Production of $\omega\pi^0$ pair in electron-positron annihilation

The process of electron-positron annihilation into a pair of $\pi^0$ and $\omega$ mesons is considered in the framework of the SU(2)$\times$SU(2) Nambu--Jona-Lasinio model. Contributions of intermediate photons, $\rho(770)$ and $\rho'(1450)$ vector mesons are taken into account. It is shown that the bulk of the cross section at energies below 2 GeV is provided by the process with intermediate $\rho'(1450)$ state. The contribution due to single photon and $\rho(770)$ exchange is in agreement with the vector meson dominance model. Numerical results are compared with experimental data.