Interplay between the chiral and deconfinement transitions from a Curci-Ferrari-based Polyakov loop potential

Abstract

We couple the two-flavor Nambu--Jona-Lasinio model to a gluonic background corresponding to the gauge-field expectation value in the center-symmetric Landau gauge. Low-energy features in this gauge are captured by a center-symmetric extension of the Curci-Ferrari model and provide a good grasp on key aspects of the confinement/deconfinement transition. Within this framework, we can investigate the interplay between the chiral and deconfinement transitions. Compared to other approaches based on multi-parameter Ans\"atze of the Polyakov loop potential fixed from comparison to finite-temperature lattice data, the modeling of the glue sector in the present set-up depends on only one phenomenological parameter that can be fixed by comparison to lattice data in the vacuum. We detail the structure of the phase diagram, with special emphasis on the finite density axis, and compute thermodynamical observables relevant for applications. We also highlight the properties of the recently introduced net quark number response of the medium as a sensible probe of the phases of QCD, in particular as a tool to disambiguate the nature of certain regions of the phase diagram where the use of the Polyakov loops could lead to misinterpretations. Finally, we critically assess the sensitivity of our results to the various parameters, both in the glue sector and in the chiral sector.