Effects of equilibrium coexisting phases in the first-order chiral transition within the Linear sigma model with quarks

Abstract

The first order chiral phase transition for quark matter with flavor imbalance is studied using the Linear sigma model with quarks, also known as Quark-meson model. Special attention is paid to the role of the scalar isovector meson. The general consensus presently is that the chiral transition changes from a smooth crossover to first-order at low temperatures. 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. Under such assumption the bulk properties are analyzed and several remarkable effects for the speed of sound and the susceptibilities are stressed.

Figures (10)

• Figure 1: The critical temperature in terms of the quark mass (a), and its dependence on the model parameter $M_{\sigma 0}$ (b). The quark mass in vacuum is related to the coupling constant by $m_{q 0}=g\, f_\pi$.
• Figure 2: The transition temperature in terms of the baryon number chemical potential for several global isospin parameters $x$. The insertion shows details of the first order transition (dotted lines), the CEPs (full circles) and the crossover transition (solid and dashed lines). Within the ECR the Eq.(\ref{['x Binodal']}) applies.
• Figure 3: The isothermal pressure at $T=5$ MeV as function of the quark number for several flavor asymmetries $x$. Solid lines corresponds to the results including the ECR. The Maxwell construction for $x=0,\,1/3$ is represented by dotted lines, while the dashed lines include contributions from unstable and meta-stable configurations.
• Figure 4: An isobar section of the equilibrium coexistence region in the $x-T$ plane corresponding to $P=45$ MeV fm$^{-3}$.
• Figure 5: The isothermal speed of sound $v_T$, for configurations keeping $x$ constant, as function of the quark number density for several temperatures and $x=1/3$ (a), and $x=2/3$ (b). The reference density is $n_0=0.15$ fm$^{-3}$.