Measurement of Generalized GDH Integrand for the Neutron and 3He at Low Q2

Despite the success of QCD at high energies where the perturbation calculations can be carried out because of the asymptotic freedom, many fundamental questions, regarding the confinement of quarks and gluons, the nuclear forces, and the nucleon mass and structure, still remain in the non-perturbative regime. Dispersive sum rules, based on universal principles, provide a data-driven approach to study the nucleon structure without model-dependencies. Among those sum rules, the well known Gerasimov-Drell-Hearn (GDH) sum rule relates the anomalous magnetic moment to a weighted integral over the photo-absorption cross section. Its generalized form is extended for the virtual photon absorption at an arbitrary four momentum transfer square ($Q^2$) and thus provides a unique relation to study the nucleon spin structure over an experimentally accessible range of $Q^2$. The measured integrals can be compared with theoretical predictions for the spin dependent Compton amplitudes. Such experimental tests at intermediate and low $Q^2$ deepen our knowledge of the transition from the asymptotic freedom regime to the color confinement regime in QCD.

Experiment E97-110 has been performed at the Thomas Jefferson National Accelerator Facility to precisely measure the generalized GDH sum rule and the moments of the neutron and $^3$He spin structure functions in the low energy region. During the experiment, a longitudinally-polarized electron beam with energies from 1.1 to 4.4 GeV was scattered from a $^3$He gas target which was polarized longitudinally or transversely at the Hall A center. Inclusive asymmetries and polarized cross-section differences, as well as the unpolarized cross sections, were measured in the quasielastic and resonance regions. In this work, the $^3$He spin dependent structure functions of $g_1(\nu, Q^2)$ and $g_2(\nu, Q^2)$ at $Q^2 = 0.032\mhyphen0.230$ GeV$^2$ have been extracted from the experimental data, and the generalized GDH sum rule of $^3$He is firstly obtained for $Q^2 < 0.1$ GeV$^2$. The results exhibit a ``turn-over'' behavior at $Q^2 = 0.1$ GeV$^2$, which strongly indicates that the GDH sum rule for real photons will be recovered at $Q^2 \rightarrow 0$.