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 $A_g=(g^+-g^-)/(g^++g^-)$ 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 $A^c_g=(-1.5\pm2.1)\times10^{-4}$ with $3.11\times 10^9$ $K^{\pm}\to\pi^\pm\pi^+\pi^-$ decays, and $A^n_g=(1.8\pm1.8)\times10^{-4}$ 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.