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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.00220 |
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Table of Contents:
- We construct a QCD coupling ${\mathcal{A}}(Q^2)$ in the Effective Charge (ECH) scheme of the canonical part $d(Q^2)$ of the (inelastic) polarised Bjorken Sum Rule (BSR) ${\overline Γ}_1^{\rm p-n}(Q^2)$. In the perturbative domain, the coupling ${\mathcal{A}}(Q^2)$ practically coincides with the perturbative coupling $a(Q^2)$ [$\equiv α_s(Q^2)/π$] in the four-loop ECH renormalisation scheme. In the deep infrared (IR) regime, ${\mathcal{A}}(Q^2)$ behaves as suggested by the Holographic Light-Front QCD up to the second derivative. Furthermore, in contrast to its perturbative counterpart $a(Q^2)$, the coupling ${\mathcal{A}}(Q^2)$ is holomorphic in the entire complex $Q^2$-plane with the exception of the negative semiaxis, reflecting the holomorphic properties of the BSR observable $d(Q^2)$ [or: ${\overline Γ}_1^{\rm p-n}(Q^2)$] as dictated by the general principles of the Quantum Field Theory. It turns out that the obtained coupling, used as ECH, reproduces quite well the experimental data for ${\overline Γ}_1^{\rm p-n}(Q^2)$ in the entire $N_f=3$ regime $0 < Q^2 \lesssim 5 \ {\rm GeV}^2$.