Gaussian sum rules in quantum chromodynamics and local duality

Abstract

A new type of hadronic sum rules are studied in QCD. They correspond to the Gauss-Weierstrass transform of hadronic spectral functions. There is an interesting analogy between these sum rules and the theory of the heat equation which provides a useful framework for formulating quantitatively the notion of local duality. In particular, finite energy sum rules are shown to follow within this framework from the principle of conservation of total heat. Explicit calculations of these sum rules in QCD - from both perturbative and non-perturbative contributions à la Shifman, Vainshtein and Zakharov [1] - have been made in a rather general way which should cover all the practical cases involving light quark systems. A particular case of the ϱ-spectral function and its duality to QCD is discussed in detail as an illustration of this new approach.