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

Abstract

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.

(13 pages, 2 Figures). Invited contribution to the special issue "Renormalons and Hyperasymptotics in QCD" of EPJ-ST

References in corpus (5)

• The strong coupling from the revised ALEPH data for hadronic $\tau$ decays
• Highly Excited Mesons, Linear Regge Trajectories and the Pattern of the Chiral Symmetry Realization
• Unraveling duality violations in hadronic tau decays
• The strong coupling from an improved $\tau$ vector isovector spectral function
• Large-Nc QCD, Harmonic Sums and the Riemann Zeros