Measurements of ${d}_{2}^{n}$ and ${A}_{1}^{n}$: Probing the neutron spin structure

Measurements of $d_{2}^{n}$ and $A_{1}^{n}$ : Probing the neutron spin structure

D. Flay et al. (Jefferson Lab Hall A Collaboration)

Phys. Rev. D 94, 052003 – Published 6 September 2016

Abstract

We report on the results of the E06-014 experiment performed at Jefferson Lab in Hall A, where a precision measurement of the twist-3 matrix element $d_{2}$ of the neutron ( $d_{2}^{n}$ ) was conducted. The quantity $d_{2}^{n}$ represents the average color Lorentz force a struck quark experiences in a deep inelastic electron scattering event off a neutron due to its interaction with the hadronizing remnants. This color force was determined from a linear combination of the third moments of the ${}^{3}{He}$ spin structure functions, $g_{1}$ and $g_{2}$ , after nuclear corrections had been applied to these moments. The structure functions were obtained from a measurement of the unpolarized cross section and of double-spin asymmetries in the scattering of a longitudinally polarized electron beam from a transversely and a longitudinally polarized ${}^{3}{He}$ target. The measurement kinematics included two average $Q^{2}$ bins of $3.2 {GeV}^{2}$ and $4.3 {GeV}^{2}$ , and Bjorken- $x$ $0.25 \leq x \leq 0.90$ covering the deep inelastic and resonance regions. We have found that $d_{2}^{n}$ is small and negative for $⟨ Q^{2} ⟩ = 3.2 {GeV}^{2}$ , and even smaller for $⟨ Q^{2} ⟩ = 4.3 {GeV}^{2}$ , consistent with the results of a lattice QCD calculation. The twist-4 matrix element $f_{2}^{n}$ was extracted by combining our measured $d_{2}^{n}$ with the world data on the first moment in $x$ of $g_{1}^{n}$ , ${Γ がんま}_{1}^{n}$ . We found $f_{2}^{n}$ to be roughly an order of magnitude larger than $d_{2}^{n}$ . Utilizing the extracted $d_{2}^{n}$ and $f_{2}^{n}$ data, we separated the Lorentz color force into its electric and magnetic components, $F_{E}^{y, n}$ and $F_{B}^{y, n}$ , and found them to be equal and opposite in magnitude, in agreement with the predictions from an instanton model but not with those from QCD sum rules. Furthermore, using the measured double-spin asymmetries, we have extracted the virtual photon-nucleon asymmetry on the neutron $A_{1}^{n}$ , the structure function ratio $g_{1}^{n} / F_{1}^{n}$ , and the quark ratios $(Δ でるた u + Δ でるた \bar{u}) / (u + \bar{u})$ and $(Δ でるた d + Δ でるた \bar{d}) / (d + \bar{d})$ . These results were found to be consistent with deep-inelastic scattering world data and with the prediction of the constituent quark model but at odds with the perturbative quantum chromodynamics predictions at large $x$ .