Isentropic thermodynamics across the hadron-quark mixed phase in a two-phase model with a PNJL quark description

Abstract

We study the hadron-quark mixed phase within a two-phase model for symmetric and asymmetric matter. For the quark sector we employ the (2+1) Polyakov-extended Nambu-Jona-Lasinio model (PNJL) with vector interactions. We investigate how the hadronic equation of state affects the phase diagram and the thermodynamic properties inside the mixed phase. The behavior of isentropic trajectories in the mixed phase depends on the fixed entropy per baryon ($s/ρ_B$), with trajectories near the critical end point (CEP) exhibiting a pronounced cooling pattern, while isentropic trajectories with low entropy per baryon undergo pronounced heating as the baryonic density increases. The adiabatic squared speed of sound displays characteristic peak and dip structures that depend on $s/ρ_B$. The polytropic index along isentropic and isothermal trajectories, including in the vicinity of the CEP are also investigated. The effects of vector interactions and isospin asymmetry on thermodynamic observables likewise depend on the chosen $s/ρ_B$ value. Finally, we discuss the population of hyperons along isentropic trajectories and their influence on the phase diagram. The main effect of hyperons is to shift the onset of deconfinement to larger densities and decrease the density extension of the mixed phase.

Figures (11)

• Figure 1: Phase transition in the $P-\rho_B$ plane for symmetric ($\alpha = 0$, top) and asymmetric ($\alpha = 0.2$, bottom) matter, computed with the NL3$\omega\rho$-PNJL two-model approach. Columns show scenarios with $\zeta = 0$ (left) and $\zeta = 0.5$ (right). Solid lines are isotherms at fixed temperatures $T =$ 10, 80, 100, 150 MeV. The region between the black dots indicates the mixed (coexistence) phase.
• Figure 2: Phase diagram of the NL3$\omega\rho$-PNJL two-phase model in the $T-\rho_B$ plane for $\alpha = 0$ (top) and $\alpha = 0.2$ (bottom) matter, and $\zeta = 0$ (left) and $\zeta = 0.5$ (right). The big black dot is the CEP and the colored dashed lines identify the coexistence phase where $0\%$ (pure-hadron), $20\%$, $50\%$, $70\%$, and $100\%$ (pure-quark) of matter is in the quark phase, respectively. The solid colored lines are isentropes for fixed $s/\rho_B =$ 0.5, 2, 5 ratios. For clarity, the pure-hadron and pure-quark boundaries, together with the isentropes from panel \ref{['fig:T-rho_nl3wr_a']}, are displayed in gray in the other three panels to highlight differences.
• Figure 3: Local entropy per baryon number density of quark (red) and hadron (blue) matter as a function of the quark concentration for $\zeta = 0$ (solid) and $\zeta = 0.5$ (dashed) in symmetric matter.
• Figure 4: Sound velocity squared $c_s ^2$ as a function of the baryon density along the isentropes $s/\rho_B =$ 0.5, 2, 5 for $\zeta = 0$ (left) and $\zeta = 0.5$ (right), and for $\alpha = 0$ (top) and $\alpha = 0.2$ (bottom) within the NL3$\omega\rho$-PNJL two-model approach. The horizontal dashed line $c_s^2 = 1/3$ indicates the high-density conformal limit.
• Figure 5: Polytropic index $\gamma$ as a function of the baryon density along the isentropes $s/\rho_B =$ 0.5, 2, 5 for $\zeta = 0$ (left) and $\zeta = 0.5$ (right), and for $\alpha = 0$ (top) and $\alpha = 0.2$ (bottom) within the NL3$\omega\rho$-PNJL two-model approach. The horizontal dotted line $\gamma = 1.75$ serves as an approximate reference value to distinguish hadronic from quark degrees of freedom.