Measurement of the $CP$-even fraction of ${D}^{0}\to {K}^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$

A determination of the $CP$-even fraction ${F}_{+}$ in the decay ${D}^{0}\to {K}^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ is presented. Using $2.93\text{}\text{}{\mathrm{fb}}^{-1}$ of ${e}^{+}{e}^{-}\to \psi \left(3770\right)\to D\overline{D}$ data collected by the BESIII detector, one charm meson is reconstructed in the signal mode and the other in a $CP$ eigenstate or the decay $D\to {K}_{S,L}^{0}{\pi }^{+}{\pi }^{-}$. Analysis of the relative rates of these double-tagged events yields the result ${F}_{+}=0.730±0.037±0.021$, where the first uncertainty is statistical and the second is systematic. This is the first model-independent measurement of ${F}_{+}$ in ${D}^{0}\to {K}^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ decays.