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

Abstract

The processes of electron-positron annihilation into $\pi^0\gamma$ and into $\pi'(1300)\gamma$ are considered within the NJL model. Intermediate vector mesons $\rho^0$, $\omega$, $\rho'(1450)$, and $\omega'(1420)$ 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.