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

TL;DR

This paper presents an amplitude analysis of the decay $D_s^{+} ightarrow \pi^{+} \pi^{-} \\pi^{+}$ using BESIII data, measuring decay amplitudes, phases, and fit fractions to understand the decay dynamics.

Contribution

It introduces a quasi-model-independent approach to measure the $\\pi\\pi$ ${\\cal S}$ wave amplitude and phase in $D_s^+$ decay, providing detailed decay channel contributions.

Findings

Measured $\\pi\\pi$ ${\\cal S}$ wave amplitude and phase.

Reported fit fractions of intermediate decay channels.

Provided detailed decay dynamics of $D_s^+$ to three pions.

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.