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We search for the decay B0 -> rho0 rho0 in a data sample of about
227 million Upsilon(4S)-> BBbar 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*10^-6
at 90% CL on the branching fraction. As a result, the uncertainty
due to penguin contributions on the CKM unitarity angle alpha
measured in B -> rho rho decays is 11 degrees at 68% CL.
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