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

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 $\mathcal{O}(q^2)$ 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.

Comments: Oral Contribution to "T(R)opical QCD 2010" (Cairns, Australia)