Updated model-independent measurement of the strong-phase differences between $D^0$ and ${\bar{D}}^0\to K_{S\mathrm{/}L}^0{\pi }^{+}{\pi }^{-}$ decays

The strong-phase differences between $D^0\to K_{S\mathrm{/}L}^0{\pi }^{+}{\pi }^{-}$ and ${\bar{D}}^0\to K_{S\mathrm{/}L}^0{\pi }^{+}{\pi }^{-}$ decays are one of the most important inputs in measuring the $C\text{\hspace{0.17em}⁣}P$ violating angle $\gamma$ via $B^{-}\to D{K}^{-}$ decays. They also play a key role in studies of charm mixing and indirect $C\text{\hspace{0.17em}⁣}P$ violation. In this paper, the strong-phase differences are determined in a model-independent way with quantum-correlated $D^0$-${\bar{D}}^0$ decays from 7.93 fb${}^{-1}$ of $e^{+}{e}^{-}$ annihilation data at $\sqrt{s}$=3.773 GeV by the BESIII experiment. These results are the most precise to date and are expected to significantly reduce associated uncertainties in determining the $C\text{\hspace{0.17em}⁣}P$ violating angle $\gamma$ and related charm mixing parameters.