Weinberg sum rules and the parity doubling of radial Regge trajectories

Assuming that the radial excitations of q¯q meson states exactly follow linear Regge trajectories with constant residues, as prescribed by dual models, and using large Nc arguments and the matching to perturbative QCD in the deep-Minkowski region we obtain that: (a) the region dominated by resonances and the one saturated by perturbation theory approach each other as Nc increases; (b) the scales Λ(V,A) separating the resonance-dominated and the perturbative-saturated region in the V,A channels, respectively, grow as Nc, whereas the difference between (ΛV)2 and (ΛA)2 stays constant or even decreases as Nc increases; (c) the number of visible resonances increases as Nc; (d) in order to satisfy the Weinberg sum rules the slopes of Regge trajectories for mesons of opposite parities must coincide, but the intercepts may differ by a quantity of O(1) at most in the large Nc limit. This suggests that modelizations of QCD where these characteristics are not present and yet the resonances follow linear Regge trajectories are not compatible with the symmetries or short-distance properties of QCD.