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

The ${\eta }^{\mathrm{\prime }}$ transition form factor is reanalyzed in view of the recent BESIII first observation of the Dalitz decay ${\eta }^{\mathrm{\prime }}\to \gamma e^{+}{e}^{-}$ 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 ${\mathrm{\Gamma }}_{{\eta }^{\mathrm{\prime }}\to \gamma \gamma }$, and the asymptotic limit. The $\eta$-${\eta }^{\mathrm{\prime }}$ 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 $J\mathrm{/}\psi$, $Z\to {\eta }^{(\mathrm{\prime })}\gamma$ decays are also considered and predictions reported.