Measurement of the $C\text{\hspace{0.17em}⁣}P$-even fraction of $D^0\to K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$

A determination of the $C\text{\hspace{0.17em}⁣}P$-even fraction $F_{+}$ in the decay $D^0\to K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ is presented. Using $2.93$ fb${}^{-1}$ of $e^{+}{e}^{-}\to \psi (3770)\to D\bar{D}$ data collected by the BESIII detector, one charm meson is reconstructed in the signal mode and the other in a $C\text{\hspace{0.17em}⁣}P$ 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 $F_{+}=0.730\pm 0.037\pm 0.021$, 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.