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In this research, we focus on exploring lepton flavor universality violating(LFUV) observables, including longitudinal polarization ($P_L$),$\tau$-polarization ($P_{\tau}$), and forward-backward asymmetry($\mathcal{A}_{FB}$). Our investigation is conducted within the RelativisticIndependent Quark Model (RIQM), emphasizing the model-dependent analysis ofthese observables in the decay channel: $B_c \to \eta_c(J/\psi)/D (D^*), l\nu_l$. With a keen eye on the experimental aspects of B-hadron decays, therapid confirmation of these quantities could signify a significant detection ofphysics beyond the Standard Model, opening up new avenues for further researchinto New Physics.

Probing $\tau$ polarization in $B_c \to (\eta_c, J/\psi, D, D^*)\, l\nu_l$