Amplitude analysis of $D^{+}\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$

Abstract

The decay $D^{+}\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ is studied with an amplitude analysis using a data set of 2.93${\mbox{\,fb}^{-1}}$ of $e^{+}{e}^{+}$ collisions at the $\ddot{I}ˆ(3770)$ 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 $K_S^0{a}_1(1260{)}^{+}$, ${\bar{K}}_1(1270{)}^0\ddot{I}{€}^{+}$ ${\bar{K}}_1(1400{)}^0\ddot{I}{€}^{+}$, ${\bar{K}}_1(1650{)}^0\ddot{I}{€}^{+}$, and $\bar{K}(1460{)}^0\ddot{I}{€}^{+}$, a three-body decays $K_S^0\ddot{I}{€}^{+}\ddot{I}{}^0$, as well as a non-resonant component $K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$. The dominant amplitude is $K_S^0{a}_1(1260{)}^{+}$, with a fit fraction of $(40.3\pm 2.1\pm 2.9)\%$, where the first and second uncertainties are statistical and systematic, respectively.

14 pages, 3 figures