Measurement of B0→π+π-π+π- decays and search for B0→ρ0ρ0

We report on a search for the decay B0→ρ0ρ0 and other charmless modes with a π+π-π+π- final state, including B0→ρ0π+π-, nonresonant B0→4π±, B0→ρ0f0(980), B0→f0(980)f0(980) and B0→f0(980)π+π-. These results are obtained from a data sample containing 657x106 BB pairs collected with the Belle detector at the KEKB asymmetric-energy e+e- collider. We set an upper limit on B(B0→ρ0ρ0) of 1.0x10-6 at the 90% confidence level (C.L.). From our B0→ρ0ρ0 measurement and an isospin analysis, we determine the Cabibbo-Kobayashi-Maskawa phase φ2 to be 91.7±14.9 degrees. We find excesses in B0→ρ0π+π- and nonresonant B0→4π± with 1.3σ and 2.5σ significance, respectively. The corresponding branching fractions are less than 12.0x10-6 and 19.3x10-6 at the 90% C.L. In addition, we set 90% C.L. upper limits as follows: B(B0→ρ0f0(980))<0.3x10-6, B(B0→f0(980)f0(980))<0.1x10-6, and B(B0→f0(980)π+π-)<3.8x10-6.