Precision Measurement of $d_2^n$: Probing the Lorentz Color Force

In order to gain a better understanding of the spin structure of the neutron, the experiment to measure the quantity $d_2^n$ was carried out from February to March of 2009 at Jefferson Lab. The experiment consisted of measuring the asymmetries $A_{\vert \vert}$ and $A_\perp$, and the total cross section $\sigma_0$ by scattering a longitudinally polarized electron beam off of a longitudinally and transversely polarized $^3$He target. The experiment covered excitation energies in the deep inelastic valence quark and resonance regions. From the asymmetries and total cross section, the spin dependent structure functions $g_1$ and $g_2$ will be extracted. Using these, the quantity $d_2^n$ is determined as the second moment of a linear combination of $g_1$ and $g_2$. $d_2^n$ is a measure of the Lorentz color force between quarks averaged over the volume of the neutron. The measurement will provide a benchmark test of Lattice QCD calculations of $d_2^n$ by lowering the uncertainty in the present value by a factor of approximately four. This measurement will also provide for further understanding of quark-gluon correlations in connection to the nucleon spin structure.