3πDecay Modes ofK±andη

Abstract

Present experimental results on $\tau$, ${\tau }^{\prime }$, and $\eta \to 3\pi$ decay are shown to imply either that these decays all pass through an intermediate virtual one-pion state; or that there exists an $S$-wave $2\pi$ resonance of low mass, such as the recently reported $\phi$, which, however, has yet to be confirmed. It is not possible simply to invoke a pure $I=1\mathrm{}$ final state in each of the three decays, since other evidence shows that, in the absence of such a resonance, the $K^{\pm }\to 3\pi$ effective weak Lagrangian density contains both nonderivative and derivative coupling. The $\eta x$ spectrum, while presently unreliable, shows evidence against such a resonance, but further experiments are needed. Here $x$ is the usual Dalitz variable, related to the ${\pi }^{+}{\pi }^{-}$ energy difference.