Improved model-independent determination of the strong-phase difference between $D^0$ and ${\bar{D}}^0\to K_{\mathrm{S},\mathrm{L}}^0{K}^{+}{K}^{-}$ decays

We present a measurement of the strong-phase difference between $D^0$ and ${\bar{D}}^0\to K_{\mathrm{S},\mathrm{L}}^0{K}^{+}{K}^{-}$ decays, performed through a study of quantum-entangled pairs of charm mesons. The measurement exploits a data sample equivalent to an integrated luminosity of 2.93~fb${}^{-1}$, collected by the BESIII detector in $e^{+}{e}^{-}$ collisions corresponding to the mass of the $\psi (3770)$ resonance. The strong-phase difference is an essential input to the determination of the Cabibbo-Kobayashi-Maskawa (CKM) angle $\gamma \mathrm{/}{\varphi }_3$ through the decay $B^{-}\to D{K}^{-}$, where $D$ can be either a $D^0$ or a ${\bar{D}}^0$ decaying to $K_{\mathrm{S},\mathrm{L}}^0{K}^{+}{K}^{-}$. This is the most precise measurement to date of the strong-phase difference in these decays.