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

Abstract

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 $D_s^+\to\pi^+\pi^-\pi^+$ decay. The sample contains 13,797 candidates with a signal purity of $\sim$80%. The amplitude and phase of the contributing $\pi\pi$ ${\cal S}$ wave are measured based on a quasi-model-independent approach, along with the amplitudes and phases of the ${\cal P}$ and ${\cal D}$ waves parametrized by Breit-Wigner models. The fit fractions of different intermediate decay channels are also reported.