Three-meson $\tau$ decays involving kaons and $\eta$ mesons in the NJL model

Branching fractions of decays $\tau \to K^0{\pi }^{-}\eta {\nu }_{\tau }$, $\tau \to K^{-}{\pi }^0\eta {\nu }_{\tau }$, $\tau \to K^{-}{K}^0\eta {\nu }_{\tau }$ and $\tau \to K^{-}\eta \eta {\nu }_{\tau }$ are calculated in the $U(3)\times U(3)$ chiral NJL quark model. The contact, vector, axial-vector and pseudoscalar channels are considered. It is shown that the axial vector channel is dominant. The obtained results are in satisfactory agreement with experiment.