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We show how to extract the Cabibbo-Kobayashi-Maskawa (CKM) matrix element$\vert V_{cb} \vert$ from exclusive semileptonic $B \to D^{(*)}$ decays byusing the Dispersive Matrix (DM) method. It is a new approach which allows todetermine in a full non-perturbative way the hadronic form factors (FFs) in thewhole kinematical range, without making any assumption on their dependence onthe momentum transfer. We investigate also the issue of Lepton FlavorUniversality (LFU) by computing a pure theoretical estimate of the ratio$R(D^{(*)})$. Our approach is applied to the preliminary LQCD computations ofthe FFs, published by the FNAL/MILC [1] and the JLQCD [2] Collaborations, forthe $B \to D^*$ decays and to the final ones, computed by FNAL/MILC [3], forthe $B \to D$ transitions . Since the FNAL/MILC Collaborations have recentlypublished the final results of their LQCD computations of the FFs [4] for the$B \to D^*$ case, we present also the results of our procedure after itsapplication on these data. We find $ \vert V_{cb} \vert = (41.0 \pm 1.2) \cdot10^{-3}$ and $\vert V_{cb} \vert = (41.3 \pm 1.7) \cdot 10^{-3}$ from $B \to D$and $B \to D^*$ decays, respectively. These estimates are consistent within$1\sigma$ with the most recent inclusive determination $\vertV_{cb}\vert_{incl} = (42.16 \pm 0.50) \cdot 10^{-3}$ [5]. Furthermore, weobtain $R(D) = 0.289(8)$ and $R(D^*) = 0.269(8)$, which are both compatiblewith the latest experimental averages [6] at the $\sim$1.6$\sigma$ level.

Non-perturbative bounds for $B \to D^{(*)}\ell\nu_{\ell}$ decays and phenomenological applications