First observation of $B\text{\hspace{0.17em}⁣}\to {\bar{D}}_1(\to \bar{D}{\pi }^{+}{\pi }^{-}){\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ and measurement of the $B\text{\hspace{0.17em}⁣}\to {\bar{D}}^{(\ast )}\pi {\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ and $B\text{\hspace{0.17em}⁣}\to {\bar{D}}^{(\ast )}{\pi }^{+}{\pi }^{-}{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ branching fractions with hadronic tagging at Belle

We report measurements of the ratios of branching fractions for $B\to {\bar{D}}^{(\ast )}\pi {\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ and $B\to {\bar{D}}^{(\ast )}{\pi }^{+}{\pi }^{-}{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ relative to $B\to {\bar{D}}^{\ast }{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ decays with $\mathrm{\ell }=e,\mu$. These results are obtained from a data sample that contains $772\times {10}^{6}B\bar{B}$ pairs collected near the $\mathrm{{\rm Y}}(4S)$ 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 $D\pi$, $D^{\ast }\pi$, and $D\pi \pi$ systems are studied. Branching fraction products are extracted, among them the first observations of $B(B^0\to D_1^{-}{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }})\times B(D_1^{-}\to D^{-}{\pi }^{+}{\pi }^{-})=(0.102\pm 0.013\pm 0.009)\mathrm{\%}$ and $B(B^{+}\to {\bar{D}}_1^0{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }})\times B({\bar{D}}_1^0\to {\bar{D}}^0{\pi }^{+}{\pi }^{-})=(0.105\pm 0.011\pm 0.008)\mathrm{\%}$.