$\tau^{-} \to \pi^{-} \pi^{0} \nu_\tau$ decay in the extended NJL model

TL;DR

This paper calculates the decay width of tau to two pions and a neutrino using an extended NJL model, incorporating contact interactions and rho meson contributions, aligning well with experimental data.

Contribution

It introduces an extended NJL model approach that includes both ground and excited rho mesons for decay width calculations, matching experimental results.

Findings

Decay width matches vector-dominance model predictions.

Results are in satisfactory agreement with experimental data.

Inclusion of excited rho states improves model accuracy.

Abstract

The width of the decay $\tau^{-} \to \pi^{-} \pi^{0} \nu_\tau$ was calculated in the extended NJL model. Contact interaction of $W$ boson with pion pair as well as the contribution of the $\rho$ mesons in ground and first radial-exited states are taken into account. The sum of the contact diagram and diagram with intermediate $\rho$ meson in the ground state leads to the result which coincides with the result of the vector-dominance model. Our results are in satisfactory agreement with experimental data.