The phase diagram of the Polyakov Nambu Jona-Lasinio approach for finite chemical potentials

TL;DR

This paper enhances the Polyakov Nambu Jona-Lasinio model by including next-to-leading order mesonic terms and a gluon-quark coupling, accurately reproducing lattice results and mapping the phase diagram at finite chemical potentials.

Contribution

It introduces higher-order mesonic contributions and a gluon-quark coupling in the PNJL model, enabling detailed phase diagram analysis at finite chemical potentials without new parameters.

Findings

Reproduces lattice results for thermodynamic properties at zero chemical potential.

Identifies a first-order phase transition with a critical end point at T_CEP=110 MeV, μ_q=320 MeV.

Aligns with pQCD results at high chemical potentials.

Abstract

We extend the SU(3) (Polyakov) Nambu Jona-Lasinio in two ways: We introduce the next to leading order contribution (in $N_c$) in the partition function. This contribution contains explicit mesonic terms. We introduce a coupling between the gluon field and the quark degrees of freedom which goes beyond a simple rescaling of the critical temperature. With both these improvements we can reproduce, for vanishing chemical potentials, the lattice results for the thermal properties of a strongly interacting system like pressure, energy density, entropy density, interaction measure and the speed of sound. Also the expansion parameter towards small but finite chemical potentials agrees with the lattice results. Extending the calculations to finite chemical potentials (what does not require any new parameter) we find a first order phase transition up to a critical end point of $T_{CEP}= 110\ MeV$ and $\mu_q = 320\ MeV$. For very large chemical potentials, we find agreement with pQCD calculations. We calculate the mass of mesons and baryons as a function of temperature and chemical potential and the transition between the hadronic and the chirally restored phase. These calculations provide an equation of state in the whole $T,\mu$ plane an essential ingredient for dynamical calculations of ultra-relativistic heavy ion collisions but also for the physics of neutron stars and neutron star collisions.