Time-dependent analysis of the decay B0 → ρ0ρ0

We study the decay B0 → ρ0ρ0 in a sample of about 427 million γ(4S) → BB decays collected with the BABAR detector at the PEP-II asymmetric-energy e+e- collider at SLAC. We find the branching fraction B = (0.84 ± 0.29 ± 0.17) × 10-6 and longitudinal polarization fraction of fL = 0.70 ± 0.14 ± 0.05, where the first uncertainty is statistical, and the second is systematic. The evidence for the B0 → ρ0ρ0signal has 3.6σ significance. We investigate the proper-time dependence of the longitudinal component in the decay and measure the CP-violating coefficients S00 L = (0.5± 0.9 ± 0.2) and C00 L = (0.4 ± 0.9 ± 0.2), corresponding to the sine and cosine terms in the time evolution of asymmetry. We study the implication of these results for penguin contributions in B → ρρ decays and for the CKM unitarity angle α.