Spin-1 Correlators at Large NC: Matching OPE and Resonance Theory up to   O(alpha_s)
  The relation between the quark-gluon description of QCD and the hadronic picture is studied up to order alpha_s. The analysis of the spin-1 correlators is developed within the large NC framework. Both representations are shown to be equivalent in the euclidean domain, where the Operator Product Expansion is valid. By considering different models for the hadronic spectrum at high energies, one is able to recover the alpha_s running in the correlators, to fix the rho(770) and a1(1260) couplings, and to produce a prediction for the values of the condensates. The Operator Product Expansion is improved by the large NC resonance theory, extending its range of validity. Dispersion relations are employed in order to study the minkowskian region and some convenient sum rules, specially sensitive to the resonance structure of QCD, are worked out. A first experimental estimate of these sum rules allows a cross-check of former determinations of the QCD parameters and helps to discern and to discard some of the considered hadronical models. Finally, the truncated resonance theory and the Minimal Hadronical Approximation arise as a natural approach to the full resonance theory, not as a model. 
J.J. Sanz-Cillero