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A search for direct $\it{CP}$ violation in the Cabibbo-suppressed decay$D_{s}^{+}\rightarrow K^{-}K^{+}K^{+}$ and in the doubly Cabibbo-suppresseddecay $D^{+}\rightarrow K^{-}K^{+}K^{+}$ is reported. The analysis is performedwith data collected by the LHCb experiment in proton-proton collisions at acentre-of-mass energy of 13 TeV corresponding to an integrated luminosity of5.6 $\textrm{fb}^{-1}$. The search is conducted by comparing the $D^+_{(s)}$and $D^-_{(s)}$ Dalitz-plot distributions through a model-independent binnedtechnique, based on fits to the $K^{-}K^{+}K^{+}$ invariant-mass distributions,with a total of 0.97 (1.27) million $D_{s}^{+}$ ($D^{+}$) signal candidates.The results are given as $p$-values for the hypothesis of $\it{CP}$conservation and are found to be 13.3% for the $D_{s}^{+}\rightarrowK^{-}K^{+}K^{+}$ decay and 31.6% for the $D^{+}\rightarrow K^{-}K^{+}K^{+}$decay. No evidence for $\it{CP}$ violation is observed in these decays.

Search for $\it{CP}$ violation in $D_{(s)}^{+}\rightarrow K^{-}K^{+}K^{+}$ decays