Insight on confinement from the QCD effective charge

Abstract

Like the Gell-Mann--Low coupling $\alpha$ of QED, the effective charge $\alpha_{g_1}$ is a physical, observable-defined running coupling that can serve as the QCD coupling $\alpha_s$. It can be represented by an analytic form consistent with renormalization-group evolution, light-front holographic QCD, and the world data on $\alpha_s$. As an observable, $\alpha_{g_1}$ has a physically relevant analytic structure that reflects the underlying partonic dynamics. It displays, in the long-distance regime, two imaginary conjugate singularities at $Q^2=\pm i\Lambda_s^2$, with $\Lambda_s$ the QCD scale. To connect this structure to confinement, we use known relations between $\alpha_s$ and the parton dressed propagators and vertices. Since, unlike vertices, propagators characterize a field variation between separate locations, the two singularities are assigned to the propagators. This results in the parton propagators displaying a long-distance behavior $e^{-\Lambda_s|x|/\sqrt{2}}|x|^{-5/2+d_a}$ where propagation is suppressed beyond distances of order $1/\Lambda_s$, as expected from confinement. This offers an intuitive interpretation of confinement as the suppression of QCD Green's functions at long distance.