Duality for heavy-quark systems

Abstract

We give a proof of the duality relation $〈{\ensuremath{\sigma}}_{\mathrm{bound}}〉\ensuremath{\simeq}〈{\ensuremath{\sigma}}_{\mathrm{free}}〉$ for nonrelativistic potential models, using Feynman propagators. There are important and calculable corrections to the duality relation, both for smooth long-range potentials and for singular short-range potentials. We illustrate the corrections for the exactly solvable harmonicoscillator, linear, and Hulth\'en potentials.