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Amplitude analysis and branching fraction measurement of the decay $D_{s}^{+} \to K^+π^+π^-$

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 $D^+_s \to K^+π^+π^-$ and determine the amplitudes of the various intermediate states. The absolute branching fraction of $D^+_s\to K^+π^+π^-$ is measured to be ($6.11\pm0.18_{\rm stat.}\pm0.11_{\rm syst.})\times 10^{-3}$. The branching fractions of the dominant intermediate processes $D_{s}^{+} \to K^+ρ^0, ρ^0 \to π^+π^-$ and $D_{s}^{+} \to K^*(892)^0π^+, K^*(892)^0 \to K^+π^-$ are determined to be $(1.96\pm0.19_{\rm stat.}\pm0.23_{\rm syst.})\times 10^{-3}$ and $(1.85\pm0.12_{\rm stat.}\pm0.13_{\rm syst.})\times 10^{-3}$, respectively. The intermediate resonances $f_0(500)$, $f_0(980)$, and $f_0(1370)$ are observed for the first time in this channel.