Quark-Resonance model

Abstract

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 $({\mu }^2/{\text{cutoff}}^2{)}^P\ln ({\text{cutoff}}^2/{\mu }^2{)}^Q$. Concerning the next-to-leading order, we show that, while the pure ${\mu }^2/{\text{cutoff}}^2$ corrections cannot be traced back to a finite number of non renormalizable interactions, those of order $({\mu }^2/{\text{cutoff}}^2)\ln ({\text{cutoff}}^2/{\mu }^2)$ receive contributions from a finite set of $1/{\text{cutoff}}^2$ 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.

Comments: 41 pages, 11 figures, preprint ROM2F 93/37