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 $\ensuremath{\eta}\ensuremath{\rightarrow}3\ensuremath{\pi}$ amplitude is consistent with pion PCAC and current algebra. In this case, the $\ensuremath{\sigma}$ term ${\ensuremath{\sigma}}_{\ensuremath{\eta}\ensuremath{\eta}}^{\ensuremath{\pi}\ensuremath{\pi}}$ must be substantially larger than that obtained in the Gell-Mann-Oakes-Renner (3, $\overline{3}$) scheme.