Quark-hadron duality, axial anomaly and mixing

Abstract

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 $\eta$ and ${\eta }^{\prime }$ 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.

9 pages, 1 figure, reference added

References in corpus (4)

• On the Pion Distribution Amplitude Shape
• Axial anomaly as a collective effect of meson spectrum
• Axial anomaly: the modern status
• Dispersive Approach to Abelian Axial Anomaly, Mixing of Pseudoscalar Mesons and Symmetries

Cited by in corpus (7)

• Can we understand an auxetic pion-photon transition form factor within QCD? BaBar faces Belle
• Transition Form Factors and Mixing of Pseudoscalar Mesons from Anomaly Sum Rule
• Axial anomaly and vector meson dominance model
• Matching lightcone- and anomaly-sum-rule predictions for the pion-photon transition form factor
• Non-Abelian axial anomaly, axial-vector duality, and the pseudoscalar glueball
• Dispersive approach to non-Abelian axial anomaly
• Transition form factors of ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$ mesons: What can be learned from anomaly sum rule?