Amplitude analysis of ${D}_{s}^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}$

Utilizing the data set corresponding to an integrated luminosity of $3.19\text{}\text{}{\mathrm{fb}}^{-1}$ collected by the BESIII detector at a center-of-mass energy of 4.178 GeV, we perform an amplitude analysis of the ${D}_{s}^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}$ decay. The sample contains 13,797 candidates with a signal purity of $\sim 80%$. The amplitude and phase of the contributing $\pi \pi \text{}S$ wave are measured based on a quasi-model-independent approach, along with the amplitudes and phases of the $P$ and $D$ waves parametrized by Breit-Wigner models. The fit fractions of different intermediate decay channels are also reported.