Manifestations of strong and electromagnetic axial anomalies in two-photon decays of η and η 0 mesons are studied. Applying a dispersive approach to axial anomaly in the singlet current, we obtain an anomaly sum rule containing strong and electromagnetic anomaly contributions. The relevant low-energy theorem was generalized to the case of mixed states and used to evaluate the subtraction constant of the strong anomaly-related form factor h0jGGjγγi. We made a numerical estimation of the contributions of gluon and electromagnetic anomalies to the two-photon decays of η and η 0 mesons and found significant suppression of the gluon anomaly contribution.
The process e + e − → γ * → π 0 γ was considered using time-like pion transition form factor, obtained in the approach of the Anomaly Sum Rules(ASR). The total cross section and angular distribution of the process was calculated. As the result of the comparison with the data it was shown that ASR approach provides their good description in the regions far from the pole. Also there was proposed a method allowing to give reasonable description of data in the region of pole within the ASR approach. The strong restrictions for the parameters of the modified ASR approach were obtained.
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