ec 2 00 1 Strong and electromagnetic contributions to the U A ( 1 ) anomaly and the P 0 → γγ 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 UA(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 η → γγ and η′ → γγ decays. We show that the only effect of the UA(1) anomaly in these processes is in the formation of the η and η′ systems. From experimental data on these decays we extract the pseudoscalar mixing angle in flavor basis as φP ∈ [38.4◦, 41.0◦].