  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 ].
