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arXiv · 2107.01293

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

J. Blümlein·M. Saragnese
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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 $α_s(M_Z)$ or the QCD scale $Λ_{\rm QCD}$ 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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J. Blümlein, M. Saragnese. 2021-07-02. The N$^3$LO Scheme-invariant QCD Evolution of the Non-singlet Structure Functions \boldmath $F^{\rm NS}_2(x,Q^2)$ and $g_1^{\rm NS}(x,Q^2)$. https://doi.org/10.1016/j.physletb.2021.136589

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