Processes $\tau^- \to \pi^- \pi^0 \nu_{\tau}$ and $e^{+}e^{-} \to \pi^{+} \pi^{-}$ in the chiral NJL model with final state interactions taken into account

TL;DR

This paper models the tau decay and electron-positron annihilation into pions using the chiral NJL model, incorporating pion final state interactions and rho meson exchange, achieving results consistent with experimental data.

Contribution

It introduces a calculation of loop corrections with rho meson exchange in the chiral NJL model beyond leading order, improving the description of pion interactions.

Findings

Results agree with experimental data for both processes.

Loop corrections significantly impact the P-wave channel.

The model effectively incorporates final state interactions.

Abstract

The processes $\tau^- \to \pi^- \pi^0 \nu_{\tau}$ and $e^{+}e^{-} \to \pi^{+} \pi^{-}$ are considered within the chiral Nambu--Jona-Lasinio model with taking into account the pion final state interactions beyond the leading $1/N_c$ approximation. The contribution of the loop correction caused by a $\rho$ meson exchange between the pions, which gives the main contribution in the P-wave channel, is caclulated. The results for both processes are in a satisfactory agreement with experimental data.