Revisiting the first-order QCD phase transition in dense strong interaction matter

TL;DR

The paper investigates the first-order QCD phase transition at low temperature and high density using a continuum Dyson-Schwinger equations framework with a Slavnov-Taylor-consistent truncation. It uncovers a distinct intermediate phase $I$ in addition to the Nambu and Wigner phases, indicating spinodal decomposition as a genuine feature of the transition, and analyzes both microscopic (quark mass function $M_q$) and macroscopic (chiral condensate, Polyakov loop) signatures. By coupling the quark sector to a hadronic liquid-gas sector through an excluded-volume mixing, it shows that LG physics can stiffen the equation of state near nuclear saturation density while spinodal dynamics introduce softening, and it provides a quantitative treatment of interface properties, including the interface tension $\sigma$, entropy density $s_A$, and bubble radius $R=2\sigma/\Delta P$. The study extends to isothermal trajectories and computes stability criteria via a total compressibility that combines bulk and interface contributions, offering insights relevant to heavy-ion experiments and neutron star phenomenology, while noting limitations such as the absence of color superconductivity and explicit moiré-like inhomogeneities.

Abstract

We revisit the phase structure and thermodynamics of QCD in the low temperature and high density region, where a strong, first-order phase transition is expected beyond the critical end point. By solving the quark gap equation in the continuum QCD approach, we reveal the coexistence of the multi-phases both in the microscopic dynamics of chiral symmetry breaking and also in the thermodynamic observables, which manifests the existence of spinodal decomposition during the first-order QCD phase transitions. We also analyse the interface structure of the co-exist Nambu and Wigner phases in the isothermal process during the first-order transition. In particular, the interface tension and interface entropy density are extracted from the isothermal trajectories, which further allows for an analysis on the formation of nuclear bubble, including the bubble radius and its stability at different temperatures. Our predictions may serve as useful inputs for further investigations in heavy-ion physics or astrophysics research.

Figures (14)

• Figure 1: Diagrammatic description of the quark gap equation in QCD. The straight line with a gray blob is the full, non-perturbative quark propagator $G_q$ in Eq. \ref{['eq:quark-prop']}, the curly line with a gray blob is the full gluon propagator, the black blob is the full quark-gluon interaction vertex, and the black dot is the classical quark gluon vertex.
• Figure 2: Light quark mass function $M_l$ ($l=u,d$) at momentum $(\pi T,\boldsymbol{0})$: the real part (left) and the imaginary part (right), for $I$, $N$ and $W$ phases as a function of chemical potential $\mu_{B}^{}$ at temperature $T=40$ and 60 MeV. The colored dots mark the boundaries of $I$ phase where it merges with $N$ or $W$ phase.
• Figure 3: Left: reduced chiral condensate $\Delta_{l,s}$ for $I$, $N$ and $W$ phases as a function of baryon chemical potential $\mu_{B}^{}$ at temperature $T=40$ and 60 MeV, which is in match with \ref{['fig:mass-branches-T']}. The results are normalised by the value of $\Delta_{l,s}$ in the vacuum, i.e. at $(T,\mu_{B}^{})=(0,0)$. Right: Polyakov loops $L(\varphi_3,\varphi_8)$ and $\bar{L}(\varphi_3,\varphi_8)$, evaluated from the gluonic background field components $\varphi_3$ and $\varphi_8$ for $I$, $N$ and $W$ phases as functions of baryon chemical potential $\mu_{B}^{}$ at temperature $T=40$ and 60 MeV, which are in match with the left panel.
• Figure 4: QCD phase diagram in the first-order transition region. The phase boundaries are defined by the existence boundaries of $I$ phase, which is shown as the boundaries of the grey area. The state-of-the-art results on the chiral crossover line their estimated critical end point are also put in, including the lattice QCD Borsanyi:2020fevHotQCD:2018pds and the functional QCD results (DSE: Gao:2020fblGunkel:2021oya, fRG: Fu:2019hdw), together with the estimates on the CEP location (colored dots).
• Figure 5: Net-baryon number density $n_B$ as a function of baryon chemical potential at different temperatures, with a multi-phase structure during first-order phase transition, for temperatures $T=30$ to $100\,$MeV in a 10 MeV step. The left and the right panel show a comparison where the liquid gas phase transition occurs or not, respectively. The Maxwell construction is indicated by the dashed vertical lines, whose end points (solid dots) indicate the boundary condition for the inhomogeneous nuclear density distribution.