Study of the decay D s + → π + π + π - η and observation of the W -annihilation decay D s + → a 0 ( 980 ) + ρ 0
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 $\mathscr{B}$($D^+_s$ → $π^+π^+π^-η$) = (3.12 ± 0.13 stat ± 0.90 syst )%. The first amplitude analysis of this decay reveals the substructures in $D^+_s$ → $π^+π^+π^-η$ nd determines the relative fractions and the phases among these substructures. The dominant intermediate process is $D^+_s$ → $a_1$(1260) + $η,a_1$(1260) + → ρ(770) 0 $π^+$ with a branching fraction of (1.73 ± 0.14 stat ±0.08 syst )%. We also observe the W-annihilation process $D^+_s$ → $a_0$(980) + ρ(770) 0 , $a_0$(980) + → $π^+η$ with a branching fraction of (0.21 ± 0.08 stat ± 0.05 syst )%, which is larger than the branching fractions of other measured pure W-annihilation decays by 1 order of magnitude.