Nucleon compton scattering I: Dispersion relations

Abstract

Nucleon Compton scattering is analyzed assuming the validity of the Mandelstam representation. The six covariant amplitudes which determine the scattering amplitude for this process are chosen in such a way that no kine-matical singularities are introduced. From the analytic properties of the covariant amplitudes implied by the Mandelstam representation, subtracted dispersion relations are written for quantities which are simply related to the elements of the total angular momentum submatrices of the scattering matrix; the subtraction constants are determined from an application of the low-energy Compton scattering theorem. The one-particle intermediate state contributions to the absorptive parts are considered exactly. The two-particle intermediate state contributions to the absorptive parts in Channels I and II are approximated by using the matrix elements of the Chew, Goldberger, Low, and Nambu single pion photoproduction analysis. For the two-particle intermediate state contribution to the absorptive part in Channel III a pole-term approximation is used after the I = 0 amplitude alone is shown to contribute. No higher mass intermediate states in any channels are considered. The numerical evaluation and comparison with experimental data of the derived dispersion relations is considered in a following paper.