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.

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.