model has been worked out in [@Volkov97; @VolkovYu00]. Its numerous applications were reviewed in [@Volkov17]. Let us stress the main features of such calculations: (a) The model reveals the mechanism of spontaneous chiral symmetry breaking. Starting from some critical value of coupling $G_S\geq G_{crit}$ the Wigner-Weyl ground state of the system is changed to the Nambu-Goldstone phase. The transition is described by the gap equation. In particular, the current quark mass $m^0$ is replaced on the constituent quark mass $m$. It is assumed that the non-local sector of the model does not contribute to $m$, and does not affect the value of the quark condensate. This assumption help us to fix a slope parameter $d$; (b) Several mixing effects take place at the level of free Lagrangian. First, as a consequence of the phase transition, the mixing between $J^{P}=0^-$ and $J^P=1^+$ states, the so-called $\pi -a_1$ transitions, occurs. Second, there are mixings between ground and excited states with the same quantum numbers; (c) The effective meson vertices and corresponding coupling constants follow from the one-quark-loop calculations. It means that one should separate divergences in a regularized form, and renormalize the meson fields. All these effects are taken into account in 