The U(3)×U(3) chiral symmetric NJL model describing pseudoscalar, vector, and axial-vector mesons in both the ground state and first radially excited states is shortly presented in this review. In this model, it is possible to describe a large number of low-energy interactions of mesons, τ lepton decays into mesons, and processes of meson production in electron–positron annihilations in satisfactory agreement with the experiments. In describing a number of processes, it turned out to be necessary to take into account the interactions of mesons in the final state.

In the extended Nambu–Jona-Lasinio (NJL) model, the decay widths of [Formula: see text], [Formula: see text] are calculated. The contributions from intermediate axial-vector mesons [Formula: see text], [Formula: see text] and the first radially excited state [Formula: see text] are taken into account. Estimates for the weak decay constants [Formula: see text] and [Formula: see text] are given. Predictions are made for the width of [Formula: see text] decay and [Formula: see text] constant.