Study of BO → ρ0 ρ0 decays, implications for the CKM angle ϕ2 and search for other B0 decay modes with a four-pion final state

We present a study of the branching fraction of the decay B0→ρ0ρ0 and the fraction of longitudinally polarized ρ0 mesons in this decay. The results are obtained from the final data sample containing 772×106 BB̄ pairs collected at the (4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. We find 166±59 B0→ρ0ρ0 events (including systematic uncertainties), corresponding to a branching fraction of B(B0→ρ0ρ0)=(1.02±0.30(stat) ±0.15(syst))×10-6 with a significance of 3.4 standard deviations and a longitudinal polarization fraction fL=0.21-0.22+0.18(stat)±0. 15(syst). We use the longitudinal polarization fraction to determine the Cabibbo-Kobayashi-Maskawa matrix angle φ2=(84.9±13.5)° through an isospin analysis in the B→ρρ system. We furthermore find 125±41 B0→f0ρ0 events, corresponding to B(B0→f0ρ0) ×B(f0→π+π-)=(0.78±0.22(stat)±0.11(syst)) ×10-6, with a significance of 3.1 standard deviations. We find no other significant contribution with the same final state, and set upper limits at 90% confidence level on the (product) branching fractions, B(B0→π+π- π+π-)<11.2×10-6, B(B0→ρ0π+π-)<12.0×10-6, B(B0→f0π+π-)×B(f0→π+π-)<3.0×10-6 and B(B0→f0f0)×B(f0→π+π-)2<0.2×10-6.