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

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 Padé 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.

Comments: 12 pages, 15 figures. v2 matches the published version