Abstract
The aim of this work is to shed light on some lesser known aspects of Polyakov-loop--extended chiral models (namely the Polyakov-loop extended Nambu--Jona-Lasinio and Quark-Meson models), especially on the correlation of the quark sector with the Polyakov loop. We show that the ordering of chiral and Polyakov-loop transitions and their difference in temperature as seen in lattice QCD calculations could be realized with a critical scale of the Polyakov-loop potential that is larger than the one in pure gauge theory. The comparison of the results for the Polyakov-loop susceptibility obtained using the self-consistent medium-dependent quark mass with those obtained while keeping these masses at a fixed value allows to disentangle chiral-symmetry restoration and center-symmetry breaking effects. Furthermore, a confined chirally restored phase is identified by a plateau in the quark contribution to thermodynamics and by sigma and pion spectral functions that coincide but have a small width. We also discuss that, for some large chemical potential values, the explicit center-symmetry breaking is so strong that statistical deconfinement is realized at infinitely small temperatures. Both the missing sensitivity of the Polyakov loop to the quark mass, except at close to the chiral transition, and the Polyakov loop being zero at zero temperature at all chemical potentials, can be interpreted as indications of a missing mechanism which accounts for the quark back-reaction on the Polyakov loop.
Highlights
And in the near future, there is and will be a big experimental effort to explore the phase diagram of strongly interacting matter, be it by the energy scan program at RHIC [1] and the NA61/SHINE experiment at CERN [2] or at the future facilities, NICA at JINR [3] and FAIR at the GSI site [4]
If we look at the Polyakov-loop susceptibility in Fig. 8, we see that there is a divergence at the chiral transition temperature but physically this is not the signal of the deconfinement transition
The expected behavior for mesons in a confined chirally restored phase (CCS) is observed in the same Fig. 13: chiral symmetry is effectively restored when the sigma and pion spectral functions essentially coincide [24] but the statistical confinement is still strong as can be seen by the fact that their width is small when compared to the fully deconfined phase
Summary
In the near future, there is and will be a big experimental effort to explore the phase diagram of strongly interacting matter, be it by the energy scan program at RHIC [1] and the NA61/SHINE experiment at CERN [2] or at the future facilities, NICA at JINR [3] and FAIR at the GSI site [4]. We will study how to disentangle the effects of the restoration of chiral symmetry from the effects of the breaking of center symmetry in order to have a deeper knowledge on how both are correlated This allows for a better understanding of the current status of the comparison between the results of these kinds of models and those obtained in lattice QCD (LQCD) calculations, while at the same time shedding further light on certain lesser known results of the models. As a result, when we discuss confinement we mean the statistical one, not the true one
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