Insight on confinement from the QCD effective charge

Like the Gell-Mann--Low coupling $α$ of QED, the effective charge αg₁ is a physical, observable-defined running coupling that can serve as the QCD coupling αₛ. It can be represented by an analytic form consistent with renormalization-group evolution, light-front holographic QCD, and the world data on αₛ. As an observable, αg₁ has a physically relevant analytic structure that reflects the underlying partonic dynamics. It displays, in the long-distance regime, two imaginary conjugate singularities at Q²=± iΛₛ², with Λₛ the QCD scale. To connect this structure to confinement, we use known relations between αₛ 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-Λₛ|x|/√2|x|-5/2+dₐ where propagation is suppressed beyond distances of order 1/Λₛ, as expected from confinement. This offers an intuitive interpretation of confinement as the suppression of QCD Green's functions at long distance.