Locality of Quark-Hadron Duality and Deviations from Quark Counting Rules Above the Resonance Region

We show how deviations from the dimensional scaling laws for exclusive processes may be related to a breakdown in the locality of quark-hadron duality. The essential principles are illustrated in a pedagogic model of a composite system with two spinless charged constituents, for which a dual picture for the low-energy resonance phenomena and high-energy scaling behavior can be established. We introduce the concept of “restricted locality” of quark-hadron duality and show how this results in deviations from the perturbative quantum chromodynamics quark counting rules above the resonance region. In particular, it can be a possible source for oscillations about the smooth quark counting rule, as seen, e.g., in the 90-degree differential cross sections for γp→π⁺n.