Comment on theη→3πpuzzle in the (3,3¯) model

Abstract

By including a $u_3$ term in $H_{\mathrm{em}}$ and taking into account rapidly varying meson poles, we show that the nonvanishing $\eta \to 3\pi$ amplitude is consistent with pion PCAC and current algebra. In this case, the $\sigma$ term ${\sigma }_{\eta \eta }^{\pi \pi }$ must be substantially larger than that obtained in the Gell-Mann-Oakes-Renner (3, $\overline{3}$) scheme.