Generalized fixed-mass sum rules

Abstract

Light-cone commutation relations have been shown to be the natural commutators to use to derive fixed mass (fixed spacelike q 2) sum rules for the structure functions which describe lepton hadron scattering. In this paper we review, in detail, the structure of the light-cone commutators and the methods used to derive sum rules. We then derive new sum rules by using two generalizations of the previous method; 1. (1) we use the light-cone commutator of moments of currents by considering derivatives of the Fourier transform of the current and 2. (2) we expand the integrals in a power series in q 2 before fixing q 2. The new sum rules involve derivatives of the structure functions with respect to q 2 and/or ν. Except for one short separate calculation we consider only conserved vector currents. For the most part we do not sum over the nucleon spin nor restrict ourselves to the forward direction. Our emphasis is on the type of information contained in the different techniques of derivation and we particularly emphasize which sum rules can be derived from the least model dependent commutator.