Large N C in Chiral Resonance Lagrangians *

In the large Nc limit, Nc → ∞, at fixed scale ΛQCD, the spectrum of QCD is known to consist of an infinite number of stable states. The degrees of freedom in the corresponding low energy effective theory are the states with masses vanishing in the chiral limit (mu = md = ms = 0) of large Nc QCD, viz. π, K, η and η′.5 The presence of the remaining massive states shows up only indirectly, trough their contributions to the low energy expansion of QCD correlation functions. In chiral perturbation theory, these are accounted for in the form of low energy constants that arise at nonleading order in the low energy Lagrangian. In this note we discuss consequences for the low energy constants in the framework of an explicit realization of this scenario where, however, only the lowest lying resonance states are retained. In Sec. 2, we briefly review the framework of the low energy expansion at large Nc. Secs. 3 and 4 deal with the accommodation of explicit resonance degrees of freedom in that setting. Sec. 5 reviews the role of constraints from QCD asymptotic behaviour in the determination of the parameters occurring in the chiral resonance Lagrangian. In Sec. 6, we discuss the implications of our