The decay $\tau \to K^{-} \eta \nu_{\tau}$ in the extended Nambu-Jona-Lasinio model taking into account the meson interaction in the final state

TL;DR

This paper calculates the branching fraction of the tau decay into K- eta nu_tau using an extended Nambu-Jona-Lasinio model, incorporating meson interactions and excited states, achieving results consistent with experimental data.

Contribution

It introduces a detailed calculation of tau decay involving meson interactions and excited states within the extended Nambu-Jona-Lasinio model without adding extra arbitrary parameters.

Findings

Results agree with experimental data

Includes meson interactions in the final state

Considers ground and excited K* states

Abstract

The branching fraction of the decay $\tau \to K^{-} \eta \nu_{\tau}$ has been calculated by using the extended Nambu-Jona-Lasinio model taking into account the meson interaction in the final state. The contact term and the channel with the intermediate ground $K^{*}(892)$ and first radially excited state $K^{*}(1410)$ have been calculated. For the purpose of describing the meson interaction in the final state, the triangle diagram with three mesons has been considered. The cutoff parameter of divergent integrals of the meson loop is equal to the appropriate parameter used in our previous work to describe the decay $\tau \to K^{-} \pi^{0} \nu_{\tau}$. Thereby, the present work does not set any additional arbitrary parameters. The obtained results are in satisfactory agreement with the experimental data.