Measurements of branching fractions and q² distributions for B → π ℓ ν and B → ρ ℓ ν decays with B → D^(*) ℓ ν decay tagging

We report measurements of the charmless semileptonic decays B⁰ → π^- / ρ^- ℓ⁺ ν and B⁺ → π⁰ / ρ⁰ ℓ⁺ ν, based on a sample of 2.75 × 10⁸B over(B, ̄) events collected at the Υ{hooked} (4 S) resonance with the Belle detector at the KEKB e⁺ e^- asymmetric collider. In this analysis, the accompanying B meson is reconstructed in the semileptonic mode B → D^(*) ℓ ν, enabling detection of the signal modes with high purity. We measure the branching fractions B (B⁰ → π^- ℓ⁺ ν) = (1.38 ± 0.19 ± 0.14 ± 0.03) × 10^-4, B (B⁰ → ρ^- ℓ⁺ ν) = (2.17 ± 0.54 ± 0.31 ± 0.08) × 10^-4, B (B⁺ → π⁰ ℓ⁺ ν) = (0.77 ± 0.14 ± 0.08 ± 0.00) × 10^-4 and B (B⁺ → ρ⁰ ℓ⁺ ν) = (1.33 ± 0.23 ± 0.17 ± 0.05) × 10^-4, where the errors are statistical, experimental systematic, and systematic due to form factor uncertainties, respectively. For each mode we also present the partial branching fractions in three q² intervals: q² < 8, 8 ≤ q² < 16, and q² ≥ 16   GeV² / c². From our partial branching fractions for B → π ℓ ν and recent results for the form factor from unquenched Lattice QCD calculations, we obtain values of the CKM matrix element | V_{u b} |.