Some Comments on the Decays ofη(550)

Abstract

Various decay modes of the $\eta \mathrm{}\left(550\right)\mathrm{}$ are discussed. The relations, through $S{U}_3$ and the Gell-Mann-Sharp-Wagner model, between the $\eta$-decay modes and the modes $\eta \to \pi \pi \gamma$, ${\pi }^0\to \gamma \gamma$ are investigated, taking into account $\eta -{\eta }^{*}$ mixing. The present experimental values for the neutral branching ratios plus the shape of the $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ Dalitz plot are shown to require a 30% $\left|\Delta \mathrm{I}\right|=3\mathrm{}$ contribution to the $\eta \to 3\pi$ amplitude. The connection between a possible charge asymmetry in $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ and branching ratio $\frac{{\Gamma }_{\eta \to {\pi }^0{e}^{*}{e}^{*}}}{{{\Gamma }_{\eta }}^{\mathrm{all}}}$ is investigated in the framework of a model proposed earlier by several authors. It is shown that there is no conflict between the existing data and this model. The Dalitz-plot distribution of $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ is discussed under various assumptions about the properties of the interaction responsible for the decay.