We present a study of the decays $B^0\to D^0{K}^{*0}$ and $B^0\to {\overline{D}}^0{K}^{*0}$ with $K^{*0}\to K^{+}{\pi }^{-}$. The $D^0$ and the ${\overline{D}}^0$ mesons are reconstructed in the final states $f=K^{+}{\pi }^{-}$, $K^{+}{\pi }^{-}{\pi }^0$, $K^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$, and their charge conjugates. Using a sample of $465\times {10}^6$ $B\overline{B}$ pairs collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at SLAC, we measure the ratio $R_{\mathrm{ADS}}\equiv [\Gamma ({\overline{B}}^0\to [f{]}_D{\overline{K}}^{*0})+\Gamma (B^0\to [\overline{f}{]}_D{K}^{*0})]/[\Gamma ({\overline{B}}^0\to [\overline{f}{]}_D{\overline{K}}^{*0})+\Gamma (B^0\to [f{]}_D{K}^{*0})]$ for the three final states. We do not find significant evidence for a signal and set the following limits at 95% probability: $R_{\mathrm{ADS}}(K\pi )<0.244$, $R_{\mathrm{ADS}}(K\pi {\pi }^0)<0.181$, and $R_{\mathrm{ADS}}(K\pi \pi \pi )<0.391$. From the combination of these three results, we find that the ratio $r_S$ between the $b\to u$ and the $b\to c$ amplitudes lies in the range [0.07,0.41] at 95% probability.

• Received 15 April 2009

DOI:https://doi.org/10.1103/PhysRevD.80.031102