Low-energy Compton scattering of polarized photons on polarized nucleons

The general structure of the cross section of $\gamma N$ scattering with polarized photon and/or nucleon in initial and/or final state is systematically described and exposed through invariant amplitudes. A low-energy expansion of the cross section up to and including the order $\mathcal{O}\left({\omega }^4\right)$ is given that involves ten structure parameters of the nucleon (dipole, quadrupole, dispersion, and spin polarizabilities). Their physical meaning is discussed in detail. Using fixed-$t$ dispersion relations, predictions for these parameters are obtained and compared with results of chiral perturbation theory. It is emphasized that Compton scattering experiments at large angles can fix the most uncertain of these structure parameters. Predictions for the cross section and double-polarization asymmetries are given and the convergence of the expansion is investigated. The feasibility of the experimental determination of some of the structure parameters is discussed.