Effects of the $U_A(1)$ Anomaly on $η\to 2 γ$ Decay

Abstract

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