$\frac{J}{\psi }$ decays and pseudoscalar-meson mixing

We have examined the branching ratios of the decays $\frac{J}{\psi }\to \mathrm{VP}$ and $\frac{J}{\psi }\to P\gamma$ in order to determine the magnitudes of components other than $N=\frac{(u\overline{u}+d\overline{d})}{\sqrt{2}}$ and $S=s\overline{s}$ in $\eta$ and ${\eta }^{\prime }$, using the data of the world average in 1990. Although the possibility that these magnitudes are very small is not excluded, there is a solution in which these magnitudes are not small, suggesting that $\eta$ and ${\eta }^{\prime }$ have glueball origins. Then, one state of two or more states in the $\eta \mathrm{}\left(1440\right)\mathrm{}$ region is considered to be a glueball. The mixing angle ${\theta }_1$ corresponding to the mixing angle ${\theta }_P$ between $\eta$ and ${\eta }^{\prime }$ is estimated to be about - 20°. The estimated $N$ component in this glueball is larger than $S$. Using the mixing angles obtained, we have calculated the decay widths for various $P\to \gamma \gamma$, $P\to V\gamma$, and $V\to P\gamma$ decays. The results are, in general, consistent with experiments.