Determination of Strong-Phase Parameters in $D\to {K}_{S,L}^{0}{\pi }^{+}{\pi }^{-}$

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 $2.93\text{}\text{}{\mathrm{fb}}^{-1}$ 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.