MATCHING LONG AND SHORT DISTANCES IN LARGE-N-C QCD

It is shown, with the example of the experimentally known Adler functi on, that there is no matching in the intermediate region between the t wo asymptotic regimes described by perturbative QCD (for the very shor t-distances) and by chiral perturbation theory (for the very long-dist ances). We then propose to consider an approximation of large-N-c QCD which consists in restricting the hadronic spectrum in the channels wi th J(P) quantum numbers 0(-), 1(-), 0(+) and 1(+) to the lightest stat e and to treat the rest of the narrow states as a perturbative QCD con tinuum; the onset of this continuum being fixed by consistency constra ints from the operator product expansion. We show how to construct the low-energy effective Lagrangian which describes this approximation. T he 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 correspondin g predictions, to O(p(4)) in the chiral expansion, with the phenomenol ogically known couplings is also made.