Strong $U_A(1)$ breaking in radiative $\hat{I}\cdot$ decays

Abstract

We study the \egg, \egm and \epg decays using an extended three-flavor Nambu-Jona-Lasinio model that includes the 't~Hooft instanton induced interaction. We find that the $\hat{I}\cdot$-meson mass, the \egg, \egm and \epg decay widths 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 $\hat{I}¸$ is about zero. The calculated $ηγγ^\ast$ transition form factor has somewhat weaker dependence on the squared four-momentum of the virtual photon. The effects of the $U_A(1)$ anomaly on the scalar quark contents in the nucleon, the $\hat{I}{\pounds }_{\ddot{I}€N}$ and $\hat{I}{\pounds }_{KN}$ terms and the baryon number one and two systems are also studied.

41 pages, LaTeX, 17 eps figures, uses epsf.sty and cite.sty