Fixed mass and scaling sum rules: Generalized truncation and current algebra constraints on Regge residues

Abstract

Using the correspondence principle (continuity in dynamics), we extend the approach of Keppel-Jones-Ward-Taha to fixed mass and scaling current algebraic sum rules so as to consider explicitly the contributions of all classes of intermediate states. A natural, generalized formulation of the truncation ideas of Cornwall, Corrigan, and Norton is introduced as a by-product of this extension. The formalism is illustrated in the familiar case of the spin independent Schwinger term sum rule. New sum rules are derived which relate the Regge residue functions of the respective structure functions to their fixed hadronic mass limits for q 2 → ∞.