The decay $\tau \to 3\pi\nu_\tau$ and axial-vector meson $a_1$ in the NJL model

Abstract

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 plays 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.