QCD analysis of $xF3$ structure functions in deep-inelastic scattering: Mellin transform with Gegenbauer polynomials up to $N^3LO$ approximation

• Shahin Atashbar Tehrani (IPM & Persian Gulf University)

We examine 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 ($N^2LO$), and next-next-next-to-leading order ($N^3LO$). 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 $N^2LO$, and MSTH23 at $N^3LO$, which are concurrent with our current analysis. We test the GLS sum rule and Adler sum rule.