$b \to c \tau \nu_{\tau}$ Decays: A Catalogue to Compare, Constrain, and Correlate New Physics Effects

In this article, we have predicted the standard model (SM) values of the asymmetric and angular observables in $B\to D^{(\ast)}\tau\nu_{\tau}$ decays, using the results of the new up-to-date analysis in $B\to D^{(*)}\ell\nu_{\ell}$. We have also revisited the SM prediction of the inclusive ratio $\mathcal{R}_{X_c}$, and have given its values in different schemes of the charm quark mass. This is the first analysis which includes all the known corrections in the SM. In addition, we have analysed the $b\to c\tau\nu_\tau$ decay modes in a model-independent framework of effective field theory beyond the standard model. Considering all the possible combinations of the effective operators in $b \to c \tau\nu_{\tau}$ decays and using the Akaike Information Criterion, we find out the scenarios which can best explain the available data on these channels. In the selected scenarios, best-fit values and correlations of the new parameters are extracted. Using these results, predictions are made on various observables in the exclusive and inclusive semitaunic $b \to c $ decays. The graphical correlations between these observables are shown, which are found to be useful in discriminating various new physics scenarios.