Asymptotic gauge symmetry and UV extension of the nonperturbative coupling in holographic QCD

TL;DR

This paper develops a nonperturbative analytic model for the strong coupling in QCD, incorporating asymptotic freedom and scale-dependent confinement, providing a unified description consistent with experimental data.

Contribution

It introduces a scale-dependent confinement strength and enforces holomorphic properties, connecting ultraviolet scaling, infrared fixed points, and flavor number in a novel analytic framework.

Findings

Accurately describes the strong coupling across all scales

Links UV scaling exponents with infrared fixed points

Matches experimental data up to the highest energies

Abstract

We extend our recent analytic study of the strong coupling $\alpha_{\rm eff}$ in the nonperturbative and near-perturbative regimes~\cite{deTeramond:2024ikl} by imposing rigorous renormalization-group results from asymptotically free gauge theories at $Q^2 \to \infty$. The asymptotic boundary conditions modify the scaling properties of $\alpha_{\rm eff}$ at large values of the momentum transfer $Q^2$, and lead to a scale-dependent confinement strength $\kappa(Q^2)$. This requires that both $\kappa(Q^2)$ and $\alpha_{\rm eff}\left(Q^2, \kappa(Q^2)\right)$ remain holomorphic in the complex $Q^2$ plane, except at the physical cuts associated with the heavy-quark thresholds and the singularity flow trajectory studied in~\cite{deTeramond:2024ikl}. For color $SU(3)$, a precise connection is found between the scaling exponent of $\kappa(Q^2)$ in the ultraviolet, the value of the infrared fixed point of the strong coupling, and the number of flavors in agreement with observations. The nonperturbative analytic model gives an accurate description of the strong coupling at all scales, up to the highest available data.