$η\to π^0 γγ$ decay in the three-flavor Nambu-Jona-Lasinio model

Abstract

We study the $η\to π^0 γγ$ decay via the quark-box diagram in the three-flavor Nambu--Jona-Lasinio model that includes the $U_A (1)$ breaking effect. We find that the $η$-meson mass, the $η\to γγ$ decay width and the $η\to π^0 γγ$ decay width are in good agreement with the experimental values when the $U_A (1)$ breaking is strong and the flavor $SU(3)$ singlet-octet mixing angle $θ$ is about zero. The photon energy and the photon invariant mass spectra in $η\to π^0 γγ$ are compared with those in the chiral perturbation theory.