Quark-hadron duality, axial anomaly and mixing

TL;DR

This paper examines the relationship between axial anomaly and quark-hadron duality in meson physics, revealing a small duality interval and proposing nonperturbative corrections to resolve discrepancies with experimental data.

Contribution

It introduces a new analysis of the anomaly sum rule in the presence of strong mixing, highlighting a contradiction with the standard duality picture and suggesting non-OPE corrections.

Findings

The duality interval in the octet channel is smaller than expected.

Experimental data on $$ and $'$ mesons challenge the usual duality assumptions.

Nonperturbative corrections may reconcile theory with observations.

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 $\eta'$ 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.