Abstract
Manifestations of strong and electromagnetic axial anomalies in two-photon decays of $\eta$ and $\eta'$ mesons are studied. Applying 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 $\langle 0 |G\tilde{G} |\gamma\gamma \rangle$. We made a numerical estimation of the contributions of gluon and electromagnetic anomalies to the two-photon decays of $\eta$ and $\eta'$ mesons and found significant suppression of the gluon anomaly contribution.
Highlights
Axial anomaly [1,2]—violation of the axial symmetry of classical theory by quantum fluctuations— is an important phenomenon inherent to QCD with many interesting consequences
Besides its connection with the real photon processes, the axial anomaly is intimately connected with the processes involving virtual photons: the dispersive form of the axial anomaly [5] leads to the anomaly sum rules (ASRs) [7,8,9] which can be used to evaluate the photon-meson transitions γðkÞγÃðqÞ → π0ðη; η0Þ at arbitrary photon virtuality
Along with the study based on the ASRs, the transition form factors have been a subject of extensive investigation
Summary
Axial (chiral) anomaly [1,2]—violation of the axial symmetry of classical theory by quantum fluctuations— is an important phenomenon inherent to QCD with many interesting consequences. Besides its connection with the real photon processes, the axial anomaly is intimately connected with the processes involving virtual photons: the dispersive form of the axial anomaly [5] (for a review, see e.g., [6]) leads to the anomaly sum rules (ASRs) [7,8,9] which can be used to evaluate the photon-meson transitions γðkÞγÃðqÞ → π0ðη; η0Þ at arbitrary photon virtuality. We derive the anomaly sum rule based on the dispersive form of axial anomaly in the singlet channel and study the contributions of electromagnetic and gluon parts of the axial anomaly to the two-photon decays of the η and η0 mesons.
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