Pad\'{e} approximants to $B\to\pi\ell\nu_{\ell}$ and $B_{s}\to K\ell\nu_{\ell}$ and determination of $|V_{ub}|$

In light of the first observation of the semileptonic decay $B^{0}_{s}\to K^{-}\mu^{+}\nu_{\mu}$ by the LHCb collaboration, we revisit the determination of the CKM parameter $|V_{ub}|$ from exclusive semileptonic $B$-meson decays. A controlled theoretical input on the Standard Model $B\to\pi$ and $B_{s}\to K$ vector and scalar form factors from Lattice QCD in the large $q^{2}$ region, in combination with experimental measurements of the differential $B\to\pi\ell\nu_{\ell}$ and $B^{0}_{s}\to K^{-}\mu^{+}\nu_{\mu}$ branching ratio distributions, has allowed us determine $|V_{ub}|=3.86(11)\times10^{-3}$ and $|V_{ub}|=3.58(9)\times10^{-3}$ from the analyses of the individual decay channels, respectively, and $|V_{ub}|=3.68(5)\times10^{-3}$ from a simultaneous analysis of both decays, which is only a $1.4\%$ error and differs by $1.8\sigma$ with respect to the value from inclusive determinations $|V_{ub}|=4.25(12)^{+15}_{-14}(23)\times10^{-3}$. Our results are based on the use of Pad\'{e} approximants to the participating form factors, highlight the importance of the decay $B_{s}\to K\mu\nu_{\mu}$ in complementing the traditional $B\to\pi\ell\nu_{\ell}$ one in the exclusive determination of $|V_{ub}|$, and allow obtain, to the best of our knowledge, the first correlated results for the $B\to\pi$ and $B_{s}\to K$ vector and scalar form factors. We hope that our study strengthens the case for precise measurements of the differential $B_{s}\to K\ell\nu_{\ell}$ decay rate with a finer resolution of the $q^{2}$ bins, as it would definitely allow achieving more conclusive results for $|V_{ub}|$.