A Precision Measurement of the Proton and Neutron $g_{2}$ and $d_{2}$ with SoLID

We propose a precision measurement of the proton and neutron spin structure function $g_{2} (x,Q^{2})$ by using a Solenoidal Large Intensity Device (SoLID) at Jefferson Lab (JLab) Hall A with the 12 GeV upgrade. We will obtain data with high statistics and large kinematic coverage for Bjorken $0.1 < x < 0.9 $ and four momentum transfer $ 1<Q^{2}<10\;GeV^{2}$ by a longitudinally polarized electron beam scattering on polarized $NH_{3}$ and $^{3}He$ targets. In addition to mapping out the $x$ and $Q^{2}$ evolution of $g_{2}$, we will extract the twist-3 matrix element $d_{2}(Q^{2})$, which is connected to the quark-gluon correlations within the nucleon. This quantity has been calculated in Lattice QCD and different nucleon structure models, which is one of the cleanest observables that can be used to test the theory.