X0(958)→ηππdecay andηX0mixing

Abstract

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