Low-energy theorems, dispersion relations, and superconvergence sum rules for Compton scattering

Abstract

A derivation of low-energy theorems for Compton scattering from spin-0 and spin-½ targets is given within the framework of dispersion theory. We work exclusively with physical helicity amplitudes and utilize the zeros of these amplitudes forced by angular momentum conservation to write unsubtracted dispersion relations. The conventional requirement of gauge invariance is replaced in our work by Lorentz in-variance together with the knowledge that the photon is a massless spin-1 particle. From the dispersion relations we extract a number of sum rules of the superconvergence type, one example of which reduces the Drell-Hearn result in the forward direction.