Measurement of the branching fraction of $B\to D^{(*)}\pi \ell \nu$ at Belle using hadronic tagging in fully reconstructed events

We report a measurement of the branching fractions of the decays $B\to D^{(*)}\pi \ell \nu$. The analysis uses $772\times {10}^6$ $B\overline{B}$ pairs produced in $e^{+}{e}^{-}\to \mathrm{\Upsilon }(4S)$ data recorded by the Belle experiment at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The tagging $B$ meson in the decay is fully reconstructed in a hadronic decay mode. On the signal side, we reconstruct the decay $B\to D^{(*)}\pi \ell \nu (\ell =e,\mu )$. The measured branching fractions are $\mathcal{B}(B^{+}\to D^{-}{\pi }^{+}{\ell }^{+}\nu )=[4.55\pm 0.27(\mathrm{stat}.)\pm 0.39(\mathrm{syst}.)]\times {10}^{-3}$, $\mathcal{B}(B^0\to {\overline{D}}^0{\pi }^{-}{\ell }^{+}\nu )=[4.05\pm 0.36(\mathrm{stat}.)\pm 0.41(\mathrm{syst}.)]\times {10}^{-3}$, $\mathcal{B}(B^{+}\to D^{*-}{\pi }^{+}{\ell }^{+}\nu )=[6.03\pm 0.43(\mathrm{stat}.)\pm 0.38(\mathrm{syst}.)]\times {10}^{-3}$, and $\mathcal{B}(B^0\to {\overline{D}}^{*0}{\pi }^{-}{\ell }^{+}\nu )=[6.46\pm 0.53(\mathrm{stat}.)\pm 0.52(\mathrm{syst}.)]\times {10}^{-3}$. These are in good agreement with the current world-average values.

Figure 1

Binned extended maximum likelihood of the MC templates to the data for the combined fit to $B^{+}\to D^{-}{\pi }^{+}{\ell }^{+}\nu$ (left) and $B^{+}\to D^{*-}{\pi }^{+}{\ell }^{+}\nu$ (right). The data are shown with error bars. The legend in the left panel indicates each component in the fit. The dots at the bottom of each panel show the pulls between the data and the fit. For better visibility, we doubled the bin width for this plot.

Figure 2

Binned extended maximum likelihood of the MC templates to the data for the combined fit to $B^0\to {\overline{D}}^0{\pi }^{-}{\ell }^{+}\nu$ (left) and $B^0\to {\overline{D}}^{*0}{\pi }^{-}{\ell }^{+}\nu$ (right). The data are shown with error bars. The legend in the left panel indicates each component in the fit. The dots at the bottom of each panel show the pulls between the data and the fit. For better visibility, we doubled the bin width for this plot.