The NNLO non-singlet QCD analysis of parton distributions based on Bernstein polynomials

Abstract

A non-singlet QCD analysis of the structure function $x{F}_3$ up to NNLO is performed based on the Bernstein polynomials approach. We use recently calculated NNLO anomalous dimension coefficients for the moments of the $x{F}_3$ structure function in $\nu N$ scattering. In the fitting procedure, Bernstein polynomial method is used to construct experimental moments from the $x{F}_3$ data of the CCFR collaboration in the region of $x$ which is inaccessible experimentally. We also consider Bernstein averages to obtain some unknown parameters which exist in the valence quark densities in a wide range of $x$ and $Q^2$. The results of valence quark distributions up to NNLO are in good agreement with the available theoretical models. In the analysis we determined the QCD-scale ${\Lambda }_{QCD,N_f=4}^{\overline{MS}}=211$ MeV (LO), 259 MeV (NLO) and 230 MeV (NNLO), corresponding to ${\alpha }_s(M_Z^2)=0.1291$ LO, ${\alpha }_s(M_Z^2)=0.1150$ NLO and ${\alpha }_s(M_Z^2)=0.1142$ NNLO. We compare our results for the QCD scale and the ${\alpha }_s(M_Z^2)$ with those obtained from deep inelastic scattering processes.

20 pages, 7 figures, published in JHEP

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Cited by in corpus (6)

• NNLO QCD contributions to the flavor non-singlet sector of ${\mathbf{F}}_2(\mathbf{x},{\mathbf{Q}}^2)$
• QCD analysis of structure functions in deep inelastic neutrino-nucleon scattering without using the orthogonal polynomials approach
• Improved analysis of moments of F3 in neutrino-nucleon scattering using the Bernstein polynomial method
• QCD analysis of $x{F}_3$ structure functions in deep-inelastic scattering: Mellin transform by Gegenbauer polynomial up to N${}^3$LO approximation
• Symmetry breaking effect on determination of polarized and unpolarized parton distributions
• QCD analysis of valence structure functions using deep inelastic lepton-nucleon scattering