A model of duality violations

A realistic model for the spin-one correlators guided by the large-$N_c$ limit of QCD is elaborated in terms of the meson decay constants, masses and energy-dependent widths, which are expanded in 1/n, where n is the radial excitation number. The matching onto OPE is performed up to NLO in 1/$N_c$. After applying the resulting constraints, the remaining free parameters are fitted to ALEPH and OPAL data on the related spectral functions. Excellent agreement with the data is found and the model yields, at large n, a spectrum of overlapping states coupling with essentially equal strength, in agreement with the large-$N_c$ predictions. This model provides a consistent and appropriate way to compute the impact of duality violations on the moments of the related spectral functions computed along the circle in the complex s-plane, and therefore to quantify its importance in the extraction of physical parameters like ${\alpha }_S\left(M_{\tau }^2\right)$.