Effects of an extraU(1)axial condensate on the strong decays of pseudoscalar mesons

Abstract

We consider a scenario (supported by some lattice results) in which a $U(1)$-breaking condensate survives across the chiral transition in QCD. This scenario has important consequences for the pseudoscalar-meson sector, which can be studied using an effective Lagrangian model. In particular, generalizing the results obtained in two previous papers, where the effects on the radiative decays $\ensuremath{\eta}$, ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ were studied, in this paper we study the effects of the $U(1)$ chiral condensate on the strong decays of the ``light'' pseudoscalar mesons, i.e., $\ensuremath{\eta}$, ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}3{\ensuremath{\pi}}^{0}$; $\ensuremath{\eta}$, ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$; ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$; ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$; and also on the strong decays of an exotic (``heavy'') $SU(3)$-singlet pseudoscalar state ${\ensuremath{\eta}}_{X}$, predicted by the model.