MEASUREMENT OF THE AMPLITUDE OF THE CP CONSERVING DECAY K(S)(0)-]PI(+)PI(-)PI(0)

We measured the amplitude for the CP-symmetry-conserving decay K(S)0 --> pi+pi- pi0 in an experiment at Fermilab. This decay manifests itself as a time dependent charge asymmetry in the interference between the coherent K(S) and K(L) decays. We collected pi+pi-pi0 decays between 0.6 and 7.6 K(S) lifetimes from the production target using a detector that consisted of a magnetic spectrometer and a lead glass electromagnetic calorimeter. K(S)0 --> pi+pi- decays that were collected simultaneously were used for normalization. The ratio rho+-0 of the CP-conserving K(S) amplitude to the K(L) amplitude is found to be: \rho+-0\ = 0.035 +0.019/-0.011 (stat.), +/- 0.004 (syst.), with a phase phi(rho) = -59-degrees +/- 48-degrees. This yields a branching ratio of (3.9 +5.4/-1.8(stat.) +0.9/-0.7(syst.)) x 10(-7).