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

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