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Two-photon decays and photoproduction on electrons of $η(550)$, $η'(958)$, $η(1295)$, and $η(1475)$ mesons

Electromagnetic interactions of the ground and first radial excited states of $η$ and $η'$ mesons in the framework of the extended $U(3)\times U(3)$ NJL model are considered. The radial excitations are described with the help of polynomial form factor of the second order over the inner quark momentum. The solution of the $U_A(1)$ problem by means of 't Hooft interaction is taken into account. For diagonalization of the free Lagrangian the $4\times4$ mixing matrix is used. Two-photon decay widths of the ground $η$ and $η'$ meson are found to be in a satisfactory agreement with the experiment. Predictions for the two-photon decay widths of $η(1295)$ and $η(1475)$ are given. The probabilities of eta meson production by two-photon mechanism in $e^+e^-$ collisions and of their photoproduction on electrons are calculated.