Production $\rho(770)$ of meson pairs in the decays $\rho(1450)\rightarrow \rho(770)\eta$ and $\tau\rightarrow \rho(770)\eta\nu_{\tau}$ and in the process $e^{+}e^{-} \rightarrow \rho(770)\eta$ in the Extended Nambu–Jona–Lasinio model

The production of $\rho(770)\eta$ meson pairs in electron-positron collisions and in the decays $\rho(1450)\rightarrow \rho(770)\eta$ and $\tau\rightarrow \rho(770)\eta\nu_{\tau}$ is calculated in the framework of the extended Nambu–Jona–Lasinio model. The contributions with intermediate $\rho$ mesons in both the ground and first radially excited states are taken into account when calculating processes associated with electron-positron annihilation and decay of the tau lepton. The width of the decay $\tau\rightarrow \rho(770)\eta\nu_{\tau}$ is theoretically estimated. The results obtained for other processes are consistent with the existing experimental data.