Strong and electromagnetic contributions to the U_A(1) anomaly and the P⁰ to gamma gamma decays

Using flavor basis we relate flavor axial anomalies to the mass matrix of pseudoscalar isoscalar fields in the context of a Linear Sigma Model which includes U_A(1) symmetry breaking. We incorporate additional contributions to these anomalies due to external electromagnetic fields invoking 't Hooft's argument on anomaly matching and work out the predictions of this formalism for eta to gamma gamma and eta' to gamma gamma decays. We show that the only effect of the U_A(1) anomaly in these processes is in the formation of the eta and eta' systems. From experimental data on their two photon decays we extract the pseudoscalar mixing angle in flavor basis as phi_P in [38.4 deg, 41.0 deg ].