Padé approximants to $B\to \pi \ell {\nu }_{\ell }$ and $B_s\to K\ell {\nu }_{\ell }$ and determination of $|V_{ub}|$

Abstract

In light of the first observation of the semileptonic decay $B_s^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ 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 $B_s^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ branching ratio distributions, has allowed us determine $|V_{ub}|=3.86(11)\times 10^{-3}$ and $|V_{ub}|=3.58(9)\times 10^{-3}$ from the analyses of the individual decay channels, respectively, and $|V_{ub}|=3.68(5)\times 10^{-3}$ 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 $|V_{ub}|=4.25(12{)}_{-14}^{+15}(23)\times 10^{-3}$. Our results are based on the use of Padé 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 $|V_{ub}|$.

Comments: 16 pages, 10 figures