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

Abstract

It is generally believed that the physical $\ensuremath{\eta}$ 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 ${X}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ using the experimental values of ${\ensuremath{\Gamma}}_{\ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}}$ and ${\ensuremath{\Gamma}}_{{\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}}$. Note that the quadratic mass formula predicts values considerably larger than the linear one. An upper bound of 20-30 keV for the ${X}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ 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.