Search for $CP$ violation with kinematic asymmetries in the $D^0 \to K^+ K^- \pi^+ \pi^-$ decay

We search for $CP$ violation in the singly-Cabibbo-suppressed decay $D^{0}\rightarrow K^{+}K^{-}\pi^{+}\pi^{-}$ using data corresponding to an integrated luminosity of $988\text{ }{\rm fb}^{-1}$ collected by the Belle detector at the KEKB $e^{+}e^{-}$ collider. We measure a set of five kinematically dependent $CP$ asymmetries, of which four asymmetries are measured for the first time. The set of asymmetry measurements can be sensitive to $CP$ violation via interference between the different partial-wave contributions to the decay and performed on other pseudoscalar decays. We find no evidence of $CP$ violation.