# Amplitude analysis of $D^{+} \rightarrow K_{S}^{0} \pi^{+} \pi^{+} \pi^{-}$

## TL;DR

This paper performs an amplitude analysis of the decay $D^{+}
ightarrow K_{S}^{0} \pi^{+} \pi^{+} ext{ extbackslash}pi^{-}$ using BESIII data, identifying key intermediate states and their contributions to understand the decay dynamics.

## Contribution

It provides the first detailed amplitude analysis of this decay mode, identifying significant intermediate states and quantifying their relative contributions and phases.

## Key findings

- Dominant amplitude is $K_{S}^{0} a_{1}(1260)^{+}$ with 40.3% fit fraction.
- Identified five quasi-two-body decay contributions and a non-resonant component.
- Measured relative fractions and phases of intermediate states.

## Abstract

The decay $D^{+} \rightarrow K_{S}^{0} \pi^{+} \pi^{+} \pi^{-}$ is studied with an amplitude analysis using a data set of 2.93${\mbox{\,fb}^{-1}}$ of $e^+e^+$ collisions at the $\psi(3770)$ peak accumulated by the BESIII detector. Intermediate states and non-resonant components, and their relative fractions and phases have been determined. The significant amplitudes, which contribute to the model that best fits the data, are composed of five quasi-two-body decays $ K_{S}^{0} a_{1}(1260)^{+}$, $ \bar{K}_{1}(1270)^{0} \pi^{+}$ $ \bar{K}_{1}(1400)^{0} \pi^{+}$, $ \bar{K}_{1}(1650)^{0} \pi^{+}$, and $ \bar{K}(1460)^{0} \pi^{+}$, a three-body decays $K_{S}^{0}\pi^{+}\rho^{0}$, as well as a non-resonant component $ K_{S}^{0}\pi^{+}\pi^{+}\pi^{-}$. The dominant amplitude is $ K_{S}^{0} a_{1}(1260)^{+}$, with a fit fraction of $(40.3\pm2.1\pm2.9)\%$, where the first and second uncertainties are statistical and systematic, respectively.

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Source: https://tomesphere.com/paper/1901.05936