons.