Limit on theB0→ρ0ρ0Branching Fraction and Implications for the Cabibbo-Kobayashi-Maskawa Angleα

We search for the decay $B^0\to {\rho }^0{\rho }^0$ in a data sample of about $227\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at SLAC. We find no significant signal and set an upper limit of $1.1\times {10}^{-6}$ at 90% C.L. on the branching fraction. As a result, the uncertainty due to penguin contributions on the Cabibbo-Kobayashi-Maskawa unitarity angle $\alpha$ measured in $B\to \rho \rho$ decays is decreased to 11° at 68% C.L.