Evidence for B(0) --> rho(0)rho(0) decays and implications for the Cabibbo-Kobayashi-Maskawa angle alpha.

We search for the decays B(0) --> rho(0)rho(0), B(0) --> rho(0)f(0)(980), and B(0) --> f(0)(980)f(0)(980) in a sample of about 384 x 10(6) Upsilon(4S) --> BB[over] decays collected with the BABAR detector at the PEP-II asymmetric-energy e(+)e(-) collider at Stanford Linear Accelerator Center. We find evidence for B(0) --> rho(0)rho(0) with 3.5 sigma significance and measure the branching fraction B = (1.07 +/- 0.33 +/- 0.19) x 10(-6) and longitudinal polarization fraction f(L) = 0.87 +/- 0.13 +/- 0.04, where the first uncertainty is statistical, and the second is systematic. The uncertainty on the Cabibbo-Kobayashi-Maskawa quark-mixing matrix unitarity angle alpha due to penguin contributions in B --> rho rho decays is 18 degrees at the 1 sigma level. We also set upper limits on the B(0) --> rho(0)f(0)(980) and B(0) --> f(0)(980)f(0)(980) decay rates.