Chiral crossover, deconfinement and quarkyonic matter within a Nambu-Jona Lasinio model with the Polyakov loop

TL;DR

This paper investigates the relationship between chiral symmetry restoration, deconfinement, and quarkyonic matter using a non-local Nambu-Jona Lasinio model with the Polyakov loop, exploring different effective potentials and their implications for QCD phase structure.

Contribution

It introduces a study of the QCD phase diagram with various Polyakov loop potentials within a non-local NJL model, highlighting the conditions for quarkyonic matter and its dependence on the potential form.

Findings

Quarkyonic phase appears at high chemical potential and low temperature in certain potentials.

The quarkyonic window is reduced when the Polyakov loop potential depends on chemical potential.

Results are consistent with some lattice studies and suggest coexistence with color superconductivity.

Abstract

We study the interplay between the chiral and the deconfinement transitions, both at high temperature and high quark chemical potential, by a non local Nambu-Jona Lasinio model with the Polyakov loop in the mean field approximation and requiring neutrality of the ground state. We consider three forms of the effective potential of the Polyakov loop: two of them with a fixed deconfinement scale, cases I and II, and the third one with a $\mu$ dependent scale, case III. In the cases I and II, at high chemical potential $\mu$ and low temperature $T$ the main contribution to the free energy is due to the Z(3)-neutral three-quark states, mimicking the quarkyonic phase of the large $N_c$ phase diagram. On the other hand in the case III the quarkyonic window is shrunk to a small region. Finally we comment on the relations of these results to lattice studies and on possible common prospects. We also briefly comment on the coexistence of quarkyonic and color superconductive phases.