Transition form factors of $\pi^0$, $\eta$ and $\eta'$ mesons: What can be learned from anomaly sum rule?

TL;DR

This paper investigates the transition form factors of light pseudoscalar mesons using the anomaly sum rule, a nonperturbative QCD approach that remains effective even when QCD factorization fails, and explores implications of recent experimental data.

Contribution

It applies the anomaly sum rule to analyze meson transition form factors and discusses potential small corrections and quark mass effects in light of recent experimental results.

Findings

Anomaly sum rule can be used to study meson form factors beyond QCD factorization.

Possible small non-OPE corrections are compatible with BaBar and Belle data.

Quark mass contributions are significant in the analysis.

Abstract

We have studied the applications of the anomaly sum rule to the transition form factors of light pseudoscalar mesons: $\pi^0$, $\eta$ and $\eta'$. This nonperturbative QCD approach can be used even if the QCD factorization is broken. The possibility of small non-OPE corrections to the spectral density in view of the recent BaBar and Belle data is explored. The accuracy of the applied method and the role of the quark mass contributions are discussed.