A measurement of the $CP$-even fraction of the decay $D^0\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ is performed with a quantum-correlated $\psi (3770)\to D\overline{D}$ data sample collected by the BESIII experiment, corresponding to an integrated luminosity of $2.93{\mathrm{fb}}^{-1}$. Using a combination of $CP$ eigenstates, $D\to {\pi }^{+}{\pi }^{-}{\pi }^0$ and $D\to K_{S,L}^0{\pi }^{+}{\pi }^{-}$ as tagging modes, the $CP$-even fraction is measured to be $F_{+}^{4\pi }=0.735\pm 0.015\pm 0.005$, where the first uncertainty is statistical and the second is systematic. This is the most precise determination of this quantity to date. It provides valuable model-independent input for the measurement of the angle $\gamma$ of the Cabibbo-Kobayashi-Maskawa matrix with $B^{\pm }\to D{K}^{\pm }$ decays, and for time-dependent studies of $CP$ violation and mixing in the $D^0\text{−}{\overline{D}}^0$ system.

• Received 22 August 2022
• Accepted 21 October 2022

DOI:https://doi.org/10.1103/PhysRevD.106.092004

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Published by the American Physical Society