Study of Ds+ →f0 (980)ρ+ and φπ+ Decays through Ds+ →π+π+π-π0

We perform the first amplitude analysis of Ds+→π+π+π-π0 decays based on data samples of electron-positron collisions recorded with the BESIII detector at center-of-mass energies between 4.128 and 4.226 GeV, corresponding to an integrated luminosity of 7.33 fb-1. We report the observation of Ds+→f0(980)ρ(770)+ with a statistical significance greater than 10σ and determine the branching fractions B(Ds+→π+π+π-π0|non-η)=(2.04±0.08stat±0.05syst)% and B(Ds+→ηπ+)=(1.56±0.09stat±0.04syst)%. Moreover, we measure the relative branching fraction between φ→π+π-π0 and φ→K+K- to be [B(φ(1020)→π+π-π0)/B(φ(1020)→K+K-)]=0.230±0.014stat±0.010syst., which deviates from the world average value by more than 4σ.