arXiv2022
We report measurements of the ratios of branching fractions for $B \to \bar{D}^{(*)}π\ell^+ν_\ell$ and $B \to \bar{D}^{(*)}π^+π^-\ell^+ν_\ell$ relative to $B \to \bar{D}^*\ell^+ν_\ell$ decays with $\ell = e, μ$. These results are obtained from a data sample that contains $772 \times 10^6 B\bar{B}$ pairs collected near the $Υ(4S)$ resonance with the Belle detector at the KEKB asymmetric energy $e^+e^-$ collider. Fully reconstructing both $B$ mesons in the event, we obtain \begin{align*} \frac{B(B^0 \to \bar{D}^0π^-\ell^+ν_\ell)}{B(B^0 \to D^{*-}\ell^+ν_\ell)} &= (7.24\pm0.36\pm0.12)\%\ ,\\ \frac{B(B^+ \to D^-π^+\ell^+ν_\ell)}{B(B^+ \to \bar{D}^{*0}\ell^+ν_\ell)} &= (6.78\pm0.24\pm0.15)\%\ ,\\ \frac{B(B^0 \to \bar{D}^{*0}π^-\ell^+ν_\ell)}{B(B^0 \to D^{*-}\ell^+ν_\ell)} &= (11.10\pm0.48\pm0.20)\%\ ,\\ \frac{B(B^+ \to D^{*-}π^+\ell^+ν_\ell)}{B(B^+ \to \bar{D}^{*0}\ell^+ν_\ell)} &= (9.50\pm0.33\pm0.27)\%\ ,\\ \frac{B(B^0 \to D^-π^+π^-\ell^+ν_\ell)}{B(B^0 \to D^{*-}\ell^+ν_\ell)} &= (2.91\pm0.37\pm0.25)\%\ ,\\ \frac{B(B^+ \to \bar{D}^0π^+π^-\ell^+ν_\ell)}{B(B^+ \to \bar{D}^{*0}\ell^+ν_\ell)} &= (3.10\pm0.26\pm0.21)\%\ ,\\ \frac{B(B^0 \to D^{*-}π^+π^-\ell^+ν_\ell)}{B(B^0 \to D^{*-}\ell^+ν_\ell)} &= (1.03\pm0.43\pm0.18)\%\ ,\\ \frac{B(B^+ \to \bar{D}^{*0}π^+π^-\ell^+ν_\ell)}{B(B^+ \to \bar{D}^{*0}\ell^+ν_\ell)} &= (1.25\pm0.27\pm0.15)\%\ , \end{align*} where the uncertainties are statistical and systematic, respectively. The invariant mass spectra of the $Dπ$, $D^*π$, and $Dππ$ systems are studied. Branching fraction products are extracted, among them the first observations of $B(B^0 \to D_1^-\ell^+ν_\ell) \times B(D_1^- \to D^-π^+π^-) = (0.102\pm0.013\pm0.009)\%$ and $B(B^+ \to \bar{D}_1^0\ell^+ν_\ell) \times B(\bar{D}_1^0 \to \bar{D}^0π^+π^-) = (0.105\pm0.011\pm0.008)\%$.