Q^2 Evolution of the Neutron Spin Structure Moments using a He-3 Target

TL;DR

This study measures the neutron's spin structure functions using a polarized helium-3 target across a range of momentum transfer values, revealing the $Q^2$ evolution of key moments and testing fundamental sum rules.

Contribution

First measurement of the $Q^2$ evolution of neutron spin structure moments $ ext{Gamma}_1$, $ ext{Gamma}_2$, and $d_2$ in the low $Q^2$ region using a $^3$He target.

Findings

$ ext{Gamma}_1(Q^2)$ varies smoothly from high to low $Q^2$.

The Burkhardt-Cottingham sum rule is satisfied within uncertainties.

The $d_2$ moment is non-zero over the measured $Q^2$ range.

Abstract

We have measured the spin structure functions $g_1$ and $g_2$ of $^3$He in a double-spin experiment by inclusively scattering polarized electrons at energies ranging from 0.862 to 5.07 GeV off a polarized $^3$He target at a 15.5$^{\circ}$ scattering angle. Excitation energies covered the resonance and the onset of the deep inelastic regions. We have determined for the first time the $Q^2$ evolution of $\Gamma_1(Q^2)=\int_0^{1} g_1(x,Q^2) dx$, $\Gamma_2(Q^2)=\int_0^1 g_2(x,Q^2) dx$ and $d_2 (Q^2) = \int_0^1 x^2[ 2g_1(x,Q^2) + 3g_2(x,Q^2)] dx$ for the neutron in the range 0.1 GeV$^2$ $\leq Q^2 \leq $ 0.9 GeV$^2$ with good precision. $ \Gamma_1(Q^2)$ displays a smooth variation from high to low $Q^2$. The Burkhardt-Cottingham sum rule holds within uncertainties and $d_2$ is non-zero over the measured range.