Low-Energy Nucleon Compton Scattering

Abstract

In the case of nucleon Compton scattering, theory and experiment disagree at the photoproduction threshold and at the peak of the first pion-nucleon resonance (1236 MeV) at 90° c.m. scattering angle. Dispersion relations are used to calculate the scattering amplitudes of this process in the low-energy region in terms of the nucleon Born pole, photoproduction, ${\pi }^0$, and $2\pi$ exchange. Several currently accepted models for $I=J=0\mathrm{}$ $\pi \pi$ scattering are considered. Using a nonresonating or a resonating $\pi \pi$ phase shift with resonance width ≳100 MeV and position ≳600 MeV, we are able to account for the discrepancy between theory and experiment around the photoproduction threshold. At the 90° c.m. resonance peak, the situation remains essentially unchanged.