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

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arxiv 2107.01293 v1 pith:QGYTEOAL submitted 2021-07-02 hep-ph hep-ex

J. Blümlein , M. Saragnese This is my paper · ORCID
classification hep-phhep-ex
keywords evolutionfunctionsnon-singletstructurebottomconstantcouplingonly
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Analytic Solution for the Helicity Evolution Equations at Small $x$ and Large $N_c\&N_f$

    hep-ph 2025-07 conditional novelty 7.0 of 10

    An exact analytic solution of the revised large-Nc and large-Nf small-x helicity evolution equations in QCD, yielding all-order polarized DGLAP anomalous dimensions and small-x growth intercepts.

  2. The variable flavor number scheme to three-loop order

    hep-ph 2026-07 accept novelty 6.0 of 10

    The variable flavor number scheme is completed to three-loop order with single- and two-mass effects, validated by renormalization-group analysis to match asymptotic heavy-flavor corrections, plus numerical Wilson-coe...

  3. Next-to-leading order evolution of structure functions without PDFs

    hep-ph 2024-12 conditional novelty 6.0 of 10

    The authors build a complete NLO momentum-space DGLAP evolution for a six-observable physical basis of DIS structure functions and compare its numerical results with conventional PDF-based evolution.

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