$Q^2$ Evolution of the Neutron Spin Structure Moments using a ${}^3\mathrm{H}\mathrm{e}$ Target

We have measured the spin structure functions $g_1$ and $g_2$ of ${}^3\mathrm{H}\mathrm{e}$ in a double-spin experiment by inclusively scattering polarized electrons at energies ranging from 0.862 to 5.058 GeV off a polarized ${}^3\mathrm{H}\mathrm{e}$ target at a $15.5°$ 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 $0.1\le Q^2\le 0.9{\mathrm{G}\mathrm{e}\mathrm{V}}^2$ 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 nonzero over the measured range.

Figure 1

$g_1$ (dark filled circles) and $g_2$ (grey filled squares) of ${}^3\mathrm{H}\mathrm{e}$ are plotted as a function of the Bjorken variable $x$ for six values of $Q^2$. The points shown with filled (open) circles or squares were determined by interpolation (extrapolation).

Figure 2

Results of ${\overline{\Gamma }}_1^n$ (top panel), ${\Gamma }_2^n$ (middle panel), ${\overline{d}}_2^n$ (bottom panels) along with the world data from DIS and theoretical predictions (see text).