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

Abstract

New data on polarized $μ-p$ and $e-p$ scattering permit a first determination of $α_s$ using the Bjorken sum rule, as well as higher precision in determining the nucleon spin decomposition. Using perturbative QCD calculations to $O(α_s^4)$ for the non-singlet combination of structure functions, we find $α_s(2.5 GeV^2) = 0.375^{+0.062}_{-0.081}$, corresponding to $α_s(M_Z^2) =0.122^{+0.005}_{-0.009}$, and using calculations to $O(α_s^3)$ for the singlet combination we find $Δu = 0.83 \pm 0.03$, $Δd= -0.43 \pm 0.03$, $Δs =-0.10 \pm 0.03$, $ΔΣ\equiv Δu + Δd + \Ds = 0.31 \pm 0.07$, 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 $Δq$ determinations are used to update predictions for the couplings of massive Cold Dark Matter particles and axions to nucleons.