Search forb→utransitions inB−→[K+π−π0]DK−

Abstract

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 $b\ensuremath{\rightarrow}c$ transition ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{0}{K}^{\ensuremath{-}}$ followed by the doubly Cabibbo-suppressed ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$, or the $b\ensuremath{\rightarrow}u$ transition ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\overline{D}}^{0}{K}^{\ensuremath{-}}$ followed by the Cabibbo-favored ${\overline{D}}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$. The interference of these two amplitudes is sensitive to the angle $\ensuremath{\gamma}$ of the unitarity triangle. We present results based on $226\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\Upsilon}(4S)\ensuremath{\rightarrow}B\overline{B}$ events collected with the BABAR detector at SLAC. We find no significant evidence for these decays and we set a limit ${R}_{\mathrm{ADS}}\ensuremath{\equiv}\frac{\ensuremath{\Gamma}([{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{]}_{D}{K}^{\ensuremath{-}})+\ensuremath{\Gamma}([{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}{]}_{D}{K}^{+})}{\ensuremath{\Gamma}([{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{]}_{D}{K}^{+})+\ensuremath{\Gamma}([{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}{]}_{D}{K}^{\ensuremath{-}})}<0.039$ at 95% confidence level, which we translate with a Bayesian approach into ${r}_{B}\ensuremath{\equiv}|A({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\overline{D}}^{0}{K}^{\ensuremath{-}})/A({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{0}{K}^{\ensuremath{-}})|<0.19$ at 95% confidence level.

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