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

Abstract

The decay $D^{+} \rightarrow K_{S}^{0} \pi^{+} \pi^{+} \pi^{-}$ is studied with an amplitude analysis using a data set of 2.93fb$^{-1}$ 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±2.1±2.9)%, where the first and second uncertainties are statistical and systematic, respectively.