The Gerasimov - Drell - Hearn Sum Rule Klaus Helbing

Sum rules measurements involving the spin structure of the nucleon like those due to Bjorken, Ellis and Jaffe and the one due to Gerasimov, Drell and Hearn allow to study the structure of strong interactions. At long distance scales in the confinement regime the Gerasimov-DrellHearn (GDH) Sum Rule (Eq. (1)) connects static properties of the nucleon like the anomalous magnetic moment and the nucleon mass with the difference of spin dependent doubly polarized total absorption cross sections of real photons. Hence, the full spin-dependent excitation spectrum of the nucleon is being related to its static properties. The sum rule has not been investigated experimentally until recently. Now, for the first time this fundamental sum rule is verified by the GDH-Collaboration with circularly polarized real photons and longitudinally polarized nucleons at the two accelerators Elsa and Mami. The investigation of the response of the proton as well as of the neutron allows to perform an isospin decomposition. Further investigations with real photons are scheduled at Slac, JLab, Spring-8, Legs and Graal. The integral (sum) of the GDH Sum Rule can be generalized to the case of virtual photons. This allows to establish a Q2 dependency and to study the transition to the perturbative regime of QCD. Ultimately, the GDH Sum Rule can be related to the Bjorken and the Ellis-Jaffe Sum Rule. This transition is the subject of several experiments e.g. at JLab for the resonance region and of the Hermes experiment at Desy for higher Q2. This contribution covers the status of theory concerning the GDH Sum Rule as well as the experimental approaches and their results for the absorption of real and virtual photons. We point out that the so-called No-Subtraction hypothesis, often considered the weakest part of the derivation of the GDH Sum Rule, in fact follows from unitarity and does not impair the fundamental character of the GDH Sum Rule. The experimental data verify the GDH Sum Rule for the proton at the level of 8 % including the systematic uncertainties from extrapolations to unmeasured energy regions. For the GDH Sum Rule on the neutron and the isovector case we find unexpected contributions at photon energies above 1 GeV. Now at Bergische Universität Wuppertal, Fachbereich C – Physik, Gaußstr. 20, D-42119 Wuppertal, Germany; [email protected]