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

TL;DR

This paper performs a detailed QCD analysis of nucleon structure functions using Laplace transforms and Jacobi polynomials at NLO and NNLO, extracting parton distributions and fundamental constants with uncertainty estimates.

Contribution

It introduces an analytical Laplace transform method combined with Jacobi polynomials for precise evolution of structure functions at multiple perturbative orders.

Findings

Determined QCD scale and strong coupling constant with uncertainties.

Produced valence-quark distribution functions consistent with other global fits.

Validated the method by comparing results with existing parton distribution sets.

Abstract

We present a detailed QCD analysis of nucleon structure functions $xF_3 (x, Q^2)$, 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 $xF_3(x, Q^2)$ structure functions using the Jacobi polynomials approach. In our work, the values of the typical QCD scale $\Lambda_{\overline{\rm MS}}^{(n_f)}$ 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.