Amplitude analysis of the $D_s^{+} rightarrow pi^{+} pi^{-} pi^{+}$ decay

Utilizing the data set corresponding to an integrated luminosity of $3.19$ fb$^{-1}$ collected by the BESIII detector at a center-of-mass energy of 4.178 GeV, we perform an amplitude analysis of the $D_s^+topi^+pi^-pi^+$ decay. The sample contains 13,797 candidate events with a signal purity of $sim$80%. We use a quasi-model-independent approach to measure the magnitude and phase of the $D_s^+topi^+pi^-pi^+$ decay, where the ${cal P}$ and ${cal D}$ waves are parameterized by a sum of three Breit-Wigner amplitudes $rho(770)^0$, $rho(1450)^0$, and $f_2(1270)$. The fit fractions of different decay channels are also reported.