The N$^3$LO Scheme-invariant QCD Evolution of the Non-singlet Structure Functions \boldmath $F^{\rm NS}_2(x,Q^2)$ and $g_1^{\rm NS}(x,Q^2)$

TL;DR

This paper develops a scheme-invariant, high-precision QCD evolution framework for non-singlet structure functions, incorporating heavy quark effects, to facilitate accurate measurements of the strong coupling constant in deep-inelastic scattering experiments.

Contribution

It introduces a N$^3$LO scheme-invariant evolution method for non-singlet structure functions including heavy quark effects, enhancing precision in QCD analyses.

Findings

Evolution depends only on $\alpha_s(M_Z)$, $\Lambda_{ m QCD}$, $m_c$, and $m_b$.

Uncertainty from unknown 4-loop anomalous dimensions is minimal.

Provides a clean method for measuring the strong coupling constant.

Abstract

We present the scheme-invariant unpolarized and polarized flavor non-singlet evolution equation to N$^3$LO for the structure functions $F_2(x,Q^2)$ and $g_1(x,Q^2)$ including the charm- and bottom quark effects in the asymptotic representation. The corresponding evolution is based on the experimental measurement of the non-singlet structure functions at a starting scale $Q_0^2$. In this way the evolution does only depend on the strong coupling constant $\alpha_s(M_Z)$ or the QCD scale $\Lambda_{\rm QCD}$ and the charm and bottom quark masses $m_c$ and $m_b$ and provides one of the cleanest ways to measure the strong coupling constant in future high luminosity deep-inelastic scattering experiments. The yet unknown parts of the 4-loop anomalous dimensions introduce only a marginal error in this analysis.