Amplitude analysis and branching fraction measurement of the decay $D^{+}\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^0\ddot{I}{€}^0$

Abstract

Using 2.93 ${\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected with the BESIII detector at the center-of-mass energy 3.773\,GeV, we perform the first amplitude analysis of the decay $D^{+}\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^0\ddot{I}{€}^0$ and determine the relative magnitudes and phases of different intermediate processes. The absolute branching fraction of $D^{+}\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^0\ddot{I}{€}^0$ is measured to be $(2.888\pm 0.058_{stat.}\pm 0.069_{syst.})\%$. The dominant intermediate processes are $D^{+}\to K_S^0{a}_1(1260{)}^{+}(\to \ddot{I}{}^{+}\ddot{I}{€}^0)$ and $D^{+}\to {\bar{K}}^{\ast 0}\ddot{I}{}^{+}$, with branching fractions of $(8.66\pm 1.04_{stat.}\pm 1.39_{syst.})\times 10^{-3}$ and $(9.70\pm 0.81_{stat.}\pm 0.53_{syst.})\times 10^{-3}$, respectively.