Relation between low-energy constants and resonance saturation

Although there are phenomenological indications that the low-energy constants in the chiral Lagrangian may be understood in terms of a finite number of hadronic resonances, it remains unclear how this follows from QCD. One of the arguments usually given is that low-energy constants are associated with chiral symmetry breaking, while QCD perturbation theory suggests that at high energy chiral symmetry is unbroken, so that only low-lying resonances contribute to the low-energy constants. We revisit this argument in the limit of large Nc, discussing its validity, in particular, for the low-energy constant L₈, and conclude that QCD may be more subtle than what this argument suggests. We illustrate our considerations in a simple Regge-like model which also applies at finite Nc.