Search for the CP violating $K_S\to 3{\pi }^0$ decay with the KLOE detector

We present a new search for the $K_S\to 3{\pi }^0$ decay performed with the KLOE detector operating at the DA$\mathrm{\Phi }$NE $\varphi$–factory. The $K_S$ mesons were tagged via registration of $K_L$ mesons which crossed the drift chamber without decaying and interacted with the KLOE electromagnetic calorimeter. The $K_S\to 3{\pi }^0$ decay was then searched requiring six prompt photons. To suppress background, originating from fake $K_S$ tags and $K_S\to 2{\pi }^0$ decays with additional two spurious clusters, we have performed a discriminant analysis based on kinematical fit, testing of the signal and background hypotheses and exploiting of the differences in kinematics of the $K_S$ decays into $2{\pi }^0$ and $3{\pi }^0$. In a sample of about 1.7$\cdot {10}^9$ $\phi \to K_S K_L$ events we have found no candidates in data and simulated background samples. Normalizing to the number of $K_S\to 2{\pi }^0$ events in the same sample, we have set the upper limit on the $K_S\to 3{\pi }^0$ branching ratio BR($K_S\to 3{\pi }^0)<2.6\cdot {10}^{-8}$ at 90% C.L., five times lower than the previous limit. This upper limit can be translated into a limit on the modulus of the ${\eta }_{000}$ parameter amounting to $\mathrm{\mid }{\eta }_{000}\mathrm{\mid }<0.0088$ at 90% C.L., improving by a factor two the latest direct measurement.