Extraction of the proton and neutron polarized structure function measurements and partial Bjorken sum from SoLID 22GeV Simulations

The strong coupling constant $\alpha_s$ describes the strength of the strong nuclear force, one of the fundamental forces in the universe. One way of extracting $\alpha_s$ is to use the Bjorken sum $\Gamma_{1}^{p-n} = \int_0^1dx (g_1^p - g_1^n)$, where $g_1^p$ and $g_1^n$ are the polarized structure functions of the proton and neutron, respectively. Using simulated data with a 22GeV electron beam, a polarized $^3$He and a polarized NH$_3$ target, and with the scattered electrons detected by the Solenoidal Large Intensity Device (SoLID) at Jefferson Lab (JLab), this study investigates the expected uncertainty in the polarized structure functions for a larger Bjorken $x$ coverage than what can be achieved with the future electron ion collider (EIC) alone. We investigate how this larger coverage will contribute to the reduction of uncertainty of the strong coupling constant, $\alpha_s$.