# On some implications of the BaBar data on the $\gamma^*\eta'$ transition form factor

## TL;DR

This paper analyzes the implications of BaBar data on the $
ightarrow$ transition form factors of $ ext{eta}$ and $ ext{eta'}$ mesons, using theoretical expansions to test meson distribution amplitudes and mixing.

## Contribution

It introduces a power series expansion of the transition form factors in terms of $ ext{omega}$, linking the form factors to meson distribution amplitudes and testing their mixing.

## Key findings

- Predictions for $ ext{gamma}^* ext{eta}$ and $ ext{gamma}^* ext{eta'}$ form factors based on Gegenbauer coefficients.
- Comparison of theoretical predictions with BaBar experimental data.
- Insights into the meson distribution amplitudes and $ ext{eta}$-$ ext{eta'}$ mixing.

## Abstract

At leading-twist accuracy the form factors for the transitions from a virtual photon to the $\eta$ or $\eta'$ can be expanded into a power series of the variable $\omega$, being related to the difference of two photon virtualities. The series possess the remarkable feature that only the Gegenbauer coefficients of the meson distribution amplitudes of order $l\leq m$ contribute to the term $\sim \omega^m$. Thus, for $\omega\to 0$ only the asymptotic meson distribution amplitude contributes, allowing for a test of the mixing of the $\eta$ and $\eta'$ decay constants. Employing the Gegenbauer coefficients determined in analysis of the form factors in the real photon limit, we present predictions for the $\gamma^*\eta$ and $\gamma^*\eta'$ form factors and compare them to the BaBar data.