Study of the Suppressed DecaysB−→[K+π−]DK−andB−→[K+π−]Dπ−

We report a study of the suppressed decays ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}[{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{]}_{D}{K}^{\ensuremath{-}}$ and ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}[{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{]}_{D}{\ensuremath{\pi}}^{\ensuremath{-}}$, where $[{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{]}_{D}$ indicates that the ${K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ pair originates from a neutral $D$ meson. These decay modes are sensitive to the unitarity triangle angle ${\ensuremath{\phi}}_{3}$. We use a data sample containing $275\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ pairs recorded at the $\ensuremath{\Upsilon}(4S)$ resonance with the Belle detector at the KEKB asymmetric ${e}^{+}{e}^{\ensuremath{-}}$ storage ring. The signal for ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}[{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{]}_{D}{K}^{\ensuremath{-}}$ is not statistically significant, and we set a limit ${r}_{B}l0.27$ at $90%$ confidence level, where ${r}_{B}$ is the magnitude of the ratio of amplitudes $|A({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\overline{D}}^{0}{K}^{\ensuremath{-}})/A({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{0}{K}^{\ensuremath{-}})|$. We observe a signal with $6.4\ensuremath{\sigma}$ statistical significance in the related mode, ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}[{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{]}_{D}{\ensuremath{\pi}}^{\ensuremath{-}}$.