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

The $\eta$ transition form factor is analysed 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 dilelectron 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 renormalisation dependent effects, and on the determination of the $VP\gamma$ couplings from $V\to P\gamma$ and $P\to V\gamma$ radiative decays are also discussed.
Comment: 16 pages, 17 figures; v2: additional comments, references added; mathces published version in EPJC