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The branching fraction of the decay $\tau \to K^{-} \eta \nu_{\tau}$ has beencalculated by using the extended Nambu-Jona-Lasinio model taking into accountthe meson interaction in the final state. The contact term and the channel withthe intermediate ground $K^{*}(892)$ and first radially excited state$K^{*}(1410)$ have been calculated. For the purpose of describing the mesoninteraction in the final state, the triangle diagram with three mesons has beenconsidered. The cutoff parameter of divergent integrals of the meson loop isequal to the appropriate parameter used in our previous work to describe thedecay $\tau \to K^{-} \pi^{0} \nu_{\tau}$. Thereby, the present work does notset any additional arbitrary parameters. The obtained results are insatisfactory agreement with the experimental data.

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