The Spin Asymmetries of the Nucleon Experiment measured two double spin asymmetries using a polarized proton target and polarized electron beam at two beam energies, 4.7 and 5.9 GeV. A large-acceptance open-configuration detector package identified scattered electrons at 40° and covered a wide range in Bjorken $x$ ($0.3<x<0.8$). Proportional to an average color Lorentz force, the twist-3 matrix element, ${\tilde{d}}_2^p$, was extracted from the measured asymmetries at $Q^2$ values ranging from 2.0 to $6.0{\mathrm{GeV}}^2$. The data display the opposite sign compared to most quark models, including the lattice QCD result, and an unexpected scale dependence. Furthermore, when combined with the neutron data in the same $Q^2$ range the results suggest a flavor independent average color Lorentz force.

• Received 28 May 2018
• Revised 18 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.022002