QCD analysis of nucleon structure functions in deep-inelastic neutrino-nucleon scattering: Laplace transform and Jacobi polynomials approach

Abstract

We present a detailed QCD analysis of nucleon structure functions $x{F}_3(x,Q^2)$, based on Laplace transforms and Jacobi polynomials approach. The analysis corresponds to the next-to-leading order and next-to-next-to-leading order approximation of perturbative QCD. The Laplace transform technique, as an exact analytical solution, is used for the solution of nonsinglet Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at low- and large-$x$ values. The extracted results are used as input to obtain the $x$ and Q${}^2$ evolution of $x{F}_3(x,Q^2)$ structure functions using the Jacobi polynomials approach. In our work, the values of the typical QCD scale ${\Lambda }_{\overline{\mathrm{MS}}}^{(n_f)}$ and the strong coupling constant ${\alpha }_s(M_Z^2)$ are determined for four quark flavors ($n_f=4$) as well. A careful estimation of the uncertainties shall be performed using the Hessian method for the valence-quark distributions, originating from the experimental errors. We compare our valence-quark parton distribution functions sets with those of other collaborations; in particular with the {\tt BBG}, {\tt CT14}, {\tt MMHT14} and {\tt NNPDF} sets, which are contemporary with the present analysis. The obtained results from the analysis are in good agreement with those from the literature.

arXiv comment14 Pages, 8 Figures, 4 Tables

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