Precision Measurement of the Neutron Asymmetry A1n at Large Bjorken x at 12 GeV Jefferson Lab

The virtual photon asymmetry $A_1$ is one of the fundamental quantities that provide information on the spin structure of the nucleon. The value of $A_1$ at high $x_{Bj}$ is of particular interest because valence quarks dominate in this region, which makes it a relatively clean region to study the nucleon structure. Several theoretical calculations, including naive SU(6) quark model, relativistic constituent quark model (RCQM), perturbative QCD (pQCD), predict the behavior for $A_1$ and the quark polarization in the high $x_{Bj}$ valence quark region. The $A_1^n$ experiment during the 6 GeV JLab era showed that $A_1^n$ turns positive at $x\sim 0.5$, while up to the highest measured $x$ value of 0.61 the down quark polarization
$\Delta d/d$ remains negative, in contrast to the pQCD prediction. Subsequent theoretical studies following the 6 GeV results claimed that quark orbital angular momentum could delay the upward turn of $\Delta d/d$ to higher $x_{Bj}$ or the non-perturbative nature of the strong interaction could keep it negative all the way to $x_{Bj}=1$ as predicted in a Schwinger-Dyson approach with di-quark model assumptions. With the 12 GeV upgrade of JLab, a new experiment on $A_1^n$ (E12-06-110)$^1$ was carried out using a 10.4 GeV beam, a polarized $^3$He target, and the HMS and the Super-HMS (spectrometers) in Hall C. This measurement reached a deeper valence quark region, reaching up to $x\sim 0.75$. This thesis reports on the 3He asymmetries $A_{\parallel}$, $A_{\bot}$, $A_1^{^3He}$, and $A_2^{^3He}$ without radiative corrections.