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

TL;DR

This paper analyzes the origins of the generalized GDH sum rule by examining polarized parton distributions and higher twist effects, revealing the roles of quark helicity and internal proton structure at various energy scales.

Contribution

It introduces a simple parameterized formula to distinguish contributions from different components in the proton to the sum rule, highlighting the significance of higher twist effects.

Findings

Quark helicity contribution is nearly constant (~0.123).

Twist-4 effects dominate at Q^2<3 GeV^2.

Twist-6 effects indicate possible extended objects inside the proton.

Abstract

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.