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 $\Lambda_\chi$ of all possible chiral invariant non-renormalizable interactions between quarks and mesons degrees of freedom. We restrict our analysis to the leading terms in the $1/N_c$ expansion. The effective expansion is in $(\mu^2/\cutoff^2 )^P \ln (\cutoff^2/\mu^2 )^Q$. Concerning the next-to-leading order, we show that, while the pure $\mu^2/\cutoff^2 $ corrections cannot be traced back to a finite number of non renormalizable interactions, those of order $(\mu^2/\cutoff^2 ) \ln (\cutoff^2/\mu^2 )$ receive contributions from a finite set of $1/\cutoff^2$ terms. Their presence modifies the behaviour of observable quantities in the intermediate $Q^2$ region. We explicitely discuss their relevance for the two point vector currents Green's function.