Polyakov loop, gluon mass, gluon condensate, and its asymmetry near deconfinement

Abstract

We consider a BRST-invariant generalization of the ``massive background Landau gauge,'' resembling the original Curci-Ferrari model that saw a revived interest due to its phenomenological success in modeling infrared Yang-Mills dynamics, including that of the phase transition. Unlike the Curci-Ferrari model, however, the mass parameter is no longer a phenomenological input, but it enters as a result of dimensional transmutation via a BRST-invariant dimension-2 gluon condensate. The associated renormalization constant is dealt with using Zimmermann's reduction of constants program, which fixes the value of the mass parameter to values close to those obtained within the Curci-Ferrari approach. Using a self-consistent background field, we can include the Polyakov loop and probe the deconfinement transition, including its interplay with the condensate and its electric--magnetic asymmetry. We report a continuous phase transition at ${T}_{c}\ensuremath{\approx}0.230\text{ }\text{ }\mathrm{GeV}$ in the SU(2) case and a first-order one at ${T}_{c}\ensuremath{\approx}0.164\text{ }\text{ }\mathrm{GeV}$ in the SU(3) case, values which are again rather close to those obtained within the Curci-Ferrari model at one-loop order.