Comparison of the Scattering of Electrons and Positrons from Protons at Small Angles

Abstract

We study the ratio of the cross section for elastic positron-proton scattering to that for elastic electron-proton scattering. In first-order $\alpha$, the leading terms of this ratio for small-angle scattering are given. As could be expected, the first term in this "expansion" is the same as that obtained in Dirac theory, and the first plus the second are unchanged from the structureless-proton result. Only in the third term do we begin to find proton structure, this in the form of a sum rule over photoproduction cross sections. Use is made of an off-mass-shell analog of the Compton low-energy theorem, and as a by-product we show that the two-photon contribution to our ratio is finite in the limit of zero electron mass.