# Quark and Polyakov-loop correlations in effective models at zero and non-vanishing density

## TL;DR

This paper investigates the correlations between quark sectors and Polyakov loops in effective models, revealing insights into phase transitions, chiral symmetry restoration, and deconfinement at zero and finite density, with implications for understanding QCD thermodynamics.

## Contribution

It provides a detailed analysis of Polyakov-loop correlations in extended chiral models, highlighting the importance of the Polyakov-loop potential scale and quark back-reaction effects.

## Key findings

- Chiral and Polyakov-loop transitions can be ordered with a larger Polyakov potential scale.
- Confined chirally restored phase identified via thermodynamic and spectral function analysis.
- Strong center-symmetry breaking at high chemical potential leads to statistical deconfinement at low temperatures.

## 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.