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Study of the $f_{0}(980)$ through the decay $D_{s}^{+}\rightarrow \pi^{+}\pi^{+}\pi^{-}\pi^{0}$

Study of the $f_{0}(980)$ through the decay $D_{s}^{+}\rightarrow \pi^{+}\pi^{+}\pi^{-}\pi^{0}$

We perform the first amplitude analysis of $D^+_s \to \pi^+\pi^+\pi^-\pi^0$ decays, based on data samples of electron-positron collisions recorded with the BESIII detector at center-of-mass energies between 4.128 and 4.226 GeV, corresponding to an integrated luminosity of 7.33~fb$^{-1}$. We report the observation of $D_{s}^{+} \to f_0(980)\rho(770)^{+}$ with a statistical significance …