$\tau^- \to \pi^- \pi^0 \nu_{\tau}$ and $e^{+}e^{-} \to \pi^{+} \pi^{-}$ processes in the chiral Nambu–Jona-Lasinio model including the interaction of pions in the final state

The $\tau^- \to \pi^- \pi^0 \nu_{\tau}$ and $e^{+}e^{-} \to \pi^{+} \pi^{-}$ processes have been described within the chiral Nambu–Jona-Lasinio model including the interaction of pions in the final state beyond the $1/N_c$ approximation. A loop correction caused by the $\rho$-meson exchange between pions, which makes the leading contribution in the $P$-wave channel, is taken into account. The results are in satisfactory agreement with experimental data for both processes.