Amplitude analysis and branching fraction measurement of the decay ${D}_{s}^{+}$ → 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 ${D}_{s}^{+}$ → K + π + π − and determine the amplitudes of the various intermediate states. The absolute branching fraction of ${D}_{s}^{+}$ → K + π + π − is measured to be (6.11 ± 0.18stat. ± 0.11syst. ) × 10 −3. The branching fractions of the dominant intermediate processes ${D}_{s}^{+}$ → K + ρ 0 , ρ 0 → π + π − and ${D}_{s}^{+}$ → K *(892)0 π + , K *(892)0 → K + π − are determined to be (1.96 ± 0.19stat. ± 0.23syst. ) × 10 −3 and (1.85 ± 0.12stat. ± 0.13syst. ) × 10 −3, respectively. The intermediate resonances f 0(500), f 0(980), and f 0(1370) are observed for the first time in this channel.