Final-State Interactions inη→3πandK20→3πDecays

We study $\eta \to 3\pi$ and ${K_2}^0\to 3\pi$ decays assuming that the nonconstancy of the matrix elements originates from the $S$- and $P$-wave pion-pion final-state interactions. The $I=J=0\mathrm{}$ and $I=J=1\mathrm{} \pi \pi$ interactions are assumed to be dominated by the $S$ meson (mass 700 MeV and width 400 MeV) and the $\rho$ meson, respectively. Our analysis shows that the $\rho$ meson swamps the $S$ meson in describing the energy spectra. The results for the energy spectra and the branching ratios are in good agreement with recent experiments.