$\hat{I}\cdot \to \ddot{I}{€}^0{\hat{I}}^3{\hat{I}}^3$ decay in the three-flavor Nambu-Jona-Lasinio model

Abstract

We study the $\hat{I}\cdot \to \ddot{I}{€}^0{\hat{I}}^3{\hat{I}}^3$ decay via the quark-box diagram in the three-flavor Nambu--Jona-Lasinio model that includes the $U_A(1)$ breaking effect. We find that the $\hat{I}\cdot$-meson mass, the $\hat{I}\cdot \to {\hat{I}}^3{\hat{I}}^3$ decay width and the $\hat{I}\cdot \to \ddot{I}{€}^0{\hat{I}}^3{\hat{I}}^3$ 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 $\hat{I}¸$ is about zero. The photon energy and the photon invariant mass spectra in $\hat{I}\cdot \to \ddot{I}{€}^0{\hat{I}}^3{\hat{I}}^3$ are compared with those in the chiral perturbation theory.

14 pages, LaTeX, 3 EPS figures, uses epsf.sty and feynman.tex