Effective Chiral Theory for Radiative Decays of Mesons

An extended $U(3)_L\bigotimes U(3)_R$ chiral theory which includes pseudoscalar and vector meson nonets as dynamic degrees of freedom is presented. We combine a hidden symmetry approach with a general procedure of including the $\eta'$ meson into chiral theory. The $U(3)_L\bigotimes U(3)_R$ and the SU(3) symmetries are broken by the mechanism based on quark mass matrix. Meson radiative decay widths are parameterized in terms of a single and real $\eta-\eta'$ mixing angle $\theta_P$, a U(3)_V symmetry breaking scale parameter c_W, and the radiative decay constants $F_\pi, F_K, F_\eta, F_{\eta'}$, for the $\pi, \eta$, K, $\eta '$ mesons, respectively. Taking $F_\pi = 93 MeV$, a global fit to decay width data yields F_K/F_\pi = 1.16 \pm 0.11, F_\eta/F_\pi = 1.14\pm 0.04, F_{\eta'}/F_\pi = 1.09 \pm 0.04, c_W = -0.19 \pm0.03, \theta_P =-(15.4 \pm 1.8)^o.