$X^0\mathrm{}\left(958\right)\mathrm{}\to \eta \pi \pi$ decay and $\eta X^0$ mixing

Within the framework of a broken-SU(6)×O(3) quark model of Lorentz-invariant hadron-coupling structures, the three-body decay process $X^0\mathrm{}\left(958\right)\mathrm{}\to \eta \pi \pi$ is investigated with a view to assessing the value of the $\eta X^0$ mixing angle. The model assumes that the amplitude for this process is dominated by a $\delta \mathrm{}\left(970\right)\mathrm{}\pi$ intermediate state so that $X^0\to \delta \pi \to \eta \pi \pi$. The results obtained seem to favor a quadratic mass formula for pseudoscalar mesons with an $\eta X^0$ mixing angle of —10°, in agreement with recent analyses.