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

• Received 6 May 2023
• Accepted 23 June 2023

DOI:https://doi.org/10.1103/PhysRevD.108.032003

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Published by the American Physical Society