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

Abstract

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 reactions replacing the $\pi^-$ by a $D_s^-$. At the same time we evaluate the semileptonic 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 reactions from the perspective that the $\Xi_c^0 (2790)$ and $\Xi_c^0 (2815)$ resonances are dynamically generated from the pseudoscalar-baryon and vector-baryon interactions. We evaluate ratios of the rates of these reactions and make predictions that can be tested in future experiments. We also find that the results are rather sensitive to the coupling of the $\Xi_c^*$ resonances to the $D^* \Sigma$ and $D^* \Lambda$ components.