\large\bf $B_c \to (J/Ψ,\,η_c)τν$ semileptonic decays within Standard model and beyond

Abstract: Deviations from the standard model prediction have been observed not only in $b \to c$ charged current interactions but also in $b \to s$ flavor changing neutral current interactions. In particular, the deviation observed in the measured ratio of branching fractions $R_D = \mathcal B(B \to D\tau\nu)/\mathcal B(B \to D\,l\,\nu)$ and $R_{D^{\ast}} =\mathcal B(B \to D^{\ast}\tau\nu)/\mathcal B(B \to D^{\ast}\,l\,\nu)$, where $l = (e,\,\mu)$, is more pronounced and the combined excess currently stands at $3.9\sigma$ level. If it persists and confirmed by future experiments, it would be a definite hint of new physics. In this context, we consider $B_c \to \eta_c\,l\,\nu$ and $B_c \to J/\Psi\,l\,\nu$ decays mediated via $b \to c\,l\,\nu$ charged current interactions and employ the most general effective Lagrangian in the presence of new physics to give prediction on various observables such as ratio of branching ratio, tau polarization fraction, and forward backward asymmetry for these decay modes.