Towards unifying perturbative and Holographic Light-Front QCD via holomorphic coupling

TL;DR

This paper develops a holomorphic QCD coupling that unifies perturbative and holographic light-front approaches, matching experimental data across a wide energy range and exhibiting desirable mathematical properties.

Contribution

It introduces a holomorphic QCD coupling in the ECH scheme that aligns with perturbative results at high energies and holographic models at low energies, with improved analytic properties.

Findings

Coupling matches perturbative QCD in the high-energy domain.

Coupling exhibits holographic behavior in the infrared regime.

Reproduces experimental data for the Bjorken Sum Rule across relevant Q^2 range.

Abstract

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) ${\overline \Gamma}_1^{{\rm p-n}}(Q^2)$. In the perturbative domain, the coupling ${\mathcal{A}}(Q^2)$ practically coincides with the perturbative coupling $a(Q^2)$ [$\equiv \alpha_s(Q^2)/\pi$] 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: ${\overline \Gamma}_1^{{\rm p-n}}(Q^2)$] 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 ${\overline \Gamma}_1^{{\rm p-n}}(Q^2)$ in the entire $N_f=3$ regime $0 < Q^2 \lesssim 5 \ {\rm GeV}^2$.