Study of the Suppressed Decays $B^{-}\to [K^{+}{\pi }^{-}{]}_D{K}^{-}$ and $B^{-}\to [K^{+}{\pi }^{-}{]}_D{\pi }^{-}$

We report a study of the suppressed decays $B^{-}\to [K^{+}{\pi }^{-}{]}_D{K}^{-}$ and $B^{-}\to [K^{+}{\pi }^{-}{]}_D{\pi }^{-}$, where $[K^{+}{\pi }^{-}{]}_D$ indicates that the $K^{+}{\pi }^{-}$ pair originates from a neutral $D$ meson. These decay modes are sensitive to the unitarity triangle angle ${\varphi }_3$. We use a data sample containing $275\times {10}^6$ $B\overline{B}$ pairs recorded at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric $e^{+}{e}^{-}$ storage ring. The signal for $B^{-}\to [K^{+}{\pi }^{-}{]}_D{K}^{-}$ is not statistically significant, and we set a limit $r_B<0.27$ at $90\%$ confidence level, where $r_B$ is the magnitude of the ratio of amplitudes $|A(B^{-}\to {\overline{D}}^0{K}^{-})/A(B^{-}\to D^0{K}^{-})|$. We observe a signal with $6.4\sigma$ statistical significance in the related mode, $B^{-}\to [K^{+}{\pi }^{-}{]}_D{\pi }^{-}$.

Figure 1

$B^{-}\to [K^{+}{\pi }^{-}{]}_D{K}^{-}$ and $B^{-}\to [K^{+}{\pi }^{-}{]}_D{\pi }^{-}$ decays.

Figure 2

$\Delta E$ fit results for (a) $B^{-}\to D_{\mathrm{s}\mathrm{u}\mathrm{p}}{K}^{-}$, (b) $B^{-}\to D_{\mathrm{s}\mathrm{u}\mathrm{p}}{\pi }^{-}$, (c) $B^{-}\to D_{\mathrm{f}\mathrm{a}\mathrm{v}}{K}^{-}$, and (d) $B^{-}\to D_{\mathrm{f}\mathrm{a}\mathrm{v}}{\pi }^{-}$. Charge conjugate decays are included in these plots.

Figure 3

$\Delta E$ fit results for (a) $B^{-}\to D_{\mathrm{s}\mathrm{u}\mathrm{p}}{K}^{-}$, (b) $B^{+}\to D_{\mathrm{s}\mathrm{u}\mathrm{p}}{K}^{+}$, (c) $B^{-}\to D_{\mathrm{s}\mathrm{u}\mathrm{p}}{\pi }^{-}$, and (d) $B^{+}\to D_{\mathrm{s}\mathrm{u}\mathrm{p}}{\pi }^{+}$.