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

**Authors:**D. Flay, M. Posik, D. S. Parno, K. Allada, W. Armstrong, T. Averett, F. Benmokhtar, W. Bertozzi, A. Camsonne, M. Canan, G. D. Cates, C. Chen, J. -P. Chen, S. Choi, E. Chudakov, F. Cusanno, M. M. Dalton, W. Deconinck, C. W. de Jager, X. Deng, A. Deur, C. Dutta, L. El Fassi, G. B. Franklin, M. Friend, H. Gao, F. Garibaldi, S. Gilad, R. Gilman, O. Glamazdin, S. Golge, J. Gomez, L. Guo, O. Hansen, D. W. Higinbotham, T. Holmstrom, J. Huang, C. Hyde, H. F. Ibrahim, X. Jiang, G. Jin, J. Katich, A. Kelleher, A. Kolarkar, W. Korsch, G. Kumbartzki, J. J. LeRose, R. Lindgren, N. Liyanage, E. Long, A. Lukhanin, V. Mamyan, D. McNulty, Z. -E. Meziani, R. Michaels, M. Mihovilovič, B. Moffit, N. Muangma, S. Nanda, A. Narayan, V. Nelyubin, B. Norum, Y. Oh, J. C. Peng, X. Qian, Y. Qiang, A. Rakhman, S. Riordan, A. Saha, B. Sawatzky, M. H. Shabestari, A. Shahinyan, S. Širca, P. Solvignon, R. Subedi, V. Sulkosky, A. Tobias, W. Troth, D. Wang, Y. Wang, B. Wojtsekhowski, X. Yan, H. Yao, Y. Ye, Z. Ye, L. Yuan, X. Zhan, Y. Zhang, Y. -W. Zhang, B. Zhao, X. Zheng

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. This quantity 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 spin structure functions $g_1$ and $g_2$ on $^{3}$He after
nuclear corrections had been applied to these moments. The 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 DIS and resonance regions. We
found $d_2^n$ to be small and negative for $ = 3.2$ GeV$^{2}$, and
smaller for $

= 4.3$ GeV$^{2}$, consistent with a lattice QCD
calculation. The twist-4 matrix element $f_{2}^{n}$ was extracted by combining
our $d_{2}^{n}$ with the world data on $\Gamma_{1}^{n} = \int_{0}^{1} g_{1}^{n}
dx$. 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 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 instanton model predictions but not with those
from QCD sum rules. Additionally, we have extracted the neutron virtual
photon-nucleon asymmetry $A_{1}^{n}$, the structure function ratio
$g_{1}^{n}/F_{1}^{n}$, and the quark ratios $(\Delta u + \Delta \bar{u})/(u +
\bar{u})$ and $(\Delta d + \Delta \bar{d})/(d + \bar{d})$. These results were
found to be consistent with DIS world data and with the prediction of the
constituent quark model but at odds with those of perturbative QCD at large
$x$.

**Comments:**55 Pages, 45 figures, 48 tables. 15 supplemental files. Grammatical and typo fixes. Revised some model descriptions and updated analyses for f_2^n and color forces

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