Measurement of $C\!P$ violation observables in $D^+\rightarrow K^-K^+\pi^+$ decays

A search for violation of the charge-parity $C\!P$ symmetry in the $D^+\rightarrow K^-K^+\pi^+$ decay is presented, with proton-proton collision data corresponding to an integrated luminosity of 5.4 fb$^{-1}$, collected at a center-of-mass energy of $13$ TeV with the LHCb detector. A novel model-independent technique is used to compare the $D^+$ and $D^-$ phase-space distributions, with instrumental asymmetries subtracted using the $D^+_{s}\rightarrow K^-K^+\pi^+$ decay as a control channel. The $p$-value for the hypothesis of $C\!P$ conservation is $8.1\%$. The $C\!P$ asymmetry observables $A_{C\!P|S}^{\phi\pi^+} = (0.95 \pm 0.43_{stat} \pm 0.26_{syst})\times 10^{-3}$ and $A_{C\!P|S}^{\overline{K}^{*0}K^+} = (-0.26 \pm 0.56_{ stat} \pm 0.18_{syst})\times 10^{-3}$ are also measured. These results show no evidence of $C\!P$ violation and represent the most sensitive search performed through the phase space of a multibody decay.