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

TL;DR

This paper compares the continuum threshold and Polyakov loop as deconfinement order parameters within QCD sum rules and a nonlocal chiral quark model, finding they provide equivalent information about the transition.

Contribution

It demonstrates that the continuum threshold and Polyakov loop are effectively interchangeable as deconfinement indicators across different conditions.

Findings

Both order parameters yield the same critical temperature at zero density.

Evidence of a quarkyonic phase appears at finite chemical potential.

The order parameters agree on the deconfinement transition in various scenarios.

Abstract

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 $\Phi$ 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 $\Phi$, 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.