Search for CP violation in $K^{0} \to 3\pi^{0}$ decays

Using data taken during the year 2000 with the NA48 detector at the CERN SPS, a search for the CP violation decay $K_{S} \to 3\pi^{0}$ has been performed. From a fit to the lifetime distribution of about 4.9 million reconstructed $K^{0}/\bar{K^{0}} \to 3\pi^{0}$ decays, the CP violationg amplitude $\eta_{000} = A(K_{S} \to 3\pi^{0})/A(K_{L} \to 3\pi^{0})$ has been found to be $\Re(\eta_{000}) = -0.002 \pm 0.011 \pm 0.015$ and Im$(\eta_{000}) -0.003 \pm 0.0013 \pm 0.017$. This corresponds to an upper limit on the branching fraction of Br($K_{S} \to 3\pi^{0}) < 7.4 \times 10^{-7}$ at 90% confidence level. The result is used to improve knowledge of $\Re(\epsilon)$ and the CPT violating quantity Im($\delta$) via the Bell-Steinberger relation.