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

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.

Categories: hep-ph hep-ex hep-lat