In the extended Nambu--Jona-Lasinio model, the decay widths of the processes $\tau \to [\omega(782), \phi(1020)] K^{ -} \nu_{ \tau}$ were calculated. The intermediate strange quark-antiquark mesons in both the ground and the first radially excited states were taken into account. The meson $K_{ 1}(1400)$, being a possible candidate for the role of the tetraquark meson, was also taken into account as an intermediate state. The result for the process $\tau \to \omega(782) K^{ -} \nu_{ \tau}$ is in satisfactory agreement with the experimental data. Simultaneously, the result for the decay $\tau \to \phi(1020) K^{ -} \nu_{ \tau}$ is in agreement with the experimental data with precision $1.3 \sigma$.
Categories: hep-ph