Calculation of the ratios and absolute rates of the $\Xi_b^- \to \pi^- (D_s^- ) \ \Xi_c^0 (2790) \left(\Xi_c^0 (2815) \right)$ and $\Xi_b^- \to \bar{\nu}_l l \ \Xi_c^0 (2790) \left(\Xi_c^0 (2815) \right)$ decays

In this work we calculate the ratios of rates of the $\Xi_b$ nonleptonic and semileptonic decays into the $\Xi_c$(2790) and $\Xi_c$(2815) ($\Xi_c^*$) resonances. These resonances are dynamically generated from the pseudoscalar-baryon and vector-baryon interactions, whose mixing is done using the chiral Weinberg-Tomozawa (WT) meson-baryon interaction extended to four flavors. The first part of the decay is a weak decay that we analyze through their quark constituents where it is noted that only the heavy quarks ($b$ and $c$) participate in the interaction, leaving the light pair ($ds$) as spectators. This first decay then produces a meson-baryon pair that creates the $\Xi_c^*$ through the WT interaction. We then proceed to calculate the decay rates to $\Xi_c$(2790) and $\Xi_c$(2815) for both the nonleptonic and semileptonic cases and then calculate the ratios between them. We do this calculation nonrelativistically and fully relativistically and notice that, even though both approaches yield somewhat different results in the rates, the ratios are very similar (difference on the order of 1\%) in both cases. The absolute values of the decay rates are also successfully calculated by obtaining the rates between our decays and $\Lambda_b \to \pi (D_s ) \ \Lambda_c (2595) \left(\Lambda_c (2625) \right)$ and $\Lambda_b \to \bar{\nu}_l l \ \Lambda_c (2595) \left(\Lambda_c (2625) \right)$ for which there are experimental results, since the momentum transfer is similar such we can cancel out the influence of the quark wave functions in the ratios.