Search for $b\to u$ transitions in $B^{-}\to [K^{+}{\pi }^{-}{\pi }^0{]}_D{K}^{-}$

We search for decays of a $B$ meson into a neutral $D$ meson and a charged kaon, with the $D$ meson decaying into a charged kaon, a charged pion, and a neutral pion. This final state can be reached through the $b\to c$ transition $B^{-}\to D^0{K}^{-}$ followed by the doubly Cabibbo-suppressed $D^0\to K^{+}{\pi }^{-}{\pi }^0$, or the $b\to u$ transition $B^{-}\to {\overline{D}}^0{K}^{-}$ followed by the Cabibbo-favored ${\overline{D}}^0\to K^{+}{\pi }^{-}{\pi }^0$. The interference of these two amplitudes is sensitive to the angle $\gamma$ of the unitarity triangle. We present results based on $226\times {10}^6$ $e^{+}{e}^{-}\to {\rm Y}(4S)\to B\overline{B}$ events collected with the BABAR detector at SLAC. We find no significant evidence for these decays and we set a limit $R_{\mathrm{ADS}}\equiv \frac{\Gamma ([K^{+}{\pi }^{-}{\pi }^0{]}_D{K}^{-})+\Gamma ([K^{-}{\pi }^{+}{\pi }^0{]}_D{K}^{+})}{\Gamma ([K^{+}{\pi }^{-}{\pi }^0{]}_D{K}^{+})+\Gamma ([K^{-}{\pi }^{+}{\pi }^0{]}_D{K}^{-})}<0.039$ at 95% confidence level, which we translate with a Bayesian approach into $r_B\equiv |A(B^{-}\to {\overline{D}}^0{K}^{-})/A(B^{-}\to D^0{K}^{-})|<0.19$ at 95% confidence level.

Figure 1

Feynman diagrams for the CKM-favored $B^{-}\to D^0{K}^{-}$ and the CKM- and color-suppressed $B^{-}\to {\overline{D}}^0{K}^{-}$ decays.

Figure 2

Likelihood fit projections of the NNet, $\Delta E$, and $m_{\mathrm{ES}}$ distributions separately for the same (top) and opposite (bottom) sign samples. To visually enhance the signal, the distributions for the latter sample are shown after cuts, with a 67% signal efficiency, on the ratios between the signal and the total likelihood of all the variables other than the one shown. The points with error bars represent the data, while the dashed, dashed-dotted, and solid lines represent the contributions from continuum, $B\overline{B}$, and $D\pi$ backgrounds, respectively. The dotted line represents the signal contribution, visible only in the same-sign sample.

Figure 3

Likelihood function for $R_{\mathrm{ADS}}$ (left) and $r_B$ (right). The latter is obtained in a Bayesian approach, assuming flat prior distributions for $r_B$ and $\xi =C\cos \gamma$. The 68% and 95% regions are shown in dark and light shading, respectively.