τ → K–ηντ Decay in the Extended Nambu–Jona-Lasinio Model Including the Final-State Interaction

The width of the $$\tau \to {{K}^{ - }}\eta {{\nu }_{\tau }}$$ decay has been calculated within the extended Nambu–Jona-Lasinio model including the final-state interaction of mesons. Both the contact term and the channel with the intermediate ground state $$K{\text{*}}(892)$$ and its first radial excitation $$K{\text{*}}(1410)$$ have been taken into account. To describe the final-state interaction, a triangle diagram with three mesons has been considered. The cutoff parameter in the diverging integrals over the meson loop has been taken the same as in our preceding work to describe the $$\tau \to {{K}^{ - }}{{\pi }^{0}}{{\nu }_{\tau }}$$ decay, so no additional parameters are introduced. Satisfactory agreement with experimental data has been obtained.