Production of $\rho (770)$, $\eta$ pairs in the decays $\rho (1450)\to \rho (770)\eta$, $\tau \to \rho (770)\eta {\nu }_{\tau }$, and in the process of $e^{+}{e}^{-}\to \rho (770)\eta$ in the Extended Nambu - Jona-Lasinio model

Production of $\rho (770)$, $\eta$ pairs at colliding of electron-positron beams and in the decays $\rho (1450)\to \rho (770)\eta$, $\tau\rightarrow \rho(770)\eta\nu_{\tau}$ is calculated in the framework of the Nambu - Jona-Lasinio model. In the process of electron-positron annihilation and the $\tau$ - lepton decay the contributions of the intermediate $\rho (770)$ vector meson in the ground and first radially excited state are taken into account. The theoretical prediction for the decay $\tau\rightarrow \rho(770)\eta\nu_{\tau}$ is given. The obtained results for other processes are in satisfactory agreement with the experimental data.