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

Abstract

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

submitted to Phys. Rev. D

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