Study of the Decay D+s → π+π+π−η and Observation of the W-annihilation Decay D+s → a0(980)+ρ0

The decay D+s → π+π+π−η is observed for the first time, using e+e− collision data corresponding to an integrated luminosity of 6.32 fb−1, collected by the BESIII detector at center-of-mass energies between 4.178 and 4.226 GeV. The absolute branching fraction for this decay is measured to be B(D+s → π+pi+π−η) = (3.12 ± 0.13stat. ± 0.09syst.)%. The first amplitude analysis of this decay reveals the sub-structures in D+s → π+π+π−η and determines the relative fractions and the phases among these sub-structures. The dominant intermediate process is D+s → a1(1260)+η, a1(1260)+ →ρ(770)0π+ with a branching fraction of (1.73 ± 0.14stat. ± 0.08syst.)%. We also observe the W-annihilation process D+s → a0(980)+ρ(770)0, a0(980)+ → π+η with a branching fraction of (0.21 ±0.08stat. ± 0.05syst.)%, which is larger than the branching fractions of other measured pure Wannihilation decays by one order of magnitude.