  Recently, the LHCb collaboration has observed the decays
$\Xi^0_{b}\to\Xi^+_{c}D^-_s$ and $\Xi^-_{b}\to\Xi^0_{c}D^-_s$. They measured
the relative branching fractions times the ratio of beauty-baryon production
cross-sections
$\mathcal{R}(\frac{\Xi^0_b}{\Lambda_b})\equiv\frac{\sigma(\Xi_b^0)}{\sigma(\Lambda^0_b)}\times\frac{B(\Xi^0_{b}\to\Xi^+_{c}D^-_s)}{B(\Lambda^0_{b}\to\Lambda^+_{c}D^-_s)}$
and
$\mathcal{R}(\frac{\Xi^-_b}{\Lambda_b})\equiv\frac{\sigma(\Xi^-_b)}{\sigma(\Lambda^0_b)}\times\frac{B(\Xi^-_{b}\to\Xi^0_{c}D^-_s)}{B(\Lambda^0_{b}\to\Lambda^+_{c}D^-_s)}$.
Once the ratio $\frac{\sigma(\Xi_b^0)}{\sigma(\Lambda^0_b)}$ or
$\frac{\sigma(\Xi_b^-)}{\sigma(\Lambda^0_b)}$ is known, one can determine the
relative branching fractions which can be used to exam the mixing of $\Xi_c$
and $\Xi'_c$. In previous literature, $\Xi_c$ and $\Xi'_c$ were assumed to
belong to SU(3)$_F$ antitriple and sextet, respectively. However, recent
experimental measurements such as the ratio
$\Gamma(\Xi_{cc}\to\Xi_c\pi^+)/\Gamma(\Xi_{cc}\to\Xi'_c\pi^+)$ indicate the
spin-flavor structures of $\Xi_{c}$ and $\Xi'_{c}$ are a mixture of $\Xi^{\bar
3}_{c}$ and $\Xi^{6}_{c}$. The exact value of mixing angle $\theta$ is still
under debate. In theoretical models, the mixing angle was fitted to be about
$16.27^\circ\pm2.30^\circ$ or $85.54^\circ\pm2.30^\circ$ based on decay
channels $\Xi_{cc} \to\Xi^{(')}_{cc} $. While in lattice calculation, a small
angle ($1.2^\circ\pm0.1^\circ$) is preferred. To address such discrepancy and
test the mixing of $\Xi_c$ and $\Xi'_c$, here we propose the analysis of
semileptonic and non-leptonic decays of $\Xi_{b}\to\Xi_{c}$ and
$\Xi_{b}\to\Xi^{'}_{c}$. We calculate the decay rate of $\Xi_{b}\to\Xi_{c}$ and
$\Xi_{b}\to\Xi^{'}_{c}$ based on light-front quark model and study the effect
of the mixing angle on the ratios of weak decays $\Xi_{b}\to\Xi_{c}$ and
$\Xi_{b}\to\Xi^{'}_{c}$.....
