Observation of the $B^0 \to ρ^0 ρ^0$ decay from an amplitude analysis of $B^0 \to (π^+π^-)(π^+π^-)$ 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 B⁰→ρ⁰ρ⁰ decay. More than 600 B⁰→(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 B⁰→ρ⁰ρ⁰ decay is observed for the first time with 7.1 standard deviations significance. The fraction of B⁰→ρ⁰ρ⁰ decays yielding a longitudinally polarised final state is measured to be fL=0.745-0.058+0.048(stat)±0.034(syst). The B⁰→ρ⁰ρ⁰ branching fraction, using the B⁰→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.