$\eta \to {\pi }^0\gamma \gamma$ decay in the three-flavor Nambu-Jona-Lasinio model

Abstract

We study the $\eta \to {\pi }^0\gamma \gamma$ 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 $\eta$-meson mass, the $\eta \to \gamma \gamma$ decay width and the $\eta \to {\pi }^0\gamma \gamma$ 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 $\theta$ is about zero. The photon energy and the photon invariant mass spectra in $\eta \to {\pi }^0\gamma \gamma$ are compared with those in the chiral perturbation theory.

Comments: 14 pages, LaTeX, 3 EPS figures, uses epsf.sty and feynman.tex