The $\eta^\prime$ transition form factor from space- and time-like experimental data

TL;DR

This paper reanalyzes the $ta^prime$ transition form factor using recent experimental data in both space- and time-like regions, providing a comprehensive parameterization and insights into mixing and decay processes.

Contribution

It introduces a new parameterization of the $ta^prime$ form factor across all energies using Pade9 approximants, and reassesses $ta$-$prime$ mixing within a large-$N_c$ chiral perturbation framework.

Findings

Accurate form factor parameterization across energy regions.

Predictions for decay widths and asymptotic behavior.

Revised $ta$-$prime$ mixing parameters.

Abstract

The $\eta^\prime$ transition form factor is reanalyzed in view of the recent BESIII first observation of the Dalitz decay $\eta^\prime\to\gamma e^+e^-$ in both space- and time-like regions at low and intermediate energies using the Pad\'e approximants method. The present analysis provides a suitable parameterization for reproducing the measured form factor in the whole energy region and allows to extract the corresponding low-energy parameters together with a prediction of its values at the origin, related to $\Gamma_{\eta^\prime\to\gamma\gamma}$, and the asymptotic limit. The $\eta$-$\eta^\prime$ mixing is reassessed within a mixing scheme compatible with the large-$N_c$ chiral perturbation theory at next-to-leading order, with particular attention to the OZI-rule--violating parameters. The $J/\psi$, $Z\to\eta^{(\prime)}\gamma$ decays are also considered and predictions reported.