Beyond Perturbation: A Unified View of QCD

The effective coupling [latex]\alpha_{\rm eff}(Q)[/latex]-calculated for [latex]\kappa = 0.534~\rm{GeV}[/latex]-demonstrates a transition between infrared and nonperturbative regimes, and when subjected to ultraviolet completion incorporating heavy quark thresholds, reveals the inherent limitations of any theoretical framework attempting to fully encompass the complexities of strong interactions.

New research combines holographic duality, light-front quantization, and analytic properties to offer a comprehensive framework for understanding strong interactions across all energy scales.