# Relation between the continuum threshold and the Polyakov loop with the QCD deconfinement transition

## TL;DR

This study confirms that the continuum threshold and the Polyakov loop serve as equivalent indicators of the QCD deconfinement transition at finite temperature and chemical potential, using sum rules and a chiral quark model.

## Contribution

It extends previous work by demonstrating the equivalence between the continuum threshold and the Polyakov loop as order parameters for deconfinement in QCD.

## Key findings

- s_0(T,μ) and Φ(T,μ) are equivalent deconfinement indicators
- Results agree with previous conclusions on order parameters
- Validates the use of sum rules with a chiral quark model

## Abstract

Using vector and axial-vector correlators within finite energy sum rules with inputs from a chiral quark model, coupled to the Polyakov loop, with nonlocal vector interactions, we extend our previous work to confirm the equivalence between the continuum threshold $s_0$ and the trace of the Polyakov loop $\Phi$ as order parameters for the deconfinement transition at finite temperature $T$ and quark chemical potential $\mu$. The obtained results are in agreement with our initial conclusion, where we showed that $s_0(T,\mu)$ and $\Phi(T,\mu)$ provide the same information for the QCD deconfinement transition.