Decays of the $\eta$ Meson

The decay modes of the ${\eta }^0$ meson have been investigated in the Lawrence Radiation Laboratory 72-in. hydrogen bubble chamber. The $\eta$'s were produced in the reaction ${\pi }^{+}+p\to {\pi }^{+}+p+\eta$ at 1225 and 1275 $\frac{\mathrm{MeV}}{c}$ and were studied by analysis of all four-prong and $\mathrm{t}\mathrm{w}\mathrm{o}-\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{n}\mathrm{g}+\gamma$ events. There appears to be a discrepancy in the measured branching ratio $R=\frac{{\Gamma }_{\eta }\mathrm{}\left(000\right)\mathrm{}}{{\Gamma }_{\eta }\mathrm{}(+-0\mathrm{})\mathrm{}}$ as compared with theoretical predictions based on various models relating $R$ to the spectrum of ${T_{\pi }}^0 \mathrm{in} {\eta }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$. The theoretical predictions calculated from the observed spectrum are uniformly higher than the observed value $R=0.90\mathrm{}\pm 0.24$. For the Brown and Singer theory of a $T=0\mathrm{}$, $S=0\mathrm{}$ dipion resonance, we find $m_{\sigma }={{407}_{-12\mathrm{}}}^{+25\mathrm{}}$ MeV, $\Gamma =117\mathrm{}\pm 15$ MeV, $R\mathrm{}\left(\mathrm{predicted}\right)\mathrm{}=1.49\mathrm{}\pm 0.07$. The fit to the linear matrix-element expansion, $a=-0.41\mathrm{}\pm 0.06$, predicts $R=1.63\mathrm{}\pm 0.02$ (the amplitude $f=1+ay$ where $y=\frac{2 T_{{\pi }^0}}{T_{{\pi }^{0}max}-1\mathrm{}}$). A fit may be obtained to both the spectrum and the branching ratio with an amplitude $f=(1-0.41y)\mathrm{}{e}^{1.6iy}$, indicating that, although the magnitude of $f$ is essentially smooth, a rapid variation in phase seems to be required to fit the branching ratio.