Target Single Spin Asymmetry in DIS $\vec{N}(e,e^\prime)$ using Transversely Polarized Proton and Neutron ($^3$He) Targets

We present an experiment to measure the transversely polarized target Single Spin Asymmetry (SSA) from inclusive DIS $\vec{N}(e,e^\prime)$ using transversely polarized NH$_3$ and $^3$He targets. This experiment will be carried out in Hall A using the large acceptance solenoid spectrometer (SoLID). The SSA, $A_{UT}$, is expected to have a $\sin(\phi_S)$-dependence, where $\phi_S$ is the azimuthal angle of the target polarization relative to the electron plane and perpendicular to the virtual photon direction. At Born level, the asymmetry is identically zero due to time-reversal invariance and parity conservation. However, it can be non-zero when two-photon exchange is included and therefore provides fertile ground for studying this processes in the absence of a large Born contribution. Parton-model predictions for the intermediate state of the nucleon during two-photon exchange predict asymmetries from $\pm (10^{-4} - 10^{-2}$) depending on model input and target nucleon. This experiment is expected to reach a statistical uncertainty of $\sim 10^{-4}$ at $Q^2 = 1.5$ GeV$^2$ up to $\sim 10^{-3}$ at $Q^2 = 7.5$ GeV$^2$ with $W > 2$ GeV and $0.05 < x < 0.65$.