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.
Highlights
The study of the phase diagram of strongly interacting matter has recently gained a lot of interest
We introduce a coupling between the gluon field and the quark degrees of freedom, which goes beyond a simple rescaling of the critical temperature
Using the temperature-dependent interaction between quarks and gluons with the parametrization given above and taking into consideration the contributions of the pseudoscalar π and k as well as the scalar σ and a0 mesons, which contribute to the next-to-leading-order terms of the partition sum, we can reproduce the pressure as function of the temperature obtained by lattice gauge calculations [3]
Summary
The study of the phase diagram of strongly interacting matter has recently gained a lot of interest. Being presently outside of the range of lattice gauge calculation, this is the realm of phenomenological models and subject of intensive studies Many of these approaches suggest that the crossover, observed for μ = 0, continues for finite μ, with an increasingly steeper slope, before it merges into a critical end point followed by a first-order phase transition for even larger μ [11,12,13]. NJL-type models have a long history and have been extensively used to describe the dynamics and thermodynamics of light hadrons and baryons They offer the possibility to study, in a simple way and with a very limited number of parameters, adjusted to vacuum physics, the basic features of low-temperature QCD, the basic mechanism for the spontaneous breakdown of chiral symmetry, but suffer from the absence of confinement, a consequence of the replacement of the local SU(Nc) gauge invariance of QCD by a global SU(Nc) symmetry.
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