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We search for the decay B0 -> rho0rho0 and other possible charmless modeswith a pi+pi-pi+pi- final state, including B0 -> rho0f0(980), B0 ->f0(980)f0(980), B0 -> f0(980)pipi, B0 -> rho0pipi and non-resonant B0 -> 4pi.These results are obtained from a data sample containing 520 x 10^6 BBar pairscollected by the Belle detector at the KEKB asymmetric-energy e+e- collider. Wemeasure a branching fraction of (0.9 +/- 0.4^{+0.3}_{-0.4}) x 10^{-6}, or B(B0-> rho0rho0) < 1.6 x 10^{-6} at the 90% confidence level. The significanceincluding systematic uncertainties is 1.8\sigma. These values correspond to thefinal state being longitudinally polarized. We also measure the branchingfraction of non-resonant B0 -> 4pi decay to be (10.2 +/- 4.7^{+2.3}_{-1.5}) x10^{-6} with 2.1\sigma significance, and set the 90% confidence level upperlimit B(B0 -> 4pi) < 17.3 x 10^{-6}. For the other related decays, B0 ->rho0f0(980), B0 -> f0(980)f0(980), B0 -> f0(980)pipi and B0 -> rho0pipi, nosignificant signals are observed and upper limits on the branching fractionsare set.

Search for B0 -> rho0rho0 and Non-Resonant B0 -> 4pi Decays