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 Padé approximants, and includes a detailed scrutiny of each individual data set that allow us to obtain $|V_{ub}|=3.53(8{)}_{\mathrm{stat}}(6{)}_{\mathrm{syst}}\times 10^{-3}$. The semileptonic $B^{+}\to {\eta }^{(\prime )}{\ell }^{+}{\nu }_{\ell }$ decays are also addressed and the $\eta$-${\eta }^{\prime }$ mixing discussed.

Comments: 29 pages, 7 figures. Comments are welcome