Search for direct CP violating charge asymmetries in $K^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ and $K^{\pm }\to {\pi }^{\pm }{\pi }^0{\pi }^0$ decays

A measurement of the direct CP violating charge asymmetries of the Dalitz plot linear slopes $A_g=(g^{+}-g^{-})\mathrm{/}(g^{+}+g^{-})$ in $K^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ and $K^{\pm }\to {\pi }^{\pm }{\pi }^0{\pi }^0$ decays by the NA48/2 experiment at CERN SPS is presented. A new technique of asymmetry measurement involving simultaneous $K^{+}$ and $K^{-}$ beams and a large data sample collected allowed a result of an unprecedented precision. The charge asymmetries were measured to be $A_g^c=(-1.5\pm 2.2)\times {10}^{-4}$ with $3.11\times {10}^9$ $K^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ decays, and $A_g^n=(1.8\pm 1.8)\times {10}^{-4}$ with $9.13\times {10}^7$ $K^{\pm }\to {\pi }^{\pm }{\pi }^0{\pi }^0$ decays. The precision of the results is limited mainly by the size of the data sample.