A contact interaction model for the $\eta$ and $\eta'$ mesons in a SDE-BSE approach to QCD: masses, decay widths and transition form factors

We construct a contact interaction model for the $\eta$ and $\eta'$ mesons in the SDE-BSE approach to QCD and compute several static properties of these mesons and their transition form factors. We find that this model gives an excellent description of the $\eta$ and $\eta'$ static properties, namely their masses, decay width and decay constants. However, a contact interaction disagrees with experimental data for $Q^2$ greater than 2 GeV$^2$, and produces transition form factors in conflict with perturbative QCD prediction. This is not surpring and the reasons for this are explained