Two photon transition form factors of neutral pseudoscalar mesons

TL;DR

This paper develops a Bethe-Salpeter framework that incorporates the non-Abelian anomaly to accurately compute the two-photon transition form factors of the ta and ta' mesons, aligning well with experimental data.

Contribution

It introduces a new Bethe-Salpeter kernel that preserves axial Ward-Green-Takahashi identity and includes non-Abelian anomaly effects for flavor mixing mesons.

Findings

Calculated ta and ta' transition form factors agree with experimental data.

The framework effectively accounts for flavor mixing and anomaly effects.

Provides a consistent theoretical approach for pseudoscalar meson properties.

Abstract

Starting from the axial vector Ward-Green-Takahashi identity, and the necessity of preserving this identity when attempting to calculate the properties describing pseudoscalar mesons, we describe a Bethe-Salpeter kernel which takes into account the non-Abelian anomaly and therefore is suitable to describe the flavor mixing states $\eta,\eta^\prime$. We then report results for the two photon transition form factors of $\eta,\eta^\prime$, and compare them with existing experimental data.