Measurement of the branching fraction and decay rate asymmetry of $B^{-}\to D_{{\pi }^{+}{\pi }^{-}{\pi }^0}{K}^{-}$

We report the observation of the decay $B^{-}\to D_{{\pi }^{+}{\pi }^{-}{\pi }^0}{K}^{-}$, where $D_{{\pi }^{+}{\pi }^{-}{\pi }^0}$ indicates a neutral $D$ meson detected in the final state ${\pi }^{+}{\pi }^{-}{\pi }^0$, excluding $K_S^0{\pi }^0$. This doubly Cabibbo-suppressed decay chain can be used to measure the CKM phase $\gamma$. Using about $229\times {10}^6$ $e^{+}{e}^{-}\to B\overline{B}$ events recorded by the BABAR experiment at the PEP-II $e^{+}{e}^{-}$ storage ring, we measure the branching fraction $\mathcal{B}(B^{-}\to D_{{\pi }^{+}{\pi }^{-}{\pi }^0}{K}^{-})=(5.5\pm 1.0(\mathrm{stat}.)\pm 0.7(\mathrm{syst}.))\times {10}^{-6}$ and the decay rate asymmetry $A(B^{-}\to D_{{\pi }^{+}{\pi }^{-}{\pi }^0}{K}^{-})=-0.02\pm 0.16(\mathrm{stat}.)\pm 0.03(\mathrm{syst}.)$ for the full decay chain.

Figure 1

(a) Distribution of the neural network variable $q$ for continuum (hatched) and signal simulated events. The $B\overline{B}$ background distribution is similar to that of signal. (b) Distribution of the neural network variable $d$ for $B\overline{B}$ background (hatched) and signal simulated events. The continuum background distribution is similar to that of the $B\overline{B}$ background. All histograms are normalized to unit area.

Figure 2

Projections of the data (data points) and fit function onto the (a) $\Delta E$, (b) $q$, and (c) $d$ axes. The curves or histograms in each plot show, from bottom to top, the cumulative contributions of the continuum, $B\overline{B}$ background, and signal components of the fit function. For each of the variables plotted, a tight event selection is applied on the other two variables with a signal efficiency of about 50%, in order to increase the signal-to-background ratio in these plots. Figures (d), (e), and (f) show the same projections for the entire data sample.