Measurement of the branching fraction, polarization, and CP asymmetries in B0→ρ0ρ0 decay, and implications for the CKM angle α

We study B-0 ->rho(0)rho(0) decays in a sample of 465x10(6) Upsilon(4S)-> B(B)overbar events collected with the BABAR detector at the PEP-II asymmetric-energy e(+)e(-) collider located at the Stanford Linear Accelerator Center (SLAC). We measure the branching fraction B=(0.92 +/- 0.32 +/- 0.14)x10(-6) and longitudinal polarization fraction f(L)=0.75(-0.14)(+0.11)+/- 0.05, where the first uncertainty is statistical and the second is systematic. The evidence for the B-0 ->rho(0)rho(0) signal has a significance of 3.1 standard deviations, including systematic uncertainties. We investigate the proper-time dependence of the longitudinal component in the decay and measure the CP-violating coefficients S-L(00)=(0.3 +/- 0.7 +/- 0.2) and C-L(00)=(0.2 +/- 0.8 +/- 0.3). We study the implication of these results for the unitarity triangle angle alpha.