Measurement of ${\overline{B}}^0\to D^{(*)0}{\overline{K}}^{(*)0}$ branching fractions

We present a study of the decays ${\overline{B}}^0\to D^{(*)0}{\overline{K}}^{(*)0}$ using a sample of $226\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at SLAC. We report evidence for the decay of $B^0$ and ${\overline{B}}^0$ mesons to the $D^{*0}{K}_S^0$ final state with an average branching fraction $\mathcal{B}({\tilde{B}}^0\to D^{*0}{\tilde{K}}^0)\equiv (\mathcal{B}({\overline{B}}^0\to D^{*0}{\overline{K}}^0)+\mathcal{B}(B^0\to D^{*0}{K}^0))/2=(3.6\pm 1.2\pm 0.3)\times {10}^{-5}$. Similarly, we measure $\mathcal{B}({\tilde{B}}^0\to D^0{\tilde{K}}^0)\equiv (\mathcal{B}({\overline{B}}^0\to D^0{\overline{K}}^0)+\mathcal{B}(B^0\to D^0{K}^0))/2=(5.3\pm 0.7\pm 0.3)\times {10}^{-5}$ for the $D^0{K}_S^0$ final state. We measure $\mathcal{B}({\overline{B}}^0\to D^0{\overline{K}}^{*0})=(4.0\pm 0.7\pm 0.3)\times {10}^{-5}$ and set a 90% confidence level upper limit $\mathcal{B}({\overline{B}}^0\to {\overline{D}}^0{\overline{K}}^{*0})<1.1\times {10}^{-5}$. We determine the upper limit for the decay amplitude ratio $|\mathcal{A}({\overline{B}}^0\to {\overline{D}}^0{\overline{K}}^{*0})/\mathcal{A}({\overline{B}}^0\to D^0{\overline{K}}^{*0})|$ to be less than 0.4 at the 90% confidence level.

Figure 1

The decay diagrams for the $b\to c$ transition ${\overline{B}}^0\to D^{(*)0}{\overline{K}}^{(*)0}$ and the $\overline{b}\to \overline{u}$ transition $B^0\to D^{(*)0}{K}^{(*)0}$.

Figure 2

Distribution of $\Delta E$ for a) ${\tilde{B}}^0\to D^0{\tilde{K}}^0$, b) ${\tilde{B}}^0\to D^{*0}{\tilde{K}}^0$, c) ${\overline{B}}^0\to D^0{\overline{K}}^{*0}$, and d) ${\overline{B}}^0\to {\overline{D}}^0{\overline{K}}^{*0}$ candidates with $|m_{\mathrm{ES}}-5280\mathrm{MeV}/c^2|<8\mathrm{MeV}/c^2$. The points are the data, the solid curve is the projection of the likelihood fit, and the dashed curve represents the background component.