High precision determination of the $Q^2$-evolution of the Bjorken Sum

We present a significantly improved determination of the Bjorken Sum for 0.6$\le Q^2\le$4.8 GeV${}^2$ using precise new $g_1^p$ and $g_1^d$ data taken with the CLAS detector at Jefferson Lab. A higher-twist analysis of the $Q^2$-dependence of the Bjorken Sum yields the twist-4 coefficient $f_2^{p-n}=-0.064\pm 0.009{\pm }_{0.036}^{0.032}$. This leads to the color polarizabilities ${\chi }_E^{p-n}=-0.032\pm 0.024$ and ${\chi }_B^{p-n}=0.032\pm 0.013$. The strong force coupling is determined to be ${\alpha }_s^{\overline{MS}}(M_Z^2)=0.1124\pm 0.0061$, which has an uncertainty a factor of 1.5 smaller than earlier estimates using polarized DIS data. This improvement makes the comparison between ${\alpha }_s$ extracted from polarized DIS and other techniques a valuable test of QCD.