Measurement of $C\text{\hspace{0.17em}⁣}P$ violation observables in $D^{+}\to K^{-}{K}^{+}{\pi }^{+}$ decays

A search for violation of the charge-parity $C\text{\hspace{0.17em}⁣}P$ symmetry in the $D^{+}\to K^{-}{K}^{+}{\pi }^{+}$ 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 $D_s^{+}\to K^{-}{K}^{+}{\pi }^{+}$ decay as a control channel. The $p$-value for the hypothesis of $C\text{\hspace{0.17em}⁣}P$ conservation is $8.1\mathrm{\%}$. The $C\text{\hspace{0.17em}⁣}P$ asymmetry observables $A_{C\text{\hspace{0.17em}⁣}P\mathrm{\mid }S}^{\phi {\pi }^{+}}=(0.95\pm {0.43}_{stat}\pm {0.26}_{syst})\times {10}^{-3}$ and $A_{C\text{\hspace{0.17em}⁣}P\mathrm{\mid }S}^{{\bar{K}}^{\ast 0}{K}^{+}}=(-0.26\pm {0.56}_{stat}\pm {0.18}_{syst})\times {10}^{-3}$ are also measured. These results show no evidence of $C\text{\hspace{0.17em}⁣}P$ violation and represent the most sensitive search performed through the phase space of a multibody decay.