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

Abstract

The branching fraction of the decay $τ\to K^{-} ην_τ$ 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 $τ\to K^{-} π^{0} ν_τ$. Thereby, the present work does not set any additional arbitrary parameters. The obtained results are in satisfactory agreement with the experimental data.