Effects of the $U_A(1)$ Anomaly on $\eta \to 2 \gamma$ Decay

Abstract

We study the $\eta \to 2 \gamma$ decay using an extended three-flavor Nambu-Jona-Lasinio model that includes the 't~Hooft instanton induced interaction. The $\eta$ meson mass and the $\eta \to 2 \gamma$ decay width are reproduced simultaneously with a rather strong instanton induced interaction. The calculated $\eta$ decay constant is $f_\eta = 2.23 f_\pi$ and it suggests that the $\eta$ meson is no longer the Goldstone boson.