The scaling infrared DSE solution as a critical end-point for the family of decoupling ones

TL;DR

This paper investigates the continuum of solutions for Yang-Mills propagators in Landau gauge, showing how the decoupling solutions approach the scaling solution as the coupling nears a critical value, unifying different infrared behaviors.

Contribution

It demonstrates that the decoupling solutions can be viewed as approaching a critical scaling solution in the Dyson-Schwinger framework, providing a unified understanding of infrared Yang-Mills propagators.

Findings

Decoupling and scaling solutions are connected through a critical coupling limit.

The asymptotic ghost dressing function fits numerical DSE results well.

Approaching the critical coupling leads to the scaling solution as a limit.

Abstract

Both regular (the zero-momentum ghost dressing function not diverging), also named decoupling, and critical (diverging), also named scaling, Yang-Mills propagators solutions can be obtained by analyzing the low-momentum behaviour of the ghost propagator Dyson-Schwinger equation (DSE) in Landau gauge. The asymptotic expression obtained for the regular or decoupling ghost dressing function up to the order ${\cal O}(q^2)$ fits pretty well the low-momentum ghost propagator obtained through the numerical integration of the coupled gluon and ghost DSE in the PT-BFM scheme. Furthermore, when the size of the coupling renormalized at some scale approaches some critical value, the PT-BFM results seems to tend to the the scaling solution as a limiting case.