Amplitude analysis and branching fraction measurement of the decay Ds+ → K ⁺ π ⁺ π ⁻

Using 6.32 fb⁻¹ of e⁺e⁻ collision data collected at the center-of-mass energies between 4.178 and 4.226 GeV with the BESIII detector, we perform an amplitude analysis of the decay Ds+→ K⁺π⁺π⁻ and determine the amplitudes of the various intermediate states. The absolute branching fraction of Ds+→ K⁺π⁺π⁻ is measured to be (6.11 ± 0.18_stat.± 0.11_syst.) × 10⁻³. The branching fractions of the dominant intermediate processes Ds+→ K⁺ρ⁰, ρ⁰→ π⁺π⁻ and Ds+→ K^*(892)⁰π⁺, K^*(892)⁰→ K⁺π⁻ are determined to be (1.96 ± 0.19_stat.± 0.23_syst.) × 10⁻³ and (1.85 ± 0.12_stat.± 0.13_syst.) × 10⁻³, respectively. The intermediate resonances f₀(500), f₀(980), and f₀(1370) are observed for the first time in this channel. [Figure not available: see fulltext.]