Thermodynamics of strongly interacting matter in a hybrid model

The equation of state and fluctuations of conserved charges in a strongly interacting medium under equilibrium conditions form the baseline upon which are built various possible scenarios in relativistic heavy-ion collision experiments. Many of these quantities have been obtained in the lattice QCD framework with reliable continuum extrapolations. Recently the Polyakov–Nambu–Jona-Lasinio model has been reparametrized to some extent to reproduce quantitatively the lattice QCD equation of state at vanishing chemical potentials. The agreement was precise except at low temperatures, possibly due to inadequate representation of the hadronic degrees of freedom in the model. This disagreement was also observed for some of the fluctuations and correlations considered. Here we address this issue by introducing the effects of hadrons through the hadron resonance gas model. The total thermodynamic potential is now a weighted sum of the thermodynamic potential of the Polyakov–Nambu–Jona-Lasinio model and that of the hadron resonance gas model. We find that the equation of state and the fluctuations and correlations obtained in this hybrid model agree satisfactorily with the lattice QCD data in the low temperature regime.

Figure 1

Switching function as a function of temperature.

Figure 2

Scaled pressure as a function of temperature. The upper panels are drawn without derivatives of switching function and lower panels include those derivatives. The left panel is for the PNJL model with six quark interactions and the right panel for the PNJL model with eight quark interactions. The continuum extrapolated lattice QCD data are taken from Ref. [14] (HotQCD) and Ref. [15] (WUB).

Figure 3

The scaled traces of the energy-momentum tensor are plotted as a function of temperature. The upper panels are drawn without derivatives of the switching function and lower panels include those derivatives. The left panel is for the PNJL model with six quark interactions and the right panel is for the PNJL model with eight quark interactions. The continuum extrapolated lattice QCD data are taken from Ref. [14] (HotQCD) and Ref. [15] (WUB).

Figure 4

The squared speed of sound is plotted as a function of temperature. The upper panels are drawn without derivatives of the switching function and the lower panels include those derivatives. The left panel is for the PNJL model with six quark interactions and the right panel is for PNJL model with eight quark interactions. The continuum extrapolated lattice QCD data are taken from Ref. [14] (HotQCD) and Ref. [15] (WUB).

Figure 5

Baryon number fluctuation as a function of temperature. The continuum extrapolated lattice data are from Ref. [104, 105] (HotQCD), Ref. [106] (WUB), and Ref. [171] (LQCD).

Figure 6

Fourth-order baryon number susceptibility as function of temperature. The continuum extrapolated lattice data are from Ref. [104, 105] (HotQCD) and Ref. [106] (WUB).

Figure 7

Ratio of fourth-order to second-order baryon number susceptibility as function of temperature. The continuum extrapolated lattice data are from Ref. [104, 105] (HotQCD) and Ref. [106] (WUB).

Figure 8

Electric charge fluctuation as function of temperature. The continuum extrapolated lattice data are from Ref. [104] (HotQCD), Ref. [106] (WUB), and [171] (LQCD).

Figure 9

Strangeness fluctuation as function of temperature. The continuum extrapolated lattice data are from Ref. [104] (HotQCD), Ref. [106] (WUB), and Ref. [171] (LQCD).

Figure 10

Baryon-electric charge correlation as function of temperature. The continuum extrapolated lattice data are from Ref. [104] (HotQCD) and Ref. [171] (LQCD).

Figure 11

Baryon-strangeness correlation as function of temperature. The continuum extrapolated lattice data are from Ref. [104] (HotQCD) and Ref. [171] (LQCD).

Figure 12

Electric charge-strangeness correlation as function of temperature. The continuum extrapolated lattice data are from Ref. [104] (HotQCD) and Ref. [171] (LQCD).