  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.
