Q²-dependence of the Gerasimov-Drell-Hearn sum rule

Abstract

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, σTL1/2, is found to play an important role in the study of the Q2 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) dominates at small Q2. The GDH integral has a strong Q2-dependence below Q2 = 1.0 GeV2 and changes its sign around Q2 = 0.3 GeV2. It becomes weakly Q2-dependent for Q2 > 1.0 GeV2 because of the quick decline of the resonance contributions. © 1998 Published by Elsevier Science B.V.