Tests of a mixing model for neutral2+mesons

The consequences of a mixing model for $f$, $f^{\prime }$ and $\theta$ are examined. These include a rather low mass for $\theta$ (excluded by recent data on $\frac{J}{\psi }\to \gamma \theta \to K^{+}{K}^{-}$) and a suppressed two-photon width of the $f^{\prime }$ (excluded by a new measurement). Possible alternatives are discussed. If the $\theta$ is a gluonic bound state, one can obtain from a more model-independent analysis a set of $f-f^{\prime }-\theta$ mixing parameters which entails the predictions $\Gamma (\theta \to \gamma \gamma )\gtrsim 0.32$ keV, $B(\frac{J}{\psi }\to \gamma \theta )\approx 2\%$, and which requires the $\theta$ to have important decay modes other than the observed $\eta \eta$ and $K\overline{K}$ ones.