Crucial inputs for a variety of $CP$-violation studies can be determined through the analysis of pairs of quantum-entangled neutral $D$ mesons, which are produced in the decay of the $\psi (3770)$ resonance. The relative strong-phase parameters between $D^0$ and ${\overline{D}}^0$ in the decays $D^0\to K_{S,L}^0{\pi }^{+}{\pi }^{-}$ are studied using $2.93{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data delivered by the BEPCII collider and collected by the BESIII detector at a center-of-mass energy of 3.773 GeV. Results are presented in regions of the phase space of the decay. These are the most precise measurements to date of the strong-phase parameters in $D\to K_{S,L}^0{\pi }^{+}{\pi }^{-}$ decays. Using these parameters, the associated uncertainty on the Cabibbo-Kobayashi-Maskawa angle $\gamma /{\varphi }_3$ is expected to be between 0.7° and 1.2° for an analysis using the decay $B^{\pm }\to D{K}^{\pm }$, $D\to K_S^0{\pi }^{+}{\pi }^{-}$, where $D$ represents a superposition of $D^0$ and ${\overline{D}}^0$ states. This is a factor of 3 smaller than that achievable with previous measurements. Furthermore, these results provide valuable input for charm-mixing studies, other measurements of $CP$ violation, and the measurement of strong-phase parameters for other $D$-decay modes.

• Received 28 February 2020
• Accepted 23 April 2020

DOI:https://doi.org/10.1103/PhysRevD.101.112002

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society