Search for direct CP-violation in $K^{\pm} \rightarrow 3\pi$ decays by NA48/2

A high precision search for direct CP-violation in $K^{\pm} \rightarrow 3\pi$ decays was performed by the NA48/2 experiment at CERN SPS. The asymmetry in the Dalitz plot linear slopes $A_{g} = (g^{+} - g^{-})/(g^{+} + g^{-})$ is measured to be $A^{c}_{g} = (-1.3 \pm 2.3) \times 10^{-4}$ by studying $\sim 3.1 \times 10^{9}$ $K^{\pm} \rightarrow \pi^{\pm}\pi^{+}\pi^{-}$ decays and $A^{n}_{g} = (2.1 \pm 1.9) \times 10^{-4}$ by studying $\sim 91 \times 10^{6}$ $K^{\pm} \rightarrow \pi^{\pm}\pi^{0}\pi^{0}$ decays. The unique double- beam system, the design of the detectors and the method of analysis provide good control of the instrumental charge asymmetries and allow to keep the precision of the result limited by statistics, reaching accuracy one order of magnitude better than in previous experiments.