Scaling, Fixed Poles, and Electroproduction Sum Rules

Bjorken's scale invariance is imposed on the general form of the Deser-Gilbert-Sudarshan (DGS) representation for forward current-hadron scattering amplitudes to deduce features of the scaling limit, the Regge limit, and the asymptotic limit for fixed total mass of the produced hadrons. Two sum rules are derived, whose validity essentially asserts that the residue of the $J=0\mathrm{}$ fixed pole in the virtual Compton amplitude is independent of the mass carried by the currents. One of these relations tests for the presence of operator Schwinger terms, and the other relates an integral over the total photoproduction cross section to an integral over a scale function observed in electroproduction. The significance of these ideas for the calculation of electromagnetic mass differences is also discussed.