We report the most precise measurements to date of the strong-phase parameters between $D^0$ and ${\overline{D}}^0$ decays to $K_{S,L}^0{\pi }^{+}{\pi }^{-}$ using a sample of $2.93{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected at a center-of-mass energy of 3.773 GeV with the BESIII detector at the BEPCII collider. Our results provide the key inputs for a binned model-independent determination of the Cabibbo-Kobayashi-Maskawa angle $\gamma /{\varphi }_3$ with $B$ decays. Using our results, the decay model sensitivity to the $\gamma /{\varphi }_3$ measurement is expected to be between 0.7° and 1.2°, approximately a factor of three smaller than that achievable with previous measurements, based on the studies of the simulated data. The improved precision of this work ensures that measurements of $\gamma /{\varphi }_3$ will not be limited by knowledge of strong phases for the next decade. Furthermore, our results provide critical input for other flavor-physics investigations, including charm mixing, other measurements of $CP$ violation, and the measurement of strong-phase parameters for other $D$-decay modes.

• Received 28 February 2020
• Revised 20 April 2020
• Accepted 21 May 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.241802

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Published by the American Physical Society