Measurement of the Proton Spin Structure Function $g_1(x,Q^2)$ for $Q^2$ from 0.15 to $1.6{\mathrm{G}\mathrm{e}\mathrm{V}}^2$ with CLAS

Double-polarization asymmetries for inclusive $ep$ scattering were measured at Jefferson Lab using 2.6 and 4.3 GeV longitudinally polarized electrons incident on a longitudinally polarized ${\mathrm{N}\mathrm{H}}_3$ target in the CLAS detector. The polarized structure function $g_1(x,Q^2)$ was extracted throughout the nucleon resonance region and into the deep inelastic regime, for $Q^2=0.15–1.64{\mathrm{G}\mathrm{e}\mathrm{V}}^2$. The contributions to the first moment ${\Gamma }_1(Q^2)=\int g_1(x,Q^2)dx$ were determined up to $Q^2=1.2{\mathrm{G}\mathrm{e}\mathrm{V}}^2$. Using a parametrization for $g_1$ in the unmeasured low $x$ regions, the complete first moment was estimated over this $Q^2$ region. A rapid change in ${\Gamma }_1$ is observed for $Q^2<1{\mathrm{G}\mathrm{e}\mathrm{V}}^2$, with a sign change near $Q^2=0.3{\mathrm{G}\mathrm{e}\mathrm{V}}^2$, indicating dominant contributions from the resonance region. At $Q^2=1.2{\mathrm{G}\mathrm{e}\mathrm{V}}^2$ our data are below the perturbative QCD evolved scaling value.

Figure 1

The photon asymmetry $A_1+\eta A_2$ vs the invariant hadronic mass $W$ (GeV) for the proton in two $Q^2$ bins. The lower $Q^2$ data were obtained with a beam energy of 2.6 GeV and the higher with 4.3 GeV. The dashed curves show our model estimates of $\eta A_2$. The error bars denote statistical uncertainties and the shaded bands near the bottom of the plot indicate the magnitude of the systematic uncertainties ($1\sigma$).

Figure 2

The polarized structure function $g_1(x)$ vs $x$ for the proton for five $Q^2$ bins. The solid lines show the parametrization described in the text. The error bars denote statistical uncertainties and the shaded area at the bottom of each plot indicates the magnitude of the systematic uncertainties ($1\sigma$).

Figure 3

The first moment ${\Gamma }_1$ vs $Q^2$ for the proton. The closed circles are obtained by integrating over our measurements of $g_1$. The open circles are obtained by using the inclusive scattering model to extend the integral down to $x={10}^{-5}$. The error bars indicate statistical uncertainties. The dark shaded region at the bottom shows the estimated systematic uncertainties ($1\sigma$) for the measured points. The line above the shaded region indicates the systematic uncertainty for the open circles. Measurements from SLAC [5] are shown as shaded squares with the double error bar indicating statistical uncertainty and ($\mathrm{\text{statistical}}+\mathrm{\text{systematic}}$) uncertainties. See the text for an explanation of the curves.