QCD analysis of $xF_3$ structure functions in deep-inelastic scattering: Mellin transform by Gegenbauer polynomial up to N$^3$LO approximation

TL;DR

This paper conducts a detailed QCD analysis of the $xF_3$ structure functions in deep-inelastic scattering using Mellin transforms and Gegenbauer polynomials at NLO, N$^2$LO, and N$^3$LO, comparing results with recent parton distribution functions.

Contribution

It introduces a novel combination of Mellin transforms with Gegenbauer polynomials for analyzing $xF_3$ structure functions at high precision levels in deep-inelastic scattering.

Findings

Results align well with experimental data.

Valence-quark PDFs agree with recent research groups.

Method proves effective across multiple perturbative orders.

Abstract

This paper provides a thorough examination of the $xF_3$ structure functions in deep-inelastic scattering through a comprehensive QCD analysis. Our approach harnesses sophisticated mathematical techniques, namely the Mellin transform combined with Gegenbauer polynomials. We have employed the Jacobi polynomials approach for analysis, conducting investigations at three levels of precision: Next-to-Leading Order (NLO), Next-to-Next-to-Leading Order (N$^2$LO), and Next-Next-Next-to-Leading Order (N$^3$LO). We have performed a comparison of our sets of valence-quark parton distribution functions with those of recent research groups, specifically CT18 and MSHT20 at NLO and N$^2$LO, and MSTH23 at N$^3$LO, which are concurrent with our current analysis. The combination of Mellin transforms with Gegenbauer polynomials proves to be a powerful tool for investigating the $xF_3$ structure functions in deep-inelastic scattering and the results obtained from our analysis demonstrate a favorable alignment with experimental data.