$\Lambda_b$ decays into $\Lambda_c^*\ell\bar{\nu}_\ell$ and $\Lambda_c^*\pi^-$ $[\Lambda_c^*=\Lambda_c(2595)$ \& $\Lambda_c(2625)]$ and heavy quark spin symmetry
We study the implications for $\Lambda_b \to \Lambda_c^*\ell\bar{\nu}_\ell$ and $\Lambda_b \to \Lambda_c^*\pi^-$ $[\Lambda_c^*=\Lambda_c(2595)$ and $\Lambda_c(2625)]$ decays that can be deduced from heavy quark spin symmetry (HQSS). Identifying the odd parity $\Lambda_c(2595)$ and $\Lambda_c(2625)$ resonances as HQSS partners, with total angular momentum--parity $j_q^P=1^-$ for the light degrees of freedom, we find that the ratios $\Gamma(\Lambda_b\rightarrow\Lambda_c(2595)\pi^-)/\Gamma(\Lambda_b\rightarrow\Lambda_c(2625)\pi^-)$ and $\Gamma(\Lambda_b\rightarrow \Lambda_c(2595) \ell \bar{\nu}_\ell)/ \Gamma(\Lambda_b\rightarrow\Lambda_c(2625) \ell \bar{\nu}_\ell)$ agree, within errors, with the experimental values given in the Review of Particle Physics. We discuss how future, and more precise, measurements of the above branching fractions could be used to shed light into the inner HQSS structure of the narrow $\Lambda_c(2595)$ odd-parity resonance. Namely, we show that such studies would constrain the existence of a sizable $j^P_q=0^-$ component in its wave-function, and/or of a two-pole pattern, in analogy to the case of the similar $\Lambda(1405)$ resonance in the strange sector, as suggested by most of the approaches that describe the $\Lambda_c(2595)$ as a hadron molecule. We also investigate the lepton flavor universality ratios $R[\Lambda_c^*] = {\cal B}(\Lambda_b \to \Lambda_c^* \tau\,\bar\nu_\tau)/{\cal B}(\Lambda_b \to \Lambda_c^* \mu\,\bar\nu_\mu)$, and discuss how $R[\Lambda_c(2595)]$ may be affected by a new source of potentially large systematic errors if there are two $\Lambda_c(2595)$ poles.