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, holographic light-front QCD (HLFQCD), 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 combine known general relations between ${\alpha }_{g_1}$ and the parton dressed propagators and vertices with a recent phenomenological representation of ${\alpha }_{g_1}$ within HLFQCD. 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.

arXiv comment8 pages, 2 figures, Supplementary material (4 pages). Published version in Phys. Let. B