Exclusive semileptonic B → πℓνℓ and Bs → Kℓνℓ decays through unitarity and lattice QCD

The Cabibbo-Kobayashi-Maskawa (CKM) matrix element $\vert V_{ub}\vert$ is obtained from exclusive semileptonic $B \to \pi \ell \nu_\ell$ and $B_s K decays adopting the unitarity-based dispersion approach for determination of hadronic form factors (FFs) in whole kinematical range. We use lattice computations relevant susceptibilities FFs large-$q^2$ regime order to derive their behavior low-$q^2$ region without assuming any specific momentum dependence constraining shape using experimental data. Then, we address extraction data, obtaining V_{ub}\vert = (3.62 \pm 0.47) \cdot 10^{-3}$ \pi$ (3.77 0.48) K$, which after averaging yield (3.69 0.34) 10^{-3}$. These results are compatible with most recent inclusive value V_{ub} \vert_{incl} 4.13\,(26) at 1$\sigma$ level. also present purely theoretical estimates ratio $\tau/\mu$ decay rates $R^{\tau/\mu}_{\pi(K)}$, normalized forward-backward asymmetry $\bar{\mathcal{A}}_{FB}^{\ell,\pi(K)}$ lepton polarization $\bar{\mathcal{A}}_{polar}^{\ell,\pi(K)}$.