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 toward small but finite chemical potentials agrees with the lattice results. Extending the calculations to finite chemical potentials (which does not require any new parameter), we find a first-order phase transition up to a critical end point of $T_{\mathrm{CEP}}=110\text{MeV}$ and ${\mu }_q=320\text{MeV}$. 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 ultrarelativistic heavy-ion collisions but also for the physics of neutron stars and neutron star collisions.

• Received 12 September 2019
• Accepted 18 March 2020

DOI:https://doi.org/10.1103/PhysRevC.101.065203

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Published by the American Physical Society