In the extended Nambu–Jona-Lasinio model, the branching fraction of $τ \to K^{* 0} (892) K^{-} ν_{τ}$ is calculated. The contributions from the contact diagram and the diagrams with intermediate axial-vector, vector and pseudoscalar mesons in the ground and first radially excited states are taken into account. It is shown that an axial-vector and vector channel with a contact diagram give a dominant contribution to the branching fraction. The obtained results for the branching fraction $τ \to K^{* 0} (892) K^{-} ν_{τ}$ are in satisfactory agreement with experimental data. A prediction for the differential distribution over the invariant mass of the meson pair $K^{* 0} (892) K^{-}$ is given.

Keywords:

PACS: 12.39.Fe, 12.39.-x, 13.35.Dx

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