First observation of B→D¯1(→D¯π+π−)ℓ+νℓ and measurement of the B→D¯(*)πℓ+νℓ and B→D¯(*)π+π−ℓ+νℓ branching fractions with hadronic tagging at Belle

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Abstract

We report measurements of the ratios of branching fractions for $B\ensuremath{\rightarrow}{\overline{D}}^{(*)}\ensuremath{\pi}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ and $B\ensuremath{\rightarrow}{\overline{D}}^{(*)}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ relative to $B\ensuremath{\rightarrow}{\overline{D}}^{*}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ decays with $\ensuremath{\ell}=e$, $\ensuremath{\mu}$. These results are obtained from a data sample that contains $772\ifmmode\times\else\texttimes\fi{}{10}^{6}B\overline{B}$ pairs collected near the $\mathrm{\ensuremath{\Upsilon}}(4S)$ resonance with the Belle detector at the KEKB asymmetric energy ${e}^{+}{e}^{\ensuremath{-}}$ collider. Fully reconstructing both $B$ mesons in the event, we obtain $\frac{\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{\overline{D}}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})}{\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})}=(7.23\ifmmode\pm\else\textpm\fi{}0.36\ifmmode\pm\else\textpm\fi{}0.14)%$, $\frac{\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{D}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})}{\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{\overline{D}}^{*0}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})}=(6.78\ifmmode\pm\else\textpm\fi{}0.24\ifmmode\pm\else\textpm\fi{}0.18)%$, $\frac{\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{\overline{D}}^{*0}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})}{\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})}=(11.10\ifmmode\pm\else\textpm\fi{}0.48\ifmmode\pm\else\textpm\fi{}0.23)%$, $\frac{\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})}{\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{\overline{D}}^{*0}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})}=(9.50\ifmmode\pm\else\textpm\fi{}0.33\ifmmode\pm\else\textpm\fi{}0.34)%$, $\frac{\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})}{\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})}=\phantom{\rule{0ex}{0ex}}(2.91\ifmmode\pm\else\textpm\fi{}0.37\ifmmode\pm\else\textpm\fi{}0.26)%$, $\frac{\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{\overline{D}}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})}{\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{\overline{D}}^{*0}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})}=(3.10\ifmmode\pm\else\textpm\fi{}0.26\ifmmode\pm\else\textpm\fi{}0.22)%$, $\frac{\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})}{\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})}=(0.99\ifmmode\pm\else\textpm\fi{}0.43\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0ex}{0ex}}0.20)%$, $\frac{\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{\overline{D}}^{*0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})}{\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{\overline{D}}^{*0}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})}=(1.25\ifmmode\pm\else\textpm\fi{}0.27\ifmmode\pm\else\textpm\fi{}0.15)%$, where the uncertainties are statistical and systematic, respectively. These are the most precise measurements of these branching fraction ratios to date. The invariant mass spectra of the $D\ensuremath{\pi}$, ${D}^{*}\ensuremath{\pi}$, and $D\ensuremath{\pi}\ensuremath{\pi}$ systems are studied, and the branching fraction products $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}_{2}^{*\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})\ifmmode\times\else\texttimes\fi{}\mathcal{B}({D}_{2}^{*\ensuremath{-}}\ensuremath{\rightarrow}{\overline{D}}^{0}{\ensuremath{\pi}}^{\ensuremath{-}})=(0.157\ifmmode\pm\else\textpm\fi{}0.015\ifmmode\pm\else\textpm\fi{}0.005)%$, $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{\overline{D}}_{0}^{*0}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0ex}{0ex}}\mathcal{B}({\overline{D}}_{0}^{*0}\ensuremath{\rightarrow}{D}^{\ensuremath{-}}{\ensuremath{\pi}}^{+})=(0.054\ifmmode\pm\else\textpm\fi{}0.022\ifmmode\pm\else\textpm\fi{}0.005)%$, $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{\overline{D}}_{2}^{*0}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})\ifmmode\times\else\texttimes\fi{}\mathcal{B}({\overline{D}}_{2}^{*0}\ensuremath{\rightarrow}{D}^{\ensuremath{-}}{\ensuremath{\pi}}^{+})=(0.163\ifmmode\pm\else\textpm\fi{}0.011\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0ex}{0ex}}0.008)%$, $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}_{1}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})\ifmmode\times\else\texttimes\fi{}\mathcal{B}({D}_{1}^{\ensuremath{-}}\ensuremath{\rightarrow}{\overline{D}}^{*0}{\ensuremath{\pi}}^{\ensuremath{-}})=(0.306\ifmmode\pm\else\textpm\fi{}0.050\ifmmode\pm\else\textpm\fi{}0.029)%$, $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}_{1}^{\ensuremath{'}\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0ex}{0ex}}\mathcal{B}({D}_{1}^{\ensuremath{'}\ensuremath{-}}\ensuremath{\rightarrow}{\overline{D}}^{*0}{\ensuremath{\pi}}^{\ensuremath{-}})=(0.206\ifmmode\pm\else\textpm\fi{}0.068\ifmmode\pm\else\textpm\fi{}0.025)%$, $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}_{2}^{*\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})\ifmmode\times\else\texttimes\fi{}\mathcal{B}({D}_{2}^{*\ensuremath{-}}\ensuremath{\rightarrow}{\overline{D}}^{*0}{\ensuremath{\pi}}^{\ensuremath{-}})=(0.051\ifmmode\pm\else\textpm\fi{}0.040\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0ex}{0ex}}0.010)%$, $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{\overline{D}}_{1}^{0}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})\ifmmode\times\else\texttimes\fi{}\mathcal{B}({\overline{D}}_{1}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\pi}}^{+})=(0.249\ifmmode\pm\else\textpm\fi{}0.023\ifmmode\pm\else\textpm\fi{}0.015)%$, $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{\overline{D}}_{1}^{\ensuremath{'}0}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0ex}{0ex}}\mathcal{B}({\overline{D}}_{1}^{\ensuremath{'}0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\pi}}^{+})=(0.138\ifmmode\pm\else\textpm\fi{}0.036\ifmmode\pm\else\textpm\fi{}0.009)%$, $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{\overline{D}}_{2}^{*0}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})\ifmmode\times\else\texttimes\fi{}\mathcal{B}({\overline{D}}_{2}^{*0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\pi}}^{+})=(0.137\ifmmode\pm\else\textpm\fi{}0.026\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0ex}{0ex}}0.009)%$, $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}_{1}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})\ifmmode\times\else\texttimes\fi{}\mathcal{B}({D}_{1}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})=(0.102\ifmmode\pm\else\textpm\fi{}0.013\ifmmode\pm\else\textpm\fi{}0.009)%$, $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{\overline{D}}_{1}^{0}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0ex}{0ex}}\mathcal{B}({\overline{D}}_{1}^{0}\ensuremath{\rightarrow}{\overline{D}}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})=(0.105\ifmmode\pm\else\textpm\fi{}0.011\ifmmode\pm\else\textpm\fi{}0.009)%$, are extracted. This is the first observation of the decays $B\ensuremath{\rightarrow}{\overline{D}}_{1}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ with ${D}_{1}\ensuremath{\rightarrow}D{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$.

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