Extracting the Partial Bjorken Sum from World Data and SoLID 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 $Q^2$ evolution of 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 22 GeV 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 $x$ coverage than previously achieved in the $Q^2$ region where the Bjorken sum is the most sensitive to $\alpha_s$ extraction. We investigate how this larger coverage will contribute to the reduction of uncertainty of the strong coupling constant, $\alpha_s$.