Dispersive analysis for $\eta\to \gamma\gamma^*$

TL;DR

This paper develops a dispersion relation connecting eta decay data to the eta transition form factor, providing precise slope measurements that align with recent data but differ from some earlier theories.

Contribution

It introduces a dispersion integral method to relate eta decay data to the transition form factor, offering new slope estimates with detailed uncertainty analysis.

Findings

Measured eta transition form factor slope: b_eta = (2.05^{+0.22}_{-0.10}) GeV^{-2}

Estimated eta' transition form factor slope: b_eta' = (1.58^{+0.15}_{-0.08}) GeV^{-2}

Results are consistent with recent data but differ from some previous models.

Abstract

A dispersion integral is derived that connects data on $\eta\to \pi^+\pi^-\gamma$ to the $\eta\to \gamma\gamma^*$ transition form factor. A detailed analysis of the uncertainties is provided. We find for the slope of the $\eta$ transition form factor at the origin $b_\eta = (2.05 {}^{+0.22}_{-0.10})\, {\rm GeV}^{-2}$. Using an additional, plausible assumption, one finds for the corresponding slope of the $\eta'$ transition form factor, $b_{\eta'} = (1.58 {}^{+0.15}_{-0.08})\, {\rm GeV}^{-2}$. Both values are consistent with all recent data, but differ from some previous theoretical analyses.