The continuum threshold and the Polyakov loop: A comparison between two deconfinement order parameters

We compare two order parameters for the deconfinement transition, induced by thermal and density effects, commonly used in the literature, namely the thermal and density evolution of the continuum threshold $s_0$, within the frame of the QCD sum rules, and the trace of the Polyakov loop $\mathrm{\Phi }$ in the framework of a nonlocal $SU(2)$ chiral quark model. We include in our discussion the evolution of the chiral quark condensate, the parameter that characterizes the chiral symmetry restoration. We found that essentially both order parameters, $s_0$ and $\mathrm{\Phi }$, provide the same information for the deconfinement transition, both for the zero and finite chemical potential cases. At zero density, the critical temperatures in both cases coincide exactly and, in the case of finite baryonic chemical potential $\mu$, we find evidence for the appearance of a quarkyonic phase.