The phase diagram of the Polyakov Nambu Jona-Lasinio approach for finite 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 $T_{CEP}=110MeV$ and ${\mu }_q=320MeV$. 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.

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Cited by in corpus (6)

• Shear viscosity and electric conductivity of a hot and dense QGP with a chiral phase transition
• Properties of the QGP created in heavy-ion collisions
• Anisotropy of magnetized quark matter
• Nonextensive effects on QCD chiral phase diagram and baryon-number fluctuations within Polyakov-Nambu-Jona-Lasinio model
• Dual meson condensates in the Polyakov-loop extended linear sigma model
• Transport properties and equation-of-state of hot and dense QGP matter near the critical end-point in the phenomenological dynamical quasi-particle model