Probing New Physics in light of recent developments in $b \rightarrow c \ell \nu$ transitions

The experimental studies of the observables associated with the $b \rightarrow c$ transitions in the semileptonic $B-$ meson decays at BaBar, Belle and LHCb have shown some deviations from the Standard Model (SM) predictions, consequently, providing a handy tool to probe the possible new physics (NP). In this context, we have first revisited the impact of recent measurements of $R({D^{(*)}})$ and $R(\Lambda_c)$ on the parametric space of the NP scenarios. In addition, we have included the $R(J/\psi)$ data in the analysis and found that their influence on the best-fit points and the parametric space is mild. Using the recent HFLAV data, after validating the well established sum rule of $R(\Lambda_c)$, we derived the similar sum rule for $R(J/\psi)$. Furthermore, according to the updated data, we have modified the correlation among the different observables, giving us their interesting interdependence. Finally, to discriminate the various NP scenarios, we have plotted the different angular observables and their ratios for $B \to D^* \tau\nu_\tau$ against the transfer momentum square $\left(q^2\right)$, using the $1\sigma$ and $2\sigma$ parametric space of considered NP scenarios. By implementing the collider bounds on NP Wilson coefficients, we find that, in the parametric space of some NP WCs is significantly restrained. To see the clear influence of NP on the amplitude of the angular observables, we have also calculated their numerical values in different $q^2$ bins and shown them through the bar plots. We hope their precise measurements will help to discriminate various NP scenarios.