Narrow Results

The branching fractions of the decays $\tau \to a_1\pi {\nu }_{\tau }$, $\tau \to K_1\pi {\nu }_{\tau }$ and $\tau \to K_{1}K{\nu }_{\tau }$ are calculated in the framework of the extended $\mathrm{\text{U}}(3)\times \mathrm{\text{U}}(3)$ chiral Nambu–Jona-Lasinio model. There are no experimental data for these decays in the present time, thus the obtained results are considered as predictions. The comparison of these results to the theoretical results of other authors is carried out.

The branching fractions of $\tau \to {\pi }^{+}{\pi }^{-}{\pi }^{-}{\nu }_{\tau }$ and $\tau \to {\pi }^{-}2{\pi }^0{\nu }_{\tau }$ are calculated within the chiral NJL model. Features of the axial-vector $a_1$ meson which play an important role in describing the $\tau$ decays are discussed. Permissible values for the mass and width of the $a_1$ meson are considered in accordance with the latest experiments.

In the extended Nambu–Jona-Lasinio model, the branching fraction of $\tau \to K^{\ast 0}(892)K^{-}{\nu }_{\tau }$ 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 $\tau \to K^{\ast 0}(892)K^{-}{\nu }_{\tau }$ are in satisfactory agreement with experimental data. A prediction for the differential distribution over the invariant mass of the meson pair $K^{\ast 0}(892)K^{-}$ is given.