Document Type


Publication Date




Publication Title

Physical Review D






052003 (51 pages)


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 d2 of the neutron dⁿ2 was conducted. The quantity dⁿ2 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 3He spin structure functions, g1 and g2, 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 3He target. The measurement kinematics included two average Q2 bins of 3.2 GeV2 and 4.3 GeV2, and Bjorken-x 0.25 <= x <= 0.90 covering the deep inelastic and resonance regions. We have found that dⁿ2 is small and negative for Q2 = 3.2 GeV2, and even smaller for Q2 = 4.3 GeV2, consistent with the results of a lattice QCD calculation. The twist-4 matrix element fⁿ2 was extracted by combining our measured dⁿ2 with the world data on the first moment in x of gⁿ1, Γⁿ1. We found fⁿ2 to be roughly an order of magnitude larger than dⁿ2. Utilizing the extracted dⁿ2 and fⁿ2 data, we separated the Lorentz color force into its electric and magnetic components, FyEn and FyBn, 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 An1, the structure function ratio gn1/Fn1, and the quark ratios (Δu +Δū)/(u + ū) and (Δd + Δ-d)/(d +-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.


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Original Publication Citation

Flay, D., Posik, M., Parno, D. S., Allada, K., Armstrong, W. R., Averett, T., . . . Jefferson Lab Hall, A. C. (2016). Measurements of dⁿ² and Aⁿ¹: Probing the neutron spin structure. Physical Review D, 94(5), 052003. doi:10.1103/PhysRevD.94.052003


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