quark masses are not changed due to an inclusion of the radially excited states. Equivalently, one can require that the single excited quark-antiquark states averaged over vacuum are vanishing (an absence of the vacuum tadpoles). It gives $d = -1.784 \,\textrm{GeV}^{-2}$. There is a simple argument in favour of this requirement: the non-local bound states do not survive in the large $N_c$ limit, therefore they cannot affect the main characteristics of the QCD ground state. The form factor $f (k_\perp^2)$ has for $d\leq \Lambda_3^{-2}$ the form of an excited-state wave function, with a node in the interval $0\leq |k_\perp |\leq \Lambda_3$. In (\[fk\]) we consider only the first two terms in a series of polynomials in $|k_\perp |^2$; inclusion of higher excited states would require polynomials of higher degree.

The Lagrangian density (\[qint\]) has to be bosonized. The boson variables can be introduced in the two stages. On the first stage, the four quark interactions can be equivalently rewritten as a Yukawa type quark-antiquark-meson interactions. In this form the model Lagrangian has a structure of a linear sigma model. On the second stage, one should integrate out the quark fields completely. Exactly this way the Lagrangian of the extended NJL 