Inclusive $b \to \{u, c\} \, \ell^- \, \bar{\nu}_\ell$ modes: polarized/unpolarized $\Lambda_b$

The increasing number of flavour anomalies motivates the investigation of new processes where tensions similar to the observed ones may emerge. It is necessary to identify observables sensitive to physics beyond the Standard Model. The analysis which follows concerns the inclusive semileptonic decays of polarized beauty baryons, computed through the Heavy Quark Expansion at $\mathcal{O}(1 / m_b^3)$ and at the leading order in $\alpha_s$. New Physics interactions have been taken into account, extending the Standard Model $b \to U \, \ell \, \bar{\nu}_\ell$ low-energy Hamiltonian, where $U = \{c, u\}$ and $\ell = \{e, \mu, \tau\}$, including the full set of $D = 6$ operators with left-handed neutrinos. Among the possible observables one can consider, the ones depending on the spin of the decaying baryon are very appealing and can be considered for physics programmes of future facilities, such as FCC-ee.