Predictions for $\Lambda_b\to \Lambda_c\tau\bar\nu$ in BLSSM with Inverse seesaw

The persistent deviations observed in semileptonic $B$ decays, in particular the lepton flavor universality ratios $\mathcal{R}(D^{(*)})$ and $\mathcal{R}(\Lambda_c)$, provide intriguing hints of physics beyond the Standard Model (SM). While current measurements remain limited by experimental uncertainties, their lower central values compared to SM expectations motivate further theoretical scrutiny. In this work we study these observables within the $B-L$ Supersymmetric Standard Model with an inverse seesaw (BLSSM-IS). We emphasize the role of penguin diagrams involving charginos, neutralinos, and right-handed sneutrinos, which induce flavor-dependent loop corrections to the effective $W\ell\nu$ vertex. These corrections can suppress the light-lepton decay rates relative to the $\tau$ mode, leading to a modest enhancement of $\mathcal{R}(D^{(*)})$ and, through the sum rule, $\mathcal{R}(\Lambda_c)$. We present updated numerical results illustrating the correlation between mesonic and baryonic observables, showing that the BLSSM-IS framework provides a natural and testable explanation of the current data. Our findings underline the importance of upcoming precision measurements at Belle II and the LHCb upgrade in clarifying the possible role of supersymmetry in lepton flavor universality violation.