We perform a general model-independent analysis of \(b \to c \tau \bar{\nu}_\tau\) transitions, including measurements of \(\mathcal{R}_D\), \(\mathcal{R}_{D^*}\), their \(q^2\) differential distributions, the longitudinal \(D^*\) polarization \(F_L^{D^*}\), and constraints from the \(B_c \to \tau \bar{\nu}_\tau\) lifetime, each of which has significant impact on the fit. A global fit to a general set of Wilson coefficients of an effective low-energy Hamiltonian is presented working with a minimal set of assumptions: new physics is present only in the third generation of leptons, there are not light right-handed neutrinos, the electroweak symmetry breaking is linearly realized and the CP-conserving limit is taken. The solutions of the fit are interpreted in terms of hypothetical new-physics mediators.
The impact of \(F_L^{D^*}\), measured by Belle last year is studied in detail. The difficulty to accommodate this measurement motivates the relaxation of some of our assumptions so the impact of a non-linear electroweak symmetry breaking and the addition of light right-handed neutrinos is studied.
From the obtained results we predict selected \(b \to c\tau\bar\nu_\tau\) observables, such as the baryonic transition \(\Lambda_b \to \Lambda_c \tau \bar{\nu}_\tau\), the forward-backward asymmetries \(\mathcal{A}_\text{FB}^{D^{(*)}}\), the \(\tau\) polarization asymmetries \(\mathcal{P}_\tau^{D^{(*)}}\), the longitudinal \(D^*\) polarization fraction \(F_L^{D^*}\) and several additional differential observables.