LFU ratios in B decays using Lattice QCD and Unitarity

We present the results of the application of the unitarity-based Dispersion Matrix approach to semileptonic charged-current $B$ decays. This method allows to achieve a non-perturbative and completely model-independent determination of the hadronic form factors. Starting from lattice results available at large values of the momentum transfer, the behaviour of the form factors in their whole kinematical range is obtained without introducing any explicit parameterization of their momentum dependence. We will focus on the analysis of Lepton Flavour Universality by computing the $\tau/\mu$ ratios of the branching fractions of the $B \to D^{(*)} \ell \nu$ and $B \to \pi \ell \nu$ decays. The most important result is that, for the first time, the discrepancies between the SM expectation values and the measurements of the Lepton Flavour Universality ratios for the $B \to D^{(*)} \ell \nu$ decays are reduced at the 1.3$\sigma$ level for each of the two channels, separately.