Determination of $\alpha_s$ and the Nucleon Spin Decomposition Using Recent Polarized Structure Function Data

New data on polarized $\mu-p$ and $e-p$ scattering permit a first determination of $\alpha_s$ using the Bjorken sum rule, as well as higher precision in determining the nucleon spin decomposition. Using perturbative QCD calculations to $O(\alpha_s^4)$ for the non-singlet combination of structure functions, we find $\alpha_s(2.5 GeV^2) = 0.375^{+0.062}_{-0.081}$, corresponding to $\alpha_s(M_Z^2) =0.122^{+0.005}_{-0.009}$, and using calculations to $O(\alpha_s^3)$ for the singlet combination we find $\Delta u = 0.83 \pm 0.03$, $\Delta d= -0.43 \pm 0.03$, $\Delta s =-0.10 \pm 0.03$, $\Delta \Sigma \equiv \Delta u + \Delta d + \Ds = 0.31 \pm 0.07$, at a renormalization scale $Q^2=10 GeV^2$. Perturbative QCD corrections play an essential role in reconciling the interpretations of data taken using different targets. We discuss higher-twist uncertainties in these determinations. The $\Delta q$ determinations are used to update predictions for the couplings of massive Cold Dark Matter particles and axions to nucleons.