Study of $B\to\pi\ell\nu_{\ell}$ and $B^{+}\to\eta^{(\prime)}\ell^{+}\nu_{\ell}$ decays and determination of $|V_{ub}|$

Abstract

We reassess the $B\to\pi\ell\nu_{\ell}$ differential branching ratio distribution experimental data released by the BaBar and Belle Collaborations supplemented with all lattice calculations of the $B\to\pi$ form factor shape available up to date obtained by the HPQCD, FNAL/MILC and RBC/UKQCD Collaborations. Our study is based on the method of Pad\'{e} approximants, and includes a detailed scrutiny of each individual data set that allow us to obtain $|V_{ub}|=3.53(8)_{\rm{stat}}(6)_{\rm{syst}}\times10^{-3}$. The semileptonic $B^{+}\to\eta^{(\prime)}\ell^{+}\nu_{\ell}$ decays are also addressed and the $\eta$-$\eta^{\prime}$ mixing discussed.