Violation of Quark-Hadron Duality (The missing oscillation in the OPE)

The origin of quark-hadron Duality Violations (DVs) can be related to the sigularities of the Laplace transform of the spectral function. With the help of rather generic properties of the large-$N_c$ approximation and a generalized form for the radial trajectories found in Regge Theory, we may locate these singularities in the complex plane and obtain an expression for the DVs which turns out to agree with general expectations. Using the two-point vector correlator as a test laboratory, we show how the usual dispersion relation may give rise to perturbation theory, the power corrections from the condensate expansion and DVs.