chiral transformations. Thus, there are four independent $U(2)_L\times U(2)_R$ invariant interactions.

The local interactions with $i=1$ represent the conventional NJL type model (see, for instance, [@Volkov86; @Bijnens93]) which describes the physics of ground-state mesons with quantum numbers $J^{PC}=0^{++}, 0^{-+}, 1^{--}$ and $1^{++}$. The covariant form factors of local interactions are given by $$\begin{aligned}
&&F^{S,P,V,A}_{a(1)}(x; x_1,x_2)=F^{S,P,V,A}_{a} \delta(x-x_1)\delta(x-x_2), \nonumber \\
&&F^{S,P,V,A}_{a} =\tau_a\, (1,i\gamma_5,\gamma_\mu, \gamma_\mu\gamma_5 ),\end{aligned}$$ where the flavour matrices $\tau_a=(1, \vec\tau)$, with the standard notation of the isospin Pauli matrices $\vec\tau$.

The non-local part of the Lagrangian density $i=2$ represents the first radial excitations of ground-states. The corresponding covariant non-local form factors have been constructed in [@VolkovW97] with the use of the following transformation $$\begin{aligned}
F^{S,\ldots}_{a(2)}(x; x_1,x_2)&=&\!\int\!\frac{d^4k}{(2\pi )^4}\frac{d^4p}{(2\pi )^4} \exp i\left[ p\left(x-\frac{x_1+x_2}{2}\right) \right.\nonumber \\
&-& \left. k\left(x_1-x_2\right)\right] F^{S,\ldots}_{a(2)}(k_\perp ),\end{aligned}$$ where $k_\mu$ is a relative momentum of the quark-antiquark pair, and $p_\mu$ is a 4-momentum of their center of mass reference frame, i.e. a meson momentum. The total momentum $p_\mu$ of the composite hadron provides a naturally preferred direction which forms the basis for a covariant three dimensional support to the interaction kernel $F^{S,\ldots}_{a(2)}(k_\perp )$ which is implemented here in accord with the concept of bilocal fields. The dependence of the interaction kernel 