Quark-Hadron Duality in Neutron (${}^3\mathrm{He}$) Spin Structure

We present experimental results of the first high-precision test of quark-hadron duality in the spin-structure function $g_1$ of the neutron and ${}^3\mathrm{He}$ using a polarized ${}^3\mathrm{He}$ target in the four-momentum-transfer-squared range from 0.7 to $4.0(\mathrm{GeV}/c{)}^2$. Global duality is observed for the spin-structure function $g_1$ down to at least $Q^2=1.8(\mathrm{GeV}/c{)}^2$ in both targets. We have also formed the photon-nucleon asymmetry $A_1$ in the resonance region for ${}^3\mathrm{He}$ and found no strong $Q^2$ dependence above $2.2(\mathrm{GeV}/c{)}^2$.

Figure 1

The spin-structure function $g_1^{{}^3\mathrm{He}}$ (per nucleon) in the resonance region at $Q^2$-values of 1.2, 1.8, 2.4, and $3.0(\mathrm{GeV}/c{)}^2$. The error bars represent the total uncertainties with the inner part being statistical only. Also plotted are the DIS world data from experiments E154 [24] and E99-117 [25] (note that these data are at different $Q^2$). The curves were generated from the NLO parton distribution functions of Refs. [17, 18, 19, 20] to which target-mass corrections were applied.

Figure 2

${\tilde{\Gamma }}_1^{{}^3\mathrm{He}}$ and ${\tilde{\Gamma }}_1^n$: test of spin duality on ${}^3\mathrm{He}$ (top) and neutron (bottom). Also plotted are the DIS parametrizations of Blümlein and Böttcher [17] (gray band), GRSV [18] (solid curve), AAC [19] (dashed curve) and LSS [20] (dotted curve) after applying target-mass corrections. The open circles are data from JLab experiment E94-010 [9]. The bands on the $x$ axis represent the systematic uncertainty of each data set.

Figure 3

Experiment $A_1^{{}^3\mathrm{He}}$ in the resonance region. DIS data are from SLAC E142 [33], E154 [24], from DESY experiment HERMES [34], and from JLab experiment E99-117 [25]. The error bars represent the total uncertainties with the inner part being statistical only. The curve represents a fit to the $A_1^{{}^3\mathrm{He}}$ DIS data (see text). The arrows in the black frame point to the $\Delta (1232)$ peak position for each of our data sets.