Revealing Color Forces with Transverse Polarized Electron Scattering

The Spin Asymmetries of the Nucleon Experiment (SANE) measured two double spin asymmetries (nearly transverse and longitudinal) using a polarized proton target and polarized electron beam at two beam energies, 4.7 GeV and 5.9 GeV. A large-acceptance open-configuration detector package identified scattered electrons at 40$^{\circ}$ 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 GeV$^2$. The data display the opposite sign compared to most quark models including the lattice 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.