QCD analysis of xF3 structure functions in deep-inelastic scattering: Mellin transform with Gegenbauer polynomials up to N3LO approximation

This paper provides a thorough examination of the xF₃ 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 (N²LO), and next-next-next-to-leading order (N³LO). 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 N²LO, and MSTH23 at N³LO, which are concurrent with our current analysis. The combination of Mellin transforms with Gegenbauer polynomials proves to be a powerful tool for investigating the xF₃ structure functions in deep-inelastic scattering and the results obtained from our analysis demonstrate a favorable alignment with experimental data.