$\eta$-Meson Decays and Strong $U_A(1)$ Breaking in the Three-Flavor Nambu-Jona-Lasinio Model

Abstract

We study the $\eta \to \gamma \gamma$ and $\eta \to {\pi }^0\gamma \gamma$ decays using an extended three-flavor Nambu-Jona-Lasinio model that includes the 't~Hooft instanton induced interaction. 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 effects of the $U_A(1)$ breaking on the baryon number one and two systems are also studied.

Comments: 12 pages, LaTeX, 2 eps figures, Talk given at the Joint Japan-Australia Workshop on Quarks, Hadrons and Nuclei, Adelaide, Australia, Nov. 15-24, 1995