Moments of the neutron $g_2$ structure function at intermediate $Q^2$

We present new experimental results for the ${}^3\mathrm{He}$ spin structure function $g_2$ in the resonance region at $Q^2$ values between 1.2 and 3.$0(\text{GeV}/c){}^2$. Spin dependent moments of the neutron were extracted. Our main result, the inelastic contribution to the neutron $d_2$ matrix element, was found to be small at $\langle Q^2\rangle =2.4{(\mathrm{GeV}/c)}^2$ and in agreement with the lattice QCD calculation. The Burkhardt-Cottingham sum rule for ${}^3\mathrm{He}$ and the neutron was tested with the measured data and using the Wandzura-Wilczek relation for the low $x$ unmeasured region.

Figure 1

The spin-structure function $g_2^{{}^3\mathrm{He}}$ (per nucleon) in the resonance region at $Q^2$ values of 1.2, 1.8, 2.4, and 3.$0(\text{GeV}/c){}^2$. The error bars represent the total uncertainties with the inner part being statistical only. Also plotted are the DIS JLab data from experiments E97-103 [5] and E99-117 [6, 7] (note that these data are at different $Q^2)$. The curves were generated from the NLO parton distribution functions of Refs. [8, 9, 10, 11].

Figure 2

Result on inelastic contribution to the neutron $x^2$-weighted moment $d_2^n\left(Q^2\right)$ from E01-012. The elastic contribution is displayed by the brown band. The inner (outer) error bar represents statistical (total) uncertainty. The resonance contributions to $d_2^n\left(Q^2\right)$ from JLab experiments E94-010 [24] and RSS [25] are also shown; the error bars are statistical only and the grey band represents the experimental systematics uncertainties. To be compared with the resonance contribution, we plotted the MAID model [26]. Also plotted are the total $d_2^n$ from SLAC E155x [27] and JLab E99-117 [6, 7] combined, and, the lattice QCD prediction [28].

Figure 3

The ${}^3\mathrm{He}$ (top panel) and neutron (bottom panel) ${\mathrm{\Gamma }}_2$ integrals from JLab E01-012 (filled squares). The error bars are statistical only, the upper band represents the experimental systematics, and the lower band the uncertainties on the unmeasured part of the BC sum. The open square data are the measured part of the integral as was performed by experiment E01-012. Also plotted are data from JLab experiments E94-010 [24, 30] and RSS [25], with also the measured part of the integral represented by open and shaded symbols and the extrapolated BC sum with filled symbols, and SLAC experiment E155x [27]. The elastic (solid line) and quasielastic (dashed line) contributions to the integrals are plotted.