An Imperative study of the angular observables in $\Lambda_b \to \Lambda_c^{+}(\to \Lambda \pi^{+})\ell^-\bar{\nu}_{\ell}$ decay and probing the footprint of new physics

We study the four-fold angular distribution of the semileptonic $\Lambda_b \to \Lambda_c^{+}(\to \Lambda \pi^{+})\ell^- \bar{\nu}_{\ell}$ decay and find out analytical expressions for various asymmetric and angular observables in the standard model (SM) and the relevant new physics (NP) scenarios. Using the available inputs on the form factors from the lattice, we predict the values with uncertainties of all these observables in the SM. We have considered NP effects only in $b\to c\tau^-\bar{\nu}_{\tau}$ transitions, and constrain the Wilson coefficients of the model-independent beyond the SM operators from the available data on $B\to D^{(*)}\ell\nu_{\ell}$ and $\Lambda_b \to \Lambda_c^{+}\ell^- \bar{\nu}_{\ell}$ decays. In this study, we focus on analysing the contributions to these decays in one- and two-operator scenarios. Furthermore, we test the new physics sensitivities (one or two-operator scenarios) of the different angular and asymmetric observables in $\Lambda_b \to \Lambda_c^+ (\to \Lambda \pi^{+}) \tau^- \bar{\nu}_{\tau}$ decays and discuss the phenomenology. We observe that it will be possible to distinguish the different NP effects from one another by measuring these observables.