Measurement of the strong-phase difference between $ {D}^{0}$ and $ \overline{{D}^{0}}\to {K}^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ in bins of phase space

A first determination of the strong-phase difference between $ {D}^{0}$ and $ \overline{{D}^{0}}\to {K}^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ is performed using $ {e}^{+}{e}^{-}\to \psi (3770)\to D\overline{D}$ data collected by the BESIII detector corresponding to an integrated luminosity of $ 20.3\text{}\text{}{\mathrm{fb}}^{-1}$. The measurements are made in four pairs of bins in phase space, which are chosen to provide optimal sensitivity to the angle $ \gamma $ of the unitarity triangle in $ {B}^{\pm }\to D{K}^{\pm }$ decays. From these measurements, it follows that the $ CP$-even fraction of the decay is $ {F}_{+}=0.754\pm 0.01{0}_{\mathrm{stat}}\pm \phantom{\rule{0ex}{0ex}}0.00{8}_{\mathrm{syst}}$. In addition, the branching fraction of $ {D}^{0}\to {K}^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ is measured to be $ (2.863\pm \phantom{\rule{0ex}{0ex}}0.02{8}_{\mathrm{stat}}\pm 0.04{5}_{\mathrm{syst}})\times {10}^{-3}$, which is twice as precise as previous results obtained at other experiments.