Observation of the B⁰ → ρ⁰ρ⁰ decay from an amplitude analysis of B⁰ → (π⁺π^-)(π⁺π^-) decays

Proton-proton collision data recorded in 2011 and 2012 by the LHCb experiment, corresponding to an integrated luminosity of 3.0 fb ^-1, are analysed to search for the charmless B ⁰→ρ ⁰ρ ⁰ decay. More than 600 B ⁰→(π ⁺π ^-)(π ⁺π ^-) signal decays are selected and used to perform an amplitude analysis, under the assumption of no CP violation in the decay, from which the B ⁰→ρ ⁰ρ ⁰ decay is observed for the first time with 7.1 standard deviations significance. The fraction of B ⁰→ρ ⁰ρ ⁰ decays yielding a longitudinally polarised final state is measured to be fL=0.745-0.058+0.048(stat)±0.034(syst). The B ⁰→ρ ⁰ρ ⁰ branching fraction, using the B ⁰→ϕK ^*(892) ⁰ decay as reference, is also reported as B(B0→ρ0ρ0)=(0.94±0.17(stat)±0.09(syst)±0.06(BF))×10-6.