Strong UA(1)breaking in radiative η decays and baryon systems

We study the η→γγ, $\eta \to \gamma {\mu }^{-}{\mu }^{+}$, 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 η-meson mass, the η→γγ, $\eta \to \gamma {\mu }^{-}{\mu }^{+}$, and $\eta \to {\pi }^0\gamma \gamma$ decay widths are in good agreement with the experimental values when the ${\mathrm{U}}_A\mathrm{}\left(1\right)\mathrm{}$ breaking is strong and the flavor SU(3) singlet-octet mixing angle θ is about zero. The calculated ηγ${\mathrm{\gamma }}^{\mathrm{*}}$ transition form factor has a somewhat weaker dependence on the squared four-momentum of the virtual photon. The effects of the ${\mathrm{U}}_A\mathrm{}\left(1\right)\mathrm{}$ anomaly on the scalar quark contents in the nucleon, the ${\Sigma }_{\pi N}$ and ${\Sigma }_{\mathrm{KN}}$ terms, and the baryon number one and two systems are also studied.