Measurement of the B0→π-ℓ+ν and B +→η(′)ℓ+ν branching fractions, the B0→π-ℓ+ν and B +→ηℓ+ν form-factor shapes, and determination of |Vub|

We report the results of a study of the exclusive charmless semileptonic decays, B+→η(′)ℓ+ν and B0→π-ℓ+ν, undertaken with approximately 464×106 BB̄ pairs collected at the Υ(4S) resonance with the BABAR detector. The analysis uses events in which the signal B decays are reconstructed with a loose neutrino reconstruction technique. We obtain partial branching fractions for B+→ηℓ+ν and B0→π-ℓ+ν decays in three and 12 bins of q2, respectively, from which we extract the f+(q2) form-factor shapes and the total branching fractions B(B+→ηℓ +ν)=(0.36±0.05stat±0.04 syst)×10-4 and B(B0→π -ℓ+ν)=(1.42±0.05stat±0. 07syst)×10-4. We also measure B(B +→η′ℓ+ν)=(0.24±0. 08stat±0.03syst)×10-4. We obtain values for the magnitude of the CKM matrix element |Vub| using three different QCD calculations.