Determination of ${\alpha }_s$ and the Nucleon Spin Decomposition Using Recent Polarized Structure Function Data

Abstract

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 ${\alpha }_s(2.5Ge{V}^2)=0.375_{-0.081}^{+0.062}$, corresponding to ${\alpha }_s(M_Z^2)=0.122_{-0.009}^{+0.005}$, and using calculations to $O({\alpha }_s^3)$ for the singlet combination we find $\Delta u=0.83\pm 0.03$, $\Delta d=-0.43\pm 0.03$, $\Delta s=-0.10\pm 0.03$, $\Delta \Sigma \equiv \Delta u+\Delta d+\text{Ds}=0.31\pm 0.07$, at a renormalization scale $Q^2=10Ge{V}^2$. 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.

Comments: 15 pages (LateX) + 5 postscript figures appended after the text; CERN-TH-7324/94, TAUP-2178-94