Polarizability of the Nucleon and Compton Scattering

Different approaches to describe Compton scattering and the polarizability of the nucleon have been discussed up to now. We show that the most appropriate ones are provided by non-subtracted dispersion theories of the fixed-$t$ and fixed-$\theta$ types, where the properties of these two versions are complementary so that advantage can be taken from both of them. In the frame of fixed-$t$ dispersion theory it was possible to precisely reproduce experimental differential cross sections obtained for the proton in a wide angular range and for energies up to 1 GeV. At energies of the first resonance region and below, precise values for the electromagnetic polarizabilities and spin-polarizabilities have been determined for the proton and the neutron. The data show that diamagnetism is a prominent property of nucleon structure, where the underlying mechanism is a $t$-channel $\sigma$-meson exchange. A similar mechanism is responsible for the backward spin-polarizability where the relevant meson is the $\pi^0$. It is a challenge for further research to integrate the $\sigma$ and $\pi^0$ intermediate states into a consistent description of the structure of the nucleon.