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

TL;DR

This paper explores the continuum transition between decoupling and scaling solutions of Yang-Mills propagators in Landau gauge, showing how the critical coupling value influences the ghost propagator behavior and comparing it with lattice results.

Contribution

It demonstrates that the scaling solution emerges as a critical limit of the decoupling solutions when the coupling approaches a specific critical value.

Findings

The asymptotic ghost dressing function fits well with numerical DSE results.

The critical coupling value is identified and compared with lattice estimates.

The scaling solution appears as a limiting case at the critical coupling.

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. This critical value of the coupling is compared with the lattice estimate for the Yang-Mills QCD coupling and the latter is shown to lie much above the former.