The low-momentum ghost dressing function and the gluon mass

Abstract

We study both regular (the zero-momentum ghost dressing function not diverging), also named decoupling, and critical (diverging), also named scaling, Yang-Mills propagators solutions by analyzing the low-momentum behaviour of the ghost propagator Dyson-Schwinger equation (DSE) in Landau gauge, assuming for the truncation a constant ghost-gluon vertex, as it is extensively done, and a simple model for a massive gluon propagator. The asymptotic expression obtained for the regular or decoupling ghost dressing function up to the order O(q2) fits pretty well the lowmomentum ghost propagator obtained through the numerical integration of the coupled gluon and ghost DSE in the PT-BFM scheme and, when the size of the coupling renormalized at some scale approaches some critical value, the PT-BFM results seems to trend to the the scaling solution as a limiting case.