Search for $B^{+}\to D^{+}{K}^0$ and $B^{+}\to D^{+}{K}^{*0}$ decays

We report a search for the rare decays $B^{+}\to D^{+}{K}^0$ and $B^{+}\to D^{+}{K}^{*0}$ in an event sample of approximately $465\times {10}^6$ $B\overline{B}$ pairs collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at SLAC National Accelerator Laboratory. We find no significant evidence for either mode and we set 90% probability upper limits on the branching fractions of $\mathcal{B}(B^{+}\to D^{+}{K}^0)<2.9\times {10}^{-6}$ and $\mathcal{B}(B^{+}\to D^{+}{K}^{*0})<3.0\times {10}^{-6}$.

Figure 1

Annihilation diagram for the decay $B^{+}\to D^{+}{K}^{(*)0}$ (top). Tree diagram (bottom left) for the decay $B^{+}\to D_s^{+}{\pi }^0$ and hadron-level diagram (bottom right) for the rescattering contribution to $B^{+}\to D^{+}{K}^{(*)0}$ via $B^{+}\to D_s^{+}{\pi }^0$.

Figure 2

Projections of the 2D likelihood function onto the $m_{\mathrm{ES}}$ (top two rows) and $\mathcal{F}$ (bottom two rows) axes for (a) $K\pi \pi$, (b) $K\pi \pi {\pi }^0$, (c) $K_S^0\pi$ and (d) $K_S^0\pi {\pi }^0$ for the $B^{+}\to D^{+}{K}_S^0$ mode, and (e) $K\pi \pi$ and (f) $K_S^0\pi$ for the $B^{+}\to D^{+}{K}^{*0}$ mode. The data are indicated with black dots and error bars and the (blue) solid curve is the projection of the fit.

Figure 3

From top left to bottom right: $m_{\mathrm{ES}}$ projection for (a) $K\pi \pi$, (b) $K\pi \pi {\pi }^0$, (c) $K_S^0\pi$, and (d) $K_S^0\pi {\pi }^0$ for the $B^{+}\to D^{+}{K}_S^0$ mode and (e) $K\pi \pi$ and (f) $K_S^0\pi$ for the $B^{+}\to D^{+}{K}^{*0}$ mode. The data are indicated with black dots and error bars and the different fit components are shown: signal (black solid curve), combinatorial $B\overline{B}$ (green dotted), continuum (magenta dot-dashed) and $B\overline{B}$ peaking background (red dotted) and the blue solid curve is the projection of the fit. We require $\mathcal{F}>0$ to visually enhance the signal component. Such a cut has an approximate efficiency of 70% for signal, while it rejects more than 80% of the continuum background.