Determination of the $CP$-even fraction of $D^0\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$

Abstract

Quantum-correlated $D\bar{D}$ pairs collected by the BESIII experiment at the $\ddot{I}ˆ(3770)$ resonance, corresponding to an integrated luminosity of 2.93 fb${}^{-1}$, are used to study the $D^0\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ decay mode. The $CP$-even fraction of $D^0\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ decays is determined to be $0.235\pm 0.010\pm 0.002$, where the first uncertainty is statistical and the second is systematic.