Measurement of $Br(K_{S} \to \pi^{+}\pi^{-}\pi^{0})$ and limit on the CP violating decay $Br(K_{S} \to 3\pi^{0})$

The NA48/1 Collaboration has measured the amplitude of the CP-conserving component of the decay $K^{0}_{S} \to \pi^{+}\pi^{-}\pi^{0}$ relative to $K^{0}_{L} \to \pi^{+}\pi^{-}\pi^{0}$ using data taken in 2002. The amplitude has been calculated by measuring the parameter $\lambda$ which describes the interference between the $K_{L}$ and $K_{S}$ decays. From a fit to 19 million reconstructed $K^{0} /\bar{K^{0}} \to \pi^{+}\pi^{-}\pi^{0}$ events the values $\Re(\lambda) = 0.038 \pm 0.010$ and $Im(\lambda) = −0.013 \pm 0.007$ have been obtained. This corresponds to a branching ratio of $Br(K_{S} \to \pi^{+}\pi^{-}\pi^{0}) = (4.7^{+2.2}_{−1.7} (stat)^{+1.7}_{−1.5} (syst)) \times 10^{−7}$ . We also searched for the CP violating decay $K_{S} \to 3\pi^{0}$ using data taken in the year 2000. The CP violating amplitude $\eta_{000} = A(K_{S} \to 3\pi^{0})/A(K_{L} \to 3\pi^{0})$ has been measured by fitting the lifetime distribution of about 4.9 million reconstructed $K^{0}/\bar{K^{0}} \to 3\pi^{0}$ decays. This results in an upper limit on the branching fraction of $BR(K_{S} \to 3\pi^{0}) < 4.7 \times 10^{−7}$ at 90% confidence level.