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-N c QCD which consists in restricting the hadronic spectrum in the channels with J P quantum numbers 0 − , 1 − , 0 + and 1 + to the lightest state and to treat the rest of the narrow states as a perturbative QCD continuum; the onset of this continuum being fixed by consistency constraints from the operator product expansion. We show how to construct the low-energy effective Lagrangian which describes this approximation. The number of free parameters in the resulting effective Lagrangian can be reduced, in the chiral limit where the light quark masses are set to zero, to just one mass scale and one dimensionless constant to all orders in chiral perturbation theory. A comparison of the corresponding predictions, to O(p 4 ) in the chiral expansion, with the phenomenologically known couplings is also made.

The counterterm combination that describes the decay of pseudoscalar mesons into charged lepton pairs at lowest order in chiral perturbation theory is considered within the framework of QCD in the limit of a large number of colors N c . When further restricted to the lowest meson dominance approximation to large-N c QCD, our results agree well with the available experimental data.

The hadronic light-by-light contribution to a(mu), the anomalous magnetic moment of the muon, is discussed from the point of view of an effective low-energy theory. As an application, the coefficient of the leading logarithm arising from the two-loop graphs involving two anomalous vertices is computed, and found to be positive. This corresponds to a positive sign for the pion-pole contribution to the hadronic light-by-light correction to a(mu), and to a sizable reduction of the discrepancy between the present experimental value of a(mu) and its theoretical counterpart in the standard model.