Analyticity properties in q2 for moments of deep inelastic structure functions

Abstract

The moments of deep inelastic structure functions introduced by Nachtmann and the familiar Cornwall-Norton moments are shown to be analytic functions of q 2 with a right-hand cut as the only physical sheet singularity. For the Nachtmann moments the analytic continuations to q 2 > 0 can again be expressed as projections of a virtual Compton amplitude. This representation is used to determine for q 2 > 0 the contribution of a single nucleon resonance as a first step towards an estimate in magnitude of these functions on the cut.