Quark-resonance model

We construct an effective Lagrangian for low energy hadronic interactions through an infinite expansion in inverse powers of the low energy cutoff Λχ of all possible chiral invariant non-renormalizable interactions between quarks and mesons degrees of freedom arising from the bosonization of a general Nambu-Jona Lasinio type Lagrangian including all multiquark effective interactions. We restrict our analysis to the leading terms in the 1/Nc expansion and to the divergent part of the resonance effective Lagrangian resulting from the integration over the quark degrees of freedom. Indeed, the effective expansion is in (Q2/Λχ2)^P ln(Λχ2/Q2)^M and we show that, while the finite terms cannot be traced back to a finite number of non renormalizable interactions, the divergent ones of order (Q2/Λχ2)ln(Λχ2/Q2) receive contributions from a finite set of 1/Λχ2 terms of the original quark-meson Lagrangian. These terms modify the behaviour of physical quantities in the intermediate Q2 region. We explicitely discuss their relevance for the two point vector currents Green's function