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$\leq Q^{2}\leq$4.8 GeV$^{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 $f_{2}^{p-n}=-0.064 \pm0.009\pm_{0.036}^{0.032}$. This leads to the color polarizabilities $\chi_{E}^{p-n}=-0.032\pm0.024$ and $\chi_{B}^{p-n}=0.032\pm0.013$. The strong force coupling is determined to be $\alpha_{s}^{\overline{\mbox{ MS}}}(M_{Z}^{2})=0.1124\pm0.0061$, 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.