Reinvestigating the semileptonic $B\to D^{(\ast)}\tau\bar{\nu}_{\tau}$ decays in the model independent scenarios and leptoquark models

In this work, we revisit the possible new physics (NP) solutions by analyzing the observables associated with $B\to D^{(\ast)}\tau\bar{\nu}_{\tau}$ decays. To explore the structure of new physics, the form factors of $B\to D^{(\ast)}$ decays play a crucial role. In this study, we utilize the form factor results obtained from a simultaneous fit to Belle data and lattice QCD calculations. Using these form factors, we conduct a global fit of the new physics Wilson coefficients, incorporating the most recent experimental data. Additionally, we use the form factors and Wilson coefficients to make predictions for physical observables, including the lepton flavor universality ratio $R_{D^{(\ast)}}$, polarized observables, and the normalized angular coefficients $\langle I\rangle$'s related to the four-fold decays $B\to D^{\ast}(\to D\pi, D\gamma)\tau\bar{\nu}_{\tau}$. These predictions are calculated in both model-independent scenarios and for three different leptoquark models.