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

Understand

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.