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 ${\mathcal{R}}_D$, ${\mathcal{R}}_{D^{\ast }}$, their $q^2$ differential distributions, the recently measured longitudinal $D^{\ast }$ polarization $F_L^{D^{\ast }}$, 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 ${\mathcal{A}}_{\text{FB}}^{D^{(\ast )}}$, the $\tau$ polarization asymmetries ${\mathcal{P}}_{\tau }^{D^{(\ast )}}$, and the longitudinal $D^{\ast }$ polarization fraction $F_L^{D^{\ast }}$. 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 ${\mathcal{R}}_{D^{(\ast )}}$ measurement by the Belle collaboration.

Comments: 47 pages, 12 figures. Version published at JHEP