Coexisting phases in the chiral transition within the Linear sigma model with quarks

TL;DR

The paper investigates the chiral transition in quark matter at finite density with isospin imbalance using the Linear Sigma Model with quarks in a mean-field plus one-loop meson framework. It shows that a continuous transition can occur via Gibbs coexistence when multiple conserved charges are present, in particular at fixed isospin fraction $x$ and chemical potentials $mu_B$ and $mu_3$. The analysis reveals a phase diagram with a high-$T$ crossover ending at a critical endpoint (CEP) and a low-$T$ first-order region, along with a coexisting region where the speed of sound $v_S$ and susceptibilities $chi_B$ and $chi_3$ exhibit characteristic features. These results have implications for dense QCD matter and astrophysical contexts, though the study neglects pion condensation, weak processes, and electromagnetic fields, with higher-order corrections expected to move the transition temperature toward lattice estimates.

Abstract

It is believed at present that the chiral transition changes from a smooth crossover to a first-order transition at low temperatures and high densities. Such regime is commonly analyzed using effective models since first principle calculations, as in lattice arrangements, are not feasible. This transition is assumed to be discontinuous, with unstable or metastable intermediate states. However, if multiple charges are simultaneously conserved the system could undergo a continuous change through a coexistence of equilibrium states. This type of transition has multiple manifestations, as in the nuclear liquid-gas transition causing the spinodal fragmentation. The coexistence of phases in the chiral transition is studied here for quark matter assuming the conservation of the isospin composition. Using the Linear sigma model with quarks several remarkable effects are found and discussed.

Figures (4)

• Figure 1: The transition temperature in terms of the bayon number chemical potential for several global isospin parameters $x$. The insertion shows details of the first order transition (dashed lines), the CEPs (full circles) and the crossover transition (full lines). Within the ECR the Eq.(\ref{['x Binodal']}) applies.
• Figure 2: An isobar section of the equilibrium coexistence region in the $x-T$ plane for $P=45$ MeV fm$^{-3}$.
• Figure 3: The speed of sound $v_S$ as function of the quark number density for several temperatures and $x=1/3$ (a) or $x=2/3$ (b). The reference density is $n_0=0.15$ fm$^{-3}$. The vertical segments at the discontinuities have the sole purpose of facilitating the interpretation of the curves.
• Figure 4: The second order susceptibility corresponding to the baryonic number as function of the quark number density for several temperatures and $x=0$ (a), $x=!/3$ (b), $x=2/3$ (c). For $x=0$ only the results using the unstable equation of state are shown. The reference density is $n_0=0.15$ fm$^{-3}$.