Radiative decays of radially excited mesons ${{\pi }^0}^{\mathrm{\prime }}$, ${{\rho }^0}^{\mathrm{\prime }}$, ${\omega }^{\mathrm{\prime }}$ in NJL model

Radiative decays ${\pi }^0({{\pi }^0}^{\mathrm{\prime }})\to \gamma +\gamma$, ${{\pi }^0}^{\mathrm{\prime }}\to {\rho }^0(\omega )+\gamma$, ${{\rho }^0}^{\mathrm{\prime }}({\omega }^{\mathrm{\prime }})\to {\pi }^0+\gamma$, and ${{\rho }^0}^{\mathrm{\prime }}({\omega }^{\mathrm{\prime }})\to {{\pi }^0}^{\mathrm{\prime }}+\gamma$ are considered in the framework of the non-local SU(2)$\times$SU(2) NJL model. Radially excited mesons are described with the help of polynomial form factor $f({k^{\mathrm{\perp }}}^2)$, where $k^{\mathrm{\perp }}$ is the quark momentum transverse to the external meson momentum. In spite of mixing of the ground and excited meson states in this model, the decay widths of ${\pi }^0\to \gamma +\gamma$ and ${\rho }^0(\omega )\to {\pi }^0+\gamma$ are found to be in good agreement with experimental data as in the standard local NJL model. Our predictions for decay widths of radially excited mesons can be verified in future experiments.