Description of the Processes $${{e}^{ + }}{{e}^{ - }} \to {{K}^{ + }}{{K}^{ - }}{{\pi }^{0}}$$ and $${{e}^{ + }}{{e}^{ - }} \to {{K}^{ + }}{{K}^{ - }}\eta $$ within the Extended NJL Model

In the framework of the $$U(3) \times U(3)$$ extended Nambu–Jona-Lasinio model, the processes $${{e}^{ + }}{{e}^{ - }} \to {{K}^{ + }}{{K}^{ - }}{{\pi }^{0}}$$ and $${{e}^{ + }}{{e}^{ - }} \to {{K}^{ + }}{{K}^{ - }}\eta $$ are described taking into account both ground and first radially excited intermediate meson states. It is shown that channels with radially excited $$\phi (1680)$$ meson are dominant in both processes. The influence on the results of the appearance of phase factors of radially excited intermediate states, the existence of which is indicated by experimental data, is discussed.