Search for B0 → ρ0ρ0 and non-resonant B0 → 4π

We search for the decay B0 → ρ0ρ0 and other possible charmless modes with a π+ π- π+ π- final state, including B0 → ρ0f0(980), B0 → f0(980)f0(980), B0 → f0(980)π π, B0 → ρ0π π and non-resonant B0 → 4π. These results are obtained from a data sample containing 520 × 106 BB pairs collected by the Belle detector at the KEKB asymmetric-energy e+e- collider. We measure a branching fraction of (0.9 ± 0.4+0.3 -0.4) × 10-6, or B(B 0 → ρ0ρ0) < 1.6 × 10-6 at the 90% confidence level. The significance including systematic uncertainties is 1.8σ. These values correspond to the final state being longitudinally polarized. We also measure the branching fraction of non-resonant B0 → 4π decay to be (10.2 ± 4.7+2.3 -1.5) × 10-6 with 2.1σ significance, and set the 90% confidence level upper limit B(B0 → 4π) < 17.3 × 10-6. For the other related decays, B0 → ρ0f0(980), B0 → f0(980)f0(980), B0 → f0(980)ρ and B0 → ρ0π π, no significant signals are observed and upper limits on the branching fractions are set.