Results on the Moments of the Spin Structure Functions: Sum Rules and Polarizabilities

Based on general physics principles, sum rules relate integrations of the structure functions to static properties, or, in the generalized situation, to the forward Compton amplitudes. Sum rules provide a powerful way to study nucleon structure and the strong interaction. Nucleon spin structure functions $g_1$ and $g_2$ have been measured over a wide range of kinematics. Moments of the spin structure functions were extracted from very low to medium range of $Q^2$ to study the spin sum rules and the spin polarizabilities. The results were compared with calculations, in particular, at low $Q^2$, with Chiral Perturbation Theory calculations. Discussions and perspectives will be presented.