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

The \(\eta \) transition form factor is analyzed for the first time in both space- and time-like regions at low and intermediate energies in a model-independent approach through the use of rational approximants. The \(\eta \rightarrow e^+e^-\gamma \) experimental data provided by the A2 Collaboration in the very low-energy region of the dielectron invariant mass distribution allows for the extraction of the most precise up-to-date slope and curvature parameters of the form factors as well as their values at zero and infinity. The impact of these new results on the mixing parameters of the \(\eta \)–\(\eta ^\prime \) system, together with the role played by renormalization dependent effects, and on the determination of the \(VP\gamma \) couplings from \(V\rightarrow P\gamma \) and \(P\rightarrow V\gamma \) radiative decays is also discussed. A preprint version of the article is available at ArXiv.