Transition Form Factors and Mixing of Pseudoscalar Mesons from Anomaly Sum Rule

TL;DR

This paper uses the anomaly sum rule to analyze transition form factors of pseudoscalar mesons, providing insights into their mixing and decay constants based on experimental data, including recent Belle results.

Contribution

It introduces a nonperturbative anomaly sum rule approach to study meson transition form factors and mixing, incorporating operator contributions to fit experimental data.

Findings

Operator contributions are necessary to match experimental data.

Constraints on decay constants and mixing parameters are derived.

Results are compatible with recent Belle measurements.

Abstract

Transition form factors of pi^0, eta, eta' mesons are investigated by means of the anomaly sum rule -- an exact nonperturbative relation which follows from the dispersive representation of the axial anomaly. Considering the problem of contributions of operators originated from a non-(local) operator product expansion, we found that they are required by the available set of experimental data, including the most recent data from the Belle Collaboration (which, if taken alone, can be described without such contributions, although are compatible with them). In this approach we analyzed the experimental data on eta and eta' meson transition form factors and obtained the constraints on the decay constants and mixing parameters.