Deconfinement transition within the Curci-Ferrari model: Renormalization scale and scheme dependences

Abstract

We analyze the confinement/deconfinement transition of pure Yang-Mills theories within the framework of the center-symmetric Landau gauge supplemented by a Curci-Ferrari mass term that models the effect of the associated Gribov copies in the infrared. In addition to providing details for earlier one-loop calculations in that framework, we explore how the results depend on the renormalization scale and/or on the renormalization scheme. We find that the predicted values for the transition temperatures of SU(2) and SU(3) Yang-Mills theories are similar in both schemes and are little sensitive to the renormalization scale μ over a wide range of values including the standard range μ∈[πT,4πT]. These values are also close both to those obtained from a minimal sensitivity principle and to those of lattice simulations, especially in the SU(3) case. These results further confirm the good behavior of perturbative calculations within the Curci-Ferrari model and support the adequacy of the latter as an effective description of Yang-Mills theories in the infrared. We perform a similar analysis for the spinodal temperatures in the SU(3) case and for the Polyakov loop, the order parameter associated with the breaking of center symmetry. Published by the American Physical Society 2024