Chiral anomaly in the η ( ′ ) → π + π − γ and η ( ′ ) → π + π − l + l − decays

We report the presence of a flavor-violating correction to the V A A A -type anomaly, δ ( ′ ) , induced by the surface terms of the anomalous quark triangle diagram, previously found in the η , η ′ → π + π − γ decay amplitudes, and investigate its impact on the corresponding semileptonic decay modes of η and η ′ . The magnitude of δ ( ′ ) can be set from the experimental data on the η ( ′ ) → π + π − γ decay width. We then estimate another low-energy constant, the slope parameter α ( ′ ) . The impact of different schemes for describing η − η ′ mixing on the value of δ ( ′ ) and α ( ′ ) is discussed. The predictions are shown to be in complete agreement with the available experimental data.