Electromagnetic mass differences and inelastic electron scattering

Abstract

The Cottingham expression for the electromagnetic mass splitting within a given isomultiplet is studied with a particular emphasis on possible subtractions and divergences. Necessary and sufficient conditions for the convergence of the integration over the photon mass and for the validity of the contour rotation in the ν-plane are derived. The mass differences are expressed in terms of measurable inelastic electron scattering cross sections both in the subtracted and in the unsubtracted case. The subtraction function for ΔI = 1 mass differences is expressed in terms of the A 2 residue function. The latter can be computed from the low energy data using finite energy sum rules, thus leading to a representation of ΔM in terms of low energy data alone. A naive application of this representation fails and the A 2 -exchange alone is unable to yield the necessary correction for ΔI = 1 mass differences. Possible reasons for this failure are discussed.