# $\tau\to \nu_\tau\rho^0\pi^-$ decay in the Nambu - Jona-Lasinio model

## TL;DR

This paper uses an extended Nambu-Jona-Lasinio model to analyze the decay of tau leptons into specific mesons, considering axial-vector and pseudoscalar contributions, and calculates decay rates and spectra.

## Contribution

It introduces a method to incorporate radial excited states in the NJL model for tau decay analysis, providing detailed form factors and decay predictions.

## Key findings

- Decay rate and mass spectrum calculated
- Radial excited states included in the model
- Form factors expressed in terms of meson properties

## Abstract

Within the context of an extended Nambu - Jona-Lasinio model, we analyze the role of the axial-vector $a_1(1260)$ and $a_1(1640)$ mesons in the decay $\tau\to\nu_\tau \rho^0\pi^-$. The contributions of pseudoscalar $\pi$ and $\pi (1300)$ states are also considered. The form factors for the decay amplitude are determined in terms of the masses and widths of these states. To describe the radial excited states $\pi (1300)$ and $a_1(1640)$ we introduce two additional parameters which can be estimated theoretically, or fixed from experiment. The decay rate and $\rho\pi$ mass spectrum are calculated.