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We have performed the calculations for the nonleptonic $\Xi_b^- \rightarrow\pi^- \ \Xi_c^0 (2790) \left(J=\frac{1}{2}\right)$ and $\Xi_b^- \rightarrow\pi^- \ \Xi_c^0 (2815) \left(J=\frac{3}{2}\right)$ and the same reactionsreplacing the $\pi^-$ by a $D_s^-$. At the same time we evaluate thesemileptonic rates for $\Xi_b^- \rightarrow \bar{\nu}_l l \ \Xi_c^0 (2790)$ and$\Xi_b^- \rightarrow \bar{\nu}_l l \ \Xi_c^0 (2815)$. We look at the reactionsfrom the perspective that the $\Xi_c^0 (2790)$ and $\Xi_c^0 (2815)$ resonancesare dynamically generated from the pseudoscalar-baryon and vector-baryoninteractions. We evaluate ratios of the rates of these reactions and makepredictions that can be tested in future experiments. We also find that theresults are rather sensitive to the coupling of the $\Xi_c^*$ resonances to the$D^* \Sigma$ and $D^* \Lambda$ components.

Predictions for $\Xi_b^- \rightarrow \pi^- \left(D_s^- \right) \ \Xi_c^0  (2790) \left(\Xi_c^0 (2815) \right)$ and $\Xi_b^- \rightarrow \bar{\nu}_l l \  \Xi_c^0 (2790) \left(\Xi_c^0 (2815) \right)$