| Summary: | We report the results of a study of the exclusive charmless semileptonic decays, B[superscript +]→η[superscript (′)]ℓ[superscript +]ν and B[superscript 0]→π[superscript -]ℓ[superscript +]ν, undertaken with approximately 464×10[superscript 6] BB̅ 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[superscript +]→ηℓ[superscript +]ν and B[superscript 0]→π-ℓ[superscript +]ν decays in three and 12 bins of q[superscript 2], respectively, from which we extract the f+(q[superscript 2]) form-factor shapes and the total branching fractions B(B[superscript +]→ηℓ[superscript +]ν)=(0.36±0.05[subscript stat]±0.04[subscript syst])×10[superscript -4] and B(B[superscript 0]→π[superscript -]ℓ[superscript +]ν)=(1.42±0.05[subscript stat]±0.07[subscript syst])×10[superscript -4]. We also measure B(B[superscript +]→η[superscript ′]ℓ[superscript +]ν)=(0.24±0.08[subscript stat]±0.03[subscript syst])×10[superscript -4]. We obtain values for the magnitude of the CKM matrix element |V[subscript ub]| using three different QCD calculations.
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