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

We calculate the coefficients in the chiral Lagrangian approximately from QCD based on a previous study of deriving the chiral Lagrangian from the first principles of QCD in which the chiral Lagrangian coefficients are defined in terms of certain Green's functions in QCD. We first show that, in the large N(c)-limit, the anomaly part contributions to the coefficients are exactly cancelled by certain terms in the normal part contributions, and the final results of the coefficie...

The construction of the effective Lagrangian relevant for the mesonic sector of QCD in the large N_c limit meets with a few rather subtle problems. We thoroughly examine these and show that, if the variables of the effective theory are chosen suitably, the known large N_c counting rules of QCD can unambiguously be translated into corresponding counting rules for the effective coupling constants. As an application, we demonstrate that the Kaplan-Manohar transformation is in co...

We report on some recent progress made in understanding weak matrix elements of mesons in the context of the next-to-leading order of the large-Nc approximation to QCD. Specifically, we first use the example of the weak contributions to the pi^+ - pi^0 mass difference to exhibit how a systematic matching can be achieved analytically between short distances and long distances within our large-Nc framework. We are then also able to compute matrix elements of the operator Q_7, a...

A detailed investigation of the low-energy chiral expansion is presented within a model truncation of QCD. The truncation allows for a phenomenological description of the quark-quark interaction in a framework which maintains the global symmetries of QCD and permits a $1/N_c$ expansion. The model dependence of the chiral coefficients is tested for several forms of the quark-quark interaction by varying the form of the running coupling, $\alpha (q^2)$, in the infrared region. ...

An overview of the field of Chiral Lagrangians is given. This includes Chiral Perturbation Theory and resummations to extend it to higher energies, applications to the muon anomalous magnetic moment, $\epsilon^\prime/\epsilon$ and others.

The chiral Lagrangian for baryons is formulated in an expansion in 1/N_c. The chiral Lagrangian implements the contracted spin-flavor symmetry of large-N_c baryons as well as nonet symmetry of the leading planar diagrams. Large-N_c consistency conditions ensure that chiral loop corrections are suppressed in 1/N_c through exact cancellation of chiral loop graphs to fixed orders in 1/N_c. Application of 1/N_c baryon chiral perturbation theory to the flavor-27 baryon mass splitt...

We report on a calculation of $\epsilon_K'/\epsilon_K$ at next-to-leading in the $1/N_c$ expansion and to lowest order in Chiral Perturbation Theory. We discuss the short-distance matching, the scale and scheme dependence as well as the long-distance short-distance matching. We include the two known chiral corrections to our result and discuss further order $p^4$ corrections to it.

I review the large Nc behavior of light resonances generated from unitarized one-loop Chiral Perturbation Theory. In contrast with the rho or K*, the scalar behavior is at odds with a qqbar "dominant component". In fact, in the light scalar region, meson-meson amplitudes vanish as Nc increases. Also, the scalar widths, obtained from their associated poles, behave as O(Nc^{1/2})<Gamma<O(Nc). We also clarify on the physical relevance of considering large Nc not too far from rea...

The reasons why a considerable effort is made to resolve the low energy structure of QCD are discussed. The effective field theory used for this purpose is illustrated with the recent progress made in the predictions for pipi scattering and in understanding the low energy properties of the theory in the large Nc limit.

It is shown that the usual large-$N_c$ counting of the coupling constant $L_{7}$ of the ${\cal O}(p^4)$ low-energy chiral $SU(3)$ Lagrangian \cite{GL85} is in conflict with general properties of QCD in the large-$N_c$ limit. The solution of this conflict within the framework of a chiral $U(3)$ Lagrangian is explained.