First Observation of the Decays ${\overline{B}}^0\to D^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ and $B^{-}\to D^0{K}^{-}{\pi }^{+}{\pi }^{-}$

First observations of the Cabibbo-suppressed decays ${\overline{B}}^0\to D^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ and $B^{-}\to D^0{K}^{-}{\pi }^{+}{\pi }^{-}$ are reported using $35{\mathrm{pb}}^{-1}$ of data collected with the LHCb detector. Their branching fractions are measured with respect to the corresponding Cabibbo-favored decays, from which we obtain $\mathcal{B}({\overline{B}}^0\to D^{+}{K}^{-}{\pi }^{+}{\pi }^{-})/\mathcal{B}({\overline{B}}^0\to D^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-})=(5.9\pm 1.1\pm 0.5)\times {10}^{-2}$ and $\mathcal{B}(B^{-}\to D^0{K}^{-}{\pi }^{+}{\pi }^{-})/\mathcal{B}(B^{-}\to D^0{\pi }^{-}{\pi }^{+}{\pi }^{-})=(9.4\pm 1.3\pm 0.9)\times {10}^{-2}$, where the uncertainties are statistical and systematic, respectively. The $B^{-}\to D^0{K}^{-}{\pi }^{+}{\pi }^{-}$ decay is particularly interesting, as it can be used in a similar way to $B^{-}\to D^0{K}^{-}$ to measure the Cabibbo-Kobayashi-Maskawa phase $\gamma$.

Figure 1

Invariant mass distributions for (a) ${\overline{B}}^0\to D^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$, (b) $B^{-}\to D^0{\pi }^{-}{\pi }^{+}{\pi }^{-}$, (c) ${\overline{B}}^0\to D^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$, and (d) $B^{-}\to D^0{K}^{-}{\pi }^{+}{\pi }^{-}$ candidates from $35{\mathrm{pb}}^{-1}$ of the data for all selected candidates. Fits as described in the text are overlaid.

Figure 2

Invariant masses within the $B^{-}\to D^0{K}^{-}{\pi }^{+}{\pi }^{-}$ system. Shown are (a) $M(K^{-}{\pi }^{+}{\pi }^{-})$, (b) $M(D{\pi }^{+}{\pi }^{-})-M(D)$, (c) $M(K^{-}{\pi }^{+})$, and (d) $M({\pi }^{+}{\pi }^{-})$. The points with error bars correspond to the signal region, and the hatched histograms represent the scaled sideband region.