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The branching fractions of $\tau$ lepton decays with the production of strange scalar mesons both in the ground and first radially excited states $\tau \to \nu_\tau [K^*_0(700), K^*_0(1430)]$ and $\tau \to \nu_\tau [K^*_0(700)\pi, K^*_0(1430)\pi, K^*_0(700) K, K^*_0 (700)\eta]$ are calculated in the extended $U(3) \times U(3)$ chiral quark NJL model. All mesons are considered as $q\bar{q}$ systems. The obtained results should be considered as predictions for future experiments., Comment: 9 pages, 5 figures

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 $U(3)\times U(3)$ 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., Comment: 8 pages, 4 figures

In previous works effective non-local $SU(2)\times SU(2)$ NJL model was derived in the framework of the fundamental QCD. All the parameters of the model are expressed through QCD parameters: current light quark mass $m_0$ and average non-perturbative $\alpha_s$. The results for scalar and pseudo-scalar mesons are in satisfactory agreement to existing data. In the present work the same model without introduction of any additional parameters is applied for a description of masses and strong decay widths of $\rho$- and $a_1$-mesons. The results for both scalar and vector sectors agree with data with only one adjusted parameter $m_0$, with account of average $\alpha_s \simeq 0.415$, which is obtained in a previous work as well., Comment: 19 pages, 2 figures, 1 table

We apply Bogolubov approach to QCD with two light quarks to demonstrate a spontaneous generation of an effective interaction, leading to the Nambu -- Jona-Lasinio model. The resulting theory contains two parameters: average low-energy value of $\alpha_s$ and current light quark mass $m_0$. All other low-energy parameters: the pion decay constant, mass of the $\pi$-meson, mass of the $\sigma$-meson and its width, the constituent quark mass, the quark condensate are expressed in terms of the two input parameters in satisfactory correspondence to experimental data and chiral phenomenology. {\it E.g.} in the approximation being used we have for $\alpha_s = 0.67$ and $m_0 = 20 MeV$: $f_\pi = 93 MeV, m_\pi = 135 MeV, m_\sigma = 492 MeV, \Gamma_\sigma = 574 MeV, m_q = 295 MeV, <\bar q q> = -(222 MeV)^3$., Comment: 19 pages, 2 figures