WidthΓX0→2γas a Test of the Mass Formula for Boson Nonets

It is generally believed that the physical $\eta$ and $X^0$ particles are not pure $S{U}_3$ states, but result from octet-singlet mixing. Depending on the assumption of a linear or quadratic mass formula, different values can be obtained for the mixing angle. The latter can be used in turn to estimate the width of $X^0\to 2\gamma$ using the experimental values of ${\Gamma }_{\eta \to \gamma \gamma }$ and ${\Gamma }_{{\pi }^0\to \gamma \gamma }$. Note that the quadratic mass formula predicts values considerably larger than the linear one. An upper bound of 20-30 keV for the $X^0\to 2\gamma$ width, which is not outside the experimental possibilities—e.g., with the Primakoff-effect technique—would be evidence against the use of a quadratic mass formula within the standard $S{U}_3$ scheme.