$|V_{cb}|$, LFU and $SU(3)_F$ symmetry breaking in $B_{(s)} \to D_{(s)}^{(*)} \ell \nu_\ell$ decays using Lattice QCD and Unitarity

Abstract

The DM method allows a non-perturbative, model-independent determination of the momentum dependence of the semileptonic form factors to be achieved. Starting from lattice results available at large values of the 4-momentum transfer and implementing non-perturbative unitarity bounds, the behaviour of the form factors in their whole kinematical range is obtained without introducing any explicit parameterization of their momentum dependence. We consider the four exclusive semileptonic B (s) → D ( * ) (s) ν decays and extract |V cb | from the experimental data for each transition. The average over the four channels iswhich is compatible with the latest inclusive determination at 1σ level. We address also the issue of Lepton Flavour Universality by computing pure theoretical estimates of the τ/ ratios of the branching fractions for each channel, where is a light lepton. In the case of a light spectator quark we obtain R(D * ) = 0.275(8) and R(D) = 0.296(8), which are compatible with the corresponding experimental values within 1.3σ. In the case of a strange spectator quark we obtain R(D * s ) = 0.2497(60) and R(D s ) = 0.298(5). The different values for R(D * s ) and R(D * ) may reflect SU(3) F symmetry breaking effects, which seem to be present in some of the lattice form factors, especially at large values of the recoil.