The decays $\tau \rightarrow (\eta,\eta')K^{-}\nu_{\tau}$ in the extended Nambu–Jona-Lasinio model

The decays $\tau \rightarrow (\eta,\eta')K^{-}\nu_{\tau}$ are described in the framework of the extended Nambu–Jona-Lasinio model. Both full and differential widths of these decays are calculated. The vector and scalar channels are considered. In the vector channel, the subprocesses with the intermediate $K^{*}(892)$ and $K^{*}(1410)$ mesons play the main role. In the scalar channel, the subprocesses with the intermediate $K_{0}^{*}(800)$ and $K_{0}^{*}(1430)$ mesons are taken into account. The scalar channel gives an insignificant contribution to the full width of the decay $\tau \rightarrow \eta K^{-} \nu_{\tau}$. The obtained results are in satisfactory agreement with the experimental data. The prediction for the width of the process $\tau \rightarrow \eta' K^{-} \nu_{\tau}$ is made.