The Gerasimov–Drell–Hearn sum rule

Abstract

∞ 0 dν ν σ 3/2 (ν) − σ 1/2 (ν) = 2π 2 α m 2 κ 2 (1)Abstract 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-Drell-Hearn (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 Q 2 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 Q 2 .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.

Determination of the proton spin structure functions for 0.05<Q2<5GeV2 using CLAS

“…(24) was modified to allow a smooth connection to a finite value at the real photon point, Q 2 = 0. The seven parameters of this function were optimized by fitting this function to all world data at W > 2 GeV and the fit function, including real photon data from ELSA and MAMI (see, e.g., the summary by Helbing [116]). Each experiment was given an adjustable normalization factor as an additional parameter which was allowed to vary within the stated uncertainty due to global scale factors like the product P b P t .…”

Precise determination of the deuteron spin structure at low to moderateQ2with CLAS and extraction of the neutron contribution

“…The goodness of the fit (χ 2 ) was calculated by comparing the fit functions for neutron asymmetries directly with neutron results extracted from 3 He data, as well as comparing the convolu- tion of our proton and neutron models with corresponding deuteron data. To anchor our fit of A 1 at the photon point, we used data from ELSA and MAMI (see, e.g., the summary by Helbing [98]). As a result, we achieved a consistent fit of proton, deuteron and neutron data over a wide kinematic range, far exceeding our own kinematic coverage.…”

First Measurement of the Helicity Asymmetry forγp→pπ0in the Resonance Region

“…Deep inelastic scattering experiments have revealed gluonic contributions to the proton spin to be consistent with zero, at least within the admittedly large errors [2]. At low energies, a different aspect of the proton spin structure is tested by a comparison of the helicity dependence of the total γp cross section integrated over all photon energies, ∞ 0 dE γ (σ 3/2 − σ 1/2 )/E γ , with the proton magnetic moment [3], a relation which is known as Gerasimov-Drell-Hearn (GDH) sum rule [4,5]. The subscripts denote the total helicity, h = 1/2 for photon and proton spin anti-aligned, h = 3/2 for both spins aligned.…”

“…The contribution of single π 0 production to the GDH integral is evaluated. The total GDH integral up to 2.9 GeV was determined to I 2.9 tot = 226 ± 5 stat ± 12 syst µb [23][24][25][26][27]; the results were summarized in [3]. Here, a contribution of 27.5 µb had been subtracted to account for the description of the very low energy region by MAID [8].…”