Models ofη0→π0+2γDecay

Recent experimental results on the ${\eta }^0\to {\pi }^{0}2\gamma$ decay indicate that the branching ratio $B\equiv \frac{{\Gamma }_{\eta }\left({\pi }^{0}2\gamma \right)}{{\Gamma }_{\eta }\left({\pi }^{+}{\pi }^{-}\gamma \right)}$ is of the order of (or compatible with) 1. Using the vector-meson-dominant model, we have computed the width and the pion energy spectrum of the ${\eta }^0\to {\pi }^{0}2\gamma$ decay, using the relevant $\mathrm{SU}\left(3\right)\mathrm{}$-symmetric coupling constants, including the $\omega -\phi$ mixing hypothesis as given by the static $\mathrm{SU}\left(6\right)\mathrm{}$ theory, which demands ${\Gamma }_{\phi }\left({\pi }^0\gamma \right)\approx 0$. We have then studied the effect of varying the mixing angle and the effective coupling constant $f_{\phi {\pi }^0\gamma }$ around the static $\mathrm{SU}\left(6\right)\mathrm{}$ value over a wide range compatible with the present experimental information, using as input the experimental ${\Gamma }_{\omega }\left({\pi }^0\gamma \right)$ as before. The model gives $B\approx 0.331\pm {10}^{-2\mathrm{}}$ at the static $\mathrm{SU}\left(6\right)\mathrm{}$ value, which increases by a factor of 10 at the mixing angle of 20°. It therefore appears that unless there is a drastic decrease in the experimental branching ratio, the vector-meson-dominant model cannot provide a dominant mechanism for the ${\eta }^0\to {\pi }^{0}2\gamma$ decay. A remark is also made about the relation between the value of the $\omega -\phi$ mixing angle and the ratios of various observed decay rates. We also study an alternative simple mechanism for the ${\eta }^0\to {\pi }^{0}2\gamma$ decay which may be suggested by the tadpole model of the electromagnetic mass difference of hadrons. We assume the existence of the $I=1\mathrm{}$, normal $0^{+}$ ($\eta \pi$) resonance $\epsilon$, and consider the intermediary of the $\epsilon$ meson ${\eta }^0\to {\pi }^0{\epsilon }^0\to {\pi }^{0}2\gamma$. Some consequences of this model are discussed.