We report a search for the decays $B^0\to K^{*0}{\overline{K}}^{*0}$ and $B^0\to K^{*0}{K}^{*0}$. We also measure other charmless decay modes with $K^{+}{\pi }^{-}{K}^{-}{\pi }^{+}$ and $K^{+}{\pi }^{-}{K}^{+}{\pi }^{-}$ final states. The results are obtained from a data sample containing $657\times {10}^6$ $B\overline{B}$ pairs collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We set upper limits on the branching fractions for $B^0\to K^{*0}{\overline{K}}^{*0}$ and $B^0\to K^{*0}{K}^{*0}$ of $0.81\times {10}^{-6}$ and $0.20\times {10}^{-6}$, respectively, at the 90% confidence level.

• Received 25 January 2010

DOI:https://doi.org/10.1103/PhysRevD.81.071101