Search for b ! u transitions in B 0 ! D 0 K 0 decays

We present a study of the decays B^0 → D^(0)K^(*0) and B^0 →[overline D]^(0)K^(*0) with K^(*0) → K^(+)π^-. The D^0 and the [overline D]^0 mesons are reconstructed in the final states f = K^(+)π^-, K^(+)π^(-)π^0, K^(+)π^(-)π^(+)π^-, and their charge conjugates. Using a sample of 465 × 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_(ADS) ≡ [Γ([overline B]^0 → [f]_D[overline K]^(*0)) + Γ(B^0 → [[overline f]]_(D)K^(*0))]/[Γ([overline B]^0 → [[overline f]]_(D)[overline K]^(*0)) + Γ(B^0 → [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_(ADS)(Kπ) < 0.244, R_(ADS)(Kππ^0) < 0.181, and R_(ADS)(Kπππ) < 0.391. From the combination of these three results, we find that the ratio r_S between the b → u and the b → c amplitudes lies in the range [0.07,0.41] at 95% probability.