Search for $b\to u$ transitions in $B^{\pm }\to [K^{\mp }{\pi }^{\pm }{\pi }^0{]}_D{K}^{\pm }$ decays

We present a study of the decays $B^{\pm }\to D{K}^{\pm }$ with $D$ mesons reconstructed in the $K^{+}{\pi }^{-}{\pi }^0$ or $K^{-}{\pi }^{+}{\pi }^0$ final states, where $D$ indicates a $D^0$ or a ${\overline{D}}^0$ meson. Using a sample of $474\times {10}^6$ $B\overline{B}$ pairs collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at SLAC, we measure the ratios $R^{\pm }\equiv \frac{\Gamma (B^{\pm }\to [K^{\mp }{\pi }^{\pm }{\pi }^0{]}_D{K}^{\pm })}{\Gamma (B^{\pm }\to [K^{\pm }{\pi }^{\mp }{\pi }^0{]}_D{K}^{\pm })}$. We obtain $R^{+}=(5_{-10}^{+12}(\mathrm{stat}{)}_{-4}^{+2}(\mathrm{syst}))\times {10}^{-3}$ and $R^{-}=({12}_{-10}^{+12}(\mathrm{stat}{)}_{-5}^{+3}(\mathrm{syst}))\times {10}^{-3}$, from which we extract the upper limits at 90% probability: $R^{+}<23\times {10}^{-3}$ and $R^{-}<29\times {10}^{-3}$. Using these measurements, we obtain an upper limit for the ratio $r_B$ of the magnitudes of the $b\to u$ and $b\to c$ amplitudes $r_B<0.13$ at 90% probability.

Figure 1

Feynman diagrams for $B^{+}\to {\overline{D}}^0{K}^{+}$ (top, $\overline{b}\to \overline{c}$ transition) and $B^{+}\to D^0{K}^{+}$ (bottom, $\overline{b}\to \overline{u}$ transition).

Figure 2

Distribution of (a,b) $m_{\mathrm{ES}}$ (with $\mathcal{F}>0.5$) and (c,d) $\mathcal{F}$ (with $m_{\mathrm{ES}}>5.27\mathrm{GeV}/c^2$) and the results of the maximum-likelihood fits for the combined $B^{+}$ and $B^{-}$ samples (extracting $R_{\mathrm{ADS}}$), for (a,c) opposite-sign and (b,d) same-sign decays. The data are well described by the overall fit result (solid blue line) which is the sum of the signal, continuum, nonpeaking, and peaking $B\overline{B}$ backgrounds.

Figure 3

Projections of the 2D likelihood for $m_{\mathrm{ES}}$ with the additional requirement $\mathcal{F}>0.5$, obtained from the fit to the $B^{+}$ (left) and $B^{-}$ (right) data sample for opposite-sign events (extracting $R^{+}$ and $R^{-}$). The labeling of the curves is the same as in Fig. 2.

Figure 4

Bayesian posterior probability density function for $r_B$ from our measurement of $R^{+}$ and $R^{-}$ and the hadronic $D$ decay parameters $r_D$, ${\delta }_D$, and $k_D$ taken from [8, 9]. The dark and light shaded zones represent the 68% and 90% probability regions, respectively.