Q–Dependence of the Gerasimov-Drell-Hearn Sum Rule

We test the Gerasimov-Drell-Hearn (GDH) sum rule numerically by calculating the total photon absorption cross sections σ1/2 and σ3/2 on the nucleon via photon excitation of baryon resonances in the constituent quark model. A total of seventeen, low-lying, non-strange baryon resonances are included in this calculation. The transverse and longitudinal interference cross section, σ 1/2, is found to play an important role in the study of the Q 2 variation of the sum rule. The results show that the GDH sum rule is saturated by these resonances at a confidence level of 94%. In particular, the P33(1232) excitation largely saturates the sum rule at Q2 = 0, and dominates at small Q2. The GDH integral has a strong Q2-dependence below Q2 = 1.0 GeV and changes its sign around Q2 = 0.3 GeV. It becomes weakly Q2-dependent for Q2 > 1.0 GeV because of the quick decline of the resonance contributions. We point out that the Q2 variation of the GDH sum rule is very important for understanding the nucleon spin structure in the non-perturbative QCD region.