Non--Singlet QCD Analysis of Deep Inelastic World Data at \boldmath $O({\alpha }_s^3)$

Abstract

A non--singlet QCD analysis of the structure function $F_2(x,q^2)$ in LO, NLO, NNLO and N${}^3$LO is performed based on the world data for charged lepton scattering. We determine the valence quark parton densities and present their parameterization and that of the correlated errors in a wide range of $x$ and $Q^2$. In the analysis we determined the QCD--scale $Λ_{\rm QCD, N_f = 4}^{\bar{\rm MS}} = 265 \pm 27 \MeV {\rm (NLO)}, 226 \pm 25 \MeV {\rm (NNLO)}, 234 \pm 26 \MeV {\rm (N^3LO)}$, with a remainder uncertainty of $\pm 2\MeV$ for the yet unknown 4--loop anomalous dimension, corresponding to ${\alpha }_s(M_Z^2)=0.1148\pm 0.0019\mathrm{NLO},0.1134\begin{array}{c}+0.0019-0.0021\end{array}\mathrm{NNLO},0.1141\begin{array}{c}+0.0020-0.0022\end{array}{\mathrm{N}}^3\mathrm{LO}$. A comparison is performed to other determinations of the QCD scale and ${\alpha }_s(M_Z^2)$ in deeply inelastic scattering. The higher twist contributions of $F_2^p(x,Q^2)$ and $F_2^d(x,Q^2)$ are extracted in the large $x$ region, subtracting the twist--2 contributions obtained in the NLO, NNLO and N${}^3$LO analysis.

35 pages, 15 figure, 1 style file

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