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

Abstract

The $η^\prime$ transition form factor is reanalyzed in view of the recent BESIII first observation of the Dalitz decay $η^\prime\toγe^+e^-$ 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 $Γ_{η^\prime\toγγ}$, and the asymptotic limit. The $η$-$η^\prime$ 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 $J/ψ$, $Z\toη^{(\prime)}γ$ decays are also considered and predictions reported.

12 pages, 15 figures. v2 matches the published version