We report a study of the suppressed decay $B^{-}\to D{K}^{-}$, $D\to K^{+}{\pi }^{-}{\pi }^0$, where $D$ denotes either a $D^0$ or a ${\overline{D}}^0$ meson. The decay is sensitive to the $CP$ -violating parameter ${\varphi }_3$. Using a data sample of $772\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the Belle detector, we measure the ratio of branching fractions of the above suppressed decay to the favored decay $B^{-}\to D{K}^{-}$, $D\to K^{-}{\pi }^{+}{\pi }^0$. Our result is $R_{DK}=[1.98\pm 0.62(\mathrm{stat})\pm 0.24(\mathrm{syst})]\times {10}^{-2}$, which indicates the first evidence of the signal for this suppressed decay with a significance of 3.2 standard deviations. We measure the direct $CP$ asymmetry between the suppressed $B^{-}$ and $B^{+}$ decays to be $A_{DK}=0.41\pm 0.30(\mathrm{stat})\pm 0.05(\mathrm{syst})$. We also report measurements for the analogous quantities $R_{D\pi }$ and $A_{D\pi }$ for the decay $B^{-}\to D{\pi }^{-}$, $D\to K^{+}{\pi }^{-}{\pi }^0$.

• Received 8 October 2013

DOI:https://doi.org/10.1103/PhysRevD.88.091104