Quark and Polyakov-loop correlations in the Polyakov-Nambu-Jona-Lasinio model

The aim of this work is to shed light to some less known aspects of Polyakov-loop extended chiral models, especially on the correlation of the quark sector and the Polyakov loop. We show that the order of chiral and Polyakov-loop transition and their difference in temperature as seen in LQCD calculations could be realised with a critical scale of the Polyakov-loop potential larger than the one in pure gauge theory. Comparing results for the Polyakov-loop susceptibility with the self-consistent medium-dependent quark mass and keeping the later at a fixed value allows to disentangle chiral-symmetry restoration and center-symmetry breaking effects. This indicates a confined chirally restored phase which is also seen as a plateau in the quark contribution to thermodynamics and by sigma and pion spectral functions that coincide but have a small width. Furthermore, we discuss that from some large chemical potential on the explicit center symmetry breaking is so strong that statistical deconfinement is realised at infinitely small temperatures. Both, the missing sensitivity of the Polyakov-loop to the quark mass except close to the chiral transition and the Polyakov loop being zero at zero temperature at all chemical potentials it is interpreted as an indication of a missing mechanism to take into account the quark back-reaction on the Polyakov loop.