Processes $e^{+}{e}^{-}\to {\pi }^0({{\pi }^0}^{\mathrm{\prime }})\gamma$ in the NJL model

The processes of electron-positron annihilation into ${\pi }^0\gamma$ and into ${\pi }^{\mathrm{\prime }}(1300)\gamma$ are considered within the NJL model. Intermediate vector mesons ${\rho }^0$, $\omega$, ${\rho }^{\mathrm{\prime }}(1450)$, and ${\omega }^{\mathrm{\prime }}(1420)$ are taken into account. The latter two mesons are treated as the first radial excited states. They are incorporated into the NJL model by means of a polynomial form factor. Numerical predictions for the cross sections of these processes are received for the center-of-mass energies below 2 GeV. Our results for the ${\pi }^0\gamma$ production are in agreement with experimental data received in the energy region 600 – 1020 MeV.