  For further decoding the inner structure of the two excited $\Xi_b$ states
observed by LHCb, we perform a systematical study of the strong decays of the
low-lying $1D$-wave $\Xi_b$ and $\Xi_b'$ excitations using the quark pair
creation model within the $j-j$ coupling scheme. Combining with the measured
masses and decay properties of $\Xi_{b}(6327)^{0}$ and $\Xi_{b}(6327)^{0}$, the
two excited states can be explained as $1D$ $\lambda$-mode $\Xi_b$ states
$\Xi_{b}|J^{P}=\frac{3}{2}^{+},2\rangle_{\lambda\lambda}$ and
$\Xi_{b}|J^{P}=\frac{5}{2}^{+},2\rangle_{\lambda\lambda}$, respectively. If
such a view were correct, $\Xi_b'\pi$ and $\Xi_b'^*\pi$ could be another
interesting channels for experimental exploring of the $\Xi_{b}(6327)^{0}$ and
$\Xi_{b}(6327)^{0}$, respectively. Those calculations are good consistent with
the results within the chiral quark model. In addition, for the other missing
$1D$-wave $\Xi_b$ and $\Xi_b'$ excitations, our predictions indicate that:(i)
the two $\rho$-mode $1D$ $\Xi_b$ states are likely to be moderate states with a
width of $\Gamma\sim50$ MeV. The $J^P=3/2^+$ state dominantly decays into
$\Sigma_bK$ and $\Xi_b'\pi$, while the $J^P=5/2^+$ state decays primarily
through $\Sigma_b^*K$ and $\Xi_b'^*\pi$. (ii) The $\lambda$-mode $1D$ $\Xi_b'$
states may be moderate states with a widths of about several to dozens of MeV.
Most of the $\lambda$-mode $1D$ $\Xi_b'$ states mainly decay into the $1P$-wave
bottomed baryon via the pionic decay processes. Meanwhile, several
$\lambda$-mode $1D$ $\Xi_b'$ states have significant decay rates into $\Lambda
B$. (iii) While, the $\rho$-mode $1D$ $\Xi_b'$ states are predicted to be very
broad states with a width of about several hundreds MeV. It will be a great
challenge to explore the $\rho$-mode $1D$ $\Xi_b'$ states in experiments for
their broad widths.
