Global fit to $b \to c \tau \nu$ transitions

Abstract

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 recently measured 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, the solutions of which are interpreted in terms of hypothetical new-physics mediators. 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 ratio $\mathcal{R}_{J/\psi}$, the forward-backward asymmetries ${\cal A}_\text{FB}^{D^{(*)}}$, the $\tau$ polarization asymmetries $\mathcal{P}_\tau^{D^{(*)}}$, and the longitudinal $D^*$ polarization fraction $F_L^{D^*}$. The latter shows presently a slight tension with any new-physics model, such that an improved measurement could have an important impact. We also discuss the potential change due the very recently announced preliminary $\mathcal{R}_{D^{(*)}}$ measurement by the Belle collaboration.