Application of the Large-N_c limit to a Chiral Lagrangian with Resonances

Two ideas have greatly contributed to our understanding of baryon structure in the framework of Quantum Chromodynamics (QCD). The first, chiral symmetry, received its fundamental justification from QCD and has been developed into the powerful technique of chiral perturbation theory. The other notion is the large-$N_c$ limit, namely the behavior of QCD in the limit where there are a large number of colors. Like chiral symmetry, the large-$N_c$ limit predicts many relations bet...

I report on recent progress in calculating electroweak processes within the framework of QCD in the 1/Nc expansion.

In pure chiral perturbation theory (ChPT) the couplings of higher order Lagrangian terms are running parameters and hence can be determined only empirically from various low-energy hadronic processes. While this scenario works well for strong interactions, it is unsatisfactory for nonleptonic and radiative nonleptonic weak interactions: It is impossible, from the outset, to determine all unknown higher-order chiral couplings by experiment; theory is tested only by certain chi...

Within Resonance Chiral Theory and in the context of QCD current correlators at next-to-leading order in 1/N(C), we have analyzed the two-body form factors which include resonances as a final state . The short-distance constraints have been studied. One of the main motivations is the estimation of the chiral low-energy constants at subleading order, that is, keeping full control of the renormalization scale dependence. As an application we show the resonance estimation of som...

A brief introduction to the low-energy effective field theory of the standard model, chiral perturbation theory, is presented.

A U_L(3) \otimes U_R(3) low-energy effective lagrangian for the nonet of pseudogoldstone bosons that appear in the large-Nc limit of QCD is presented including terms up to four derivatives and explicit symmetry breaking terms up to quadratic in the quark masses. The one-loop renormalization of the couplings is worked out using the heat-kernel technique and dimensional renormalization. The calculation is carried through for U_L(n_l) \otimes U_R(n_l), thus allowing for a generi...

The basic ideas and some recent developments of the chiral perturbation theory approach to hadron dynamics at low-energies are reviewed. (Invited talk at the HADRON'93 Conference Como, Italy June 1993.)

The effective field theory relevant for the analysis of QCD at low energies is reviewed. The foundations of the method are discussed in some detail and a few illustrative examples are described.

We study the resonance properties within chiral perturbation theory by explicitly taking into account the U_A(1) anomaly effect. This assures we have the appropriate degrees of freedom of low energy QCD in the large Nc limit. We calculate the various resonance properties, such as mass, width and residues, for the physical case, i.e. Nc=3. Then we extrapolate the values of Nc to study the trajectories of resonance poles.

It is shown, with the example of the experimentally known Adler function, that there is no matching in the intermediate region between the two asymptotic regimes described by perturbative QCD (for the very short-distances) and by chiral perturbation theory (for the very long-distances). We then propose to consider an approximation of large-Nc QCD which consists in restricting the hadronic spectrum in the channels with J^P quantum numbers 0^-, 1^-, 0^+ and 1^+ to the lightest ...