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Quark-hadron duality, axial anomaly and mixing

Interplay between axial anomaly and quark-hadron duality in the presence of strong mixing is considered. The anomaly sum rule for meson transition form factors based on the dispersive representation of axial anomaly and quark-hadron duality in octet channel is analyzed. The comparison of this sum rule to the experimental data on $η$ and $η'$ mesons transition form factors shows that the interval of duality in this channel is rather small, contradicting the usual understanding of quark-hadron duality. The same values of interval of duality are supported by considering the two-point correlator in the local duality limit. This contradiction may be resolved by introducing of some nonperturbative non-OPE correction to the relevant spectral density. The form and value of this correction are discussed.