dorsal/arxiv
View Schema$Q^2$--Dependence of the Gerasimov-Drell-Hearn Sum Rule
| Authors | W. X. Ma, D. H. Lu, A. W. Thomas, Z. P. Li |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9712036 |
| URL | https://arxiv.org/abs/nucl-th/9712036 |
| DOI | 10.1016/S0375-9474(98)00202-4 |
| Journal | Nucl.Phys.A635:497-508,1998 |
Abstract
We test the Gerasimov-Drell-Hearn (GDH) sum rule numerically by calculating the total photon absorption cross sections $\sigma_{1/2}$ and $\sigma_{3/2}$ 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, $\sigma_{1/2}^{TL}$, 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 $P_{33}(1232)$ excitation largely saturates the sum rule at $Q^2 = 0$, and dominates at small $Q^2$. The GDH integral has a strong $Q^2$-dependence below $Q^2= 1.0 {GeV}^2$ and changes its sign around $Q^2= 0.3 {GeV}^2$. It becomes weakly $Q^2$-dependent for $Q^2 > 1.0 {GeV}^2$ because of the quick decline of the resonance contributions. We point out that the $Q^2$ variation of the GDH sum rule is very important for understanding the nucleon spin structure in the non-perturbative QCD region.
{
"annotation_id": "248b0767-333d-4a8a-8408-71d0be5bef1b",
"date_created": "2026-03-02T18:00:22.213000Z",
"date_modified": "2026-03-02T18:00:22.213000Z",
"file_hash": "39eaa31f7e94e8070ec5b1ec95a25fc40008332435ef4d3cdf8f9051931a59c6",
"private": false,
"record": {
"abstract": "We test the Gerasimov-Drell-Hearn (GDH) sum rule numerically by calculating\nthe total photon absorption cross sections $\\sigma_{1/2}$ and $\\sigma_{3/2}$ on\nthe nucleon via photon excitation of baryon resonances in the constituent quark\nmodel. A total of seventeen, low-lying, non-strange baryon resonances are\nincluded in this calculation. The transverse and longitudinal interference\ncross section, $\\sigma_{1/2}^{TL}$, is found to play an important role in the\nstudy of the $Q^2$ variation of the sum rule. The results show that the GDH sum\nrule is saturated by these resonances at a confidence level of 94%. In\nparticular, the $P_{33}(1232)$ excitation largely saturates the sum rule at\n$Q^2 = 0$, and dominates at small $Q^2$. The GDH integral has a strong\n$Q^2$-dependence below $Q^2= 1.0 {GeV}^2$ and changes its sign around $Q^2= 0.3\n{GeV}^2$. It becomes weakly $Q^2$-dependent for $Q^2 \u003e 1.0 {GeV}^2$ because of\nthe quick decline of the resonance contributions. We point out that the $Q^2$\nvariation of the GDH sum rule is very important for understanding the nucleon\nspin structure in the non-perturbative QCD region.",
"arxiv_id": "nucl-th/9712036",
"authors": [
"W. X. Ma",
"D. H. Lu",
"A. W. Thomas",
"Z. P. Li"
],
"categories": [
"nucl-th"
],
"doi": "10.1016/S0375-9474(98)00202-4",
"journal_ref": "Nucl.Phys.A635:497-508,1998",
"title": "$Q^2$--Dependence of the Gerasimov-Drell-Hearn Sum Rule",
"url": "https://arxiv.org/abs/nucl-th/9712036"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "952f4ae6-0456-474c-9fef-6cb6143c400f",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}