The Spin Structure of <sup>3</sup>He and the Neutron at Low Q<sup>2</sup>: A Measurement of the Generalized GDH Integrand

Abstract

Since the 1980's, the study of nucleon (proton or neutron) spin structure has been an active field both experimentally and theoretically. One of the primary goals of this work is to test our understanding of Quantum Chromodynamics (QCD), the fundamental theory of the strong interaction. In the high energy region of asymptotically free quarks, QCD has been verified. However, verifiable predictions in the low energy region are harder to obtain due to the complex interactions between the nucleon's constituents: quarks and gluons. In the non-pertubative regime, low-energy effective field theories such as chiral perturbation theory provide predictions for the spin structure functions in the form of sum rules. Spin-dependent sum rules such as the Gerasimov-Drell-Hearn (GDH) sum rule are important tools available to study nucleon spin structure. Originally derived for real photon absorption, the Gerasimov-Drell-Hearn (GDH) sum rule was first extended for virtual photon absorption in 1989. The extension of the sum rule provides a unique relation, valid at any momentum transfer ($Q^{2}$), that can be used to study the nucleon spin structure and make comparisons between theoretical predictions and experimental data. Experiment E97-110 was performed at the Thomas Jefferson National Accelerator Facility (Jefferson Lab) to examine the spin structure of the neutron and $^{3}$He. The Jefferson Lab longitudinally-polarized electron beam with incident energies between 1.1 and 4.4 GeV was scattered from a longitudinally or transversely polarized $^{3}$He gas target in the Hall A end station. Asymmetries and polarized cross-section differences were measured in the quasielastic and resonance regions to extract the spin structure functions $g_{1}(x,Q^{2})$ and $g_{2}(x,Q^{2})$ at low momentum transfers (0.02 $< Q^{2} <$ 0.3 GeV$^{2}$). The goal of the experiment was to perform a precise measurement of the $Q^{2}$ dependence of the extended GDH integral and of the moments of the neutron and $^{3}$He spin structure functions at low $Q^{2}$. This $Q^{2}$ range allows us to test predictions of chiral perturbation theory and check the GDH sum rule by extrapolating the integral to the real photon point. This thesis will discuss preliminary results from the E97-110 data analysis.