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

TL;DR

This paper reports new measurements of the neutron's $g_2$ structure function in the resonance region at intermediate $Q^2$, testing sum rules and comparing with lattice QCD, revealing small resonance contributions and minor deviations at lower $Q^2$.

Contribution

It provides the first experimental determination of the neutron $d_2$ matrix element in the resonance region at intermediate $Q^2$, and tests the Burkhardt-Cottingham sum rule with new data.

Findings

Resonance contribution to neutron $d_2$ is small at $<Q^2>=2.4$ (GeV/c)$^2$.

Data agrees with Lattice QCD calculations.

Small deviations from sum rule observed at lower $Q^2$.

Abstract

We present new experimental results of the $^3$He spin structure function $g_2$ in the resonance region at $Q^2$ values between 1.2 and 3.0 (GeV/c)$^2$. Spin dependent moments of the neutron were then extracted. Our main result, the resonance contribution to the neutron $d_2$ matrix element, was found to be small at $<Q^2>$=2.4 (GeV/c)$^2$ and in agreement with the Lattice QCD calculation. The Burkhardt-Cottingham sum rule for $^3$He and the neutron was tested with the measured data and using the Wandzura-Wilczek relation for the low $x$ unmeasured region. A small deviation was observed at $Q^2$ values between 0.5 and 1.2 (GeV/c)$^2$ for the neutron.