A Precision Measurement of the Neutron Twist-3 Matrix Element $d_2^n$: Probing Color Forces

Abstract

Double-spin asymmetries and absolute cross sections were measured at large Bjorken $x$ (0.25 $\le x\le$ 0.90), in both the deep-inelastic and resonance regions, by scattering longitudinally polarized electrons at beam energies of 4.7 and 5.9 GeV from a transversely and longitudinally polarized ${}^3$He target. In this dedicated experiment, the spin structure function $g_2$ on ${}^3$He was determined with precision at large $x$, and the neutron twist-three matrix element $d_2^n$ was measured at $⟨Q^2⟩$ of 3.21 and 4.32 GeV${}^2$/$c^2$, with an absolute precision of about $10^{-5}$. Our results are found to be in agreement with lattice QCD calculations and resolve the disagreement found with previous data at $⟨Q^2⟩=$ 5 GeV${}^2$/$c^2$. Combining $d_2^n$ and a newly extracted twist-four matrix element, $f_2^n$, the average neutron color electric and magnetic forces were extracted and found to be of opposite sign and about 30 MeV/fm in magnitude.

Corrected a typo in the author list and Figure 1 legend. 6 pages, 2 figures, 2 tables