Nucleon spin structure III: Origins of the generalized Gerasimov-Drell-Hearn sum rule

The generalized Gerasimov-Drell-Hearn (GDH) sum rule is understood based on the polarized parton distributions of the proton with the higher twist contributions. A simple parameterized formula is proposed to clearly present the contributions of different components in proton to $\Gamma_1^p(Q^2)$. We find that the contribution of quark helicity to $\Gamma_1^p(Q^2)$ is almost constant ($\sim 0.123$); the twist-4 effect dominates the suppression of $\Gamma_1^p(Q^2)$ at $Q^2<3GeV^2$, while the twist-6 effect arises a dramatic change of $\Gamma_1^p(Q^2)$ at $Q^2<0.3 GeV^2$, it implies a possible extended objects with size $0.2-0.3~ fm$ inside the proton.