arXiv2006
We report measurements of the charmless semileptonic decays $B^0 \to π^- / ρ^- \ell^{+} ν$ and $B^+ \to π^0 / ρ^0 \ell^{+} ν$, based on a sample of $2.75 \times 10^8$ $B \bar{B}$ events collected at the $Υ(4S)$ 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 $B \to D^{(*)} \ell ν$, enabling detection of the signal modes with high purity. We measure the branching fractions ${\mathcal B}(B^0 \to π^- \ell^+ ν) = (1.38\pm 0.19\pm 0.14\pm 0.03) \times 10^{-4}$, ${\mathcal B}(B^0 \to ρ^- \ell^+ ν) = (2.17\pm 0.54\pm 0.31\pm 0.08) \times 10^{-4}$, ${\mathcal B}(B^+ \to π^0 \ell^+ ν) = (0.77\pm 0.14\pm 0.08\pm 0.00) \times 10^{-4}$ and ${\mathcal B}(B^+ \to ρ^0 \ell^+ ν) = (1.33\pm 0.23\pm 0.17\pm 0.05) \times 10^{-4}$, 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 $q^2$ intervals: $q^2 < 8$, $8 \leq q^2 < 16$, and $q^2 \geq 16$ GeV$^2/c^2$. From our partial branching fractions for $B \to π\ell ν$ and recent results for the form factor from unquenched Lattice QCD calculations, we obtain values of the CKM matrix element $|V_{ub}|$.