The decay $\tau \to (\pi, \pi') \nu_{\tau}$ in the Nambu - Jona-Lasinio model

TL;DR

This paper calculates the decay widths of tau lepton decays into pions using the Nambu-Jona-Lasinio model, comparing standard and extended versions, and finds results consistent with experimental data and lattice calculations.

Contribution

It provides detailed calculations of tau decay widths into pions within the NJL model, including extended versions with axial-vector mesons, and compares results with experimental and lattice data.

Findings

Decay widths are in good agreement with experimental data.

Extended NJL model results align with lattice calculations.

Numerical constants $F_{\pi}$ and $F_{\pi'}$ match known values.

Abstract

In the Nambu - Jona-Lasinio model the decay widths $\tau \to (\pi, \pi'(1300)) \nu_{\tau}$ were calculated. For the calculation of the decay width $\tau \to \pi \nu_{\tau}$ the standard NJL model was used with taking into account the intermediate axial-vector meson and the extended Nambu - Jona-Lasinio model with the intermediate $a_1(1260)$ and $a_1'(1647)$ mesons. These results are in good agreement with each other. For the calculation of the decay width $\tau \to \pi' \nu_{\tau}$ extended Nambu - Jona-Lasinio model was used. The results are in satisfactory agreement with the experimental data. Numerical estimates for the constant $F_{\pi}$ and $F_{\pi'}$ are also in satisfactory agreement with both the experimental values for $F_{\pi}$ and the results obtained by calculations on the lattice.