The phases of QCD reached in terrestrial and cosmic colliders

TL;DR

This work surveys the QCD phase diagram through lattice QCD, effective field theories, and chiral models, emphasizing $N_f=2+1$ with insights extending toward physical $N_f=1+1+1$. It highlights lattice determinations of a crossover at $mu_B=0$ with $T_{co}$ around $156$--$158$ MeV and small curvatures $ppa_2$, $ppa_4$, while EFTs reproduce these curvatures and illuminate dynamical aspects such as pion screening and kinetic masses near $T_{co}$. The paper then outlines the conjectured full physical QCD phase diagram, including a hadron–quark coexistence surface terminating at a critical line and the potential cold critical point, with implications for neutron-star cores and possible continuity to color-superconducting phases. In the large-$N_c$ limit, it discusses how chiral and deconfinement transitions decouple at leading order, influencing the thermodynamics of dense matter and offering a simpler lens on neutron-star physics. Together, these results bridge heavy-ion phenomenology, neutron-star astrophysics, and fundamental QCD thermodynamics, outlining concrete targets for lattice and EFT studies across multiple flavors and chemical potentials.

Abstract

We review the current state of knowledge of the phase diagram of QCD through lattice, effective field theories, and chiral models. Several sections through the three dimensional phase diagram are known for $N_f=2+1$ with good precision. Due to technical advances in lattice techniques over the last decade or so, new aspects of the phase diagram can now be explored. We review current lattice results. The newly acquired knowledge can be used to reconstruct the full phase diagram for physical QCD, \ie, $N_f=1+1+1$. We remark on the computations which would help understand this better, and what the current constraints are on matter in neutron star cores. We also remark on the physics of the chiral transition and neutron stars in the 't Hooft large $N_c$ limit.

Figures (8)

• Figure 1: The thermodynamics of a gluon gas has two dimensional Gibbs space labelled by $E$ and $S$. The phase diagram, shown here, is one dimensional andlabelled by $T$. If there are confined and deconfined phases, then Gibbs' phase rule indicates that the phase diagram has a single first order transition, labeled here as $T_d$.
• Figure 2: The most parsimonious phase diagram for QCD with $N_f=2+1$ based on current lattice results and experiments. At fixed and non-vanishing pion mass it would yield only a crossover (panel on the left). An estimate of $\mu_{ B}^1$, where the crossover line crosses the axis is given in the text. This is a shadow of a critical line in the chiral limit, with a measured curvature (panel on the right). This critical line bounds a surface in chiral QCD at which different signs of ${\@fontswitch\mathcal{S}}$ coexist.
• Figure 3: The panel on the left shows that the screening mass of the pion, $m_\pi^D$, is found to be continuous across $T_c$ in lattice computations. The data points show continuum extrapolated results from the lattice. This is reproduced well by the EFT (dark shading for the 68% error band, light shading for the 95% error band), which has a UV cutoff $\Lambda$. This particular fit uses $\Lambda=300$ MeV, but equally good fits are obtained using $\Lambda=450$ MeV. The vertical hatched band shows $T_{co}$ (the narrow band is from the lattice, the wider band from the EFT). The panel on the right shows the kinetic mass, $m_\pi^K$. Since it becomes comparable to $\Lambda$ at about $T_{co}$, pions are no longer the low-energy excitations of QCD.
• Figure 4: The conjectured phase diagram for $N_f=2+1$ QCD with a finite quark mass (panel on the left). The crossover at $\mu_{ B}=0$ develops into a line of crossovers which turns into a line of phase coexistence (a first order transition between hadron and quark phases) at the critical point $(T^E,\mu_{ B}^E)$. When extended in quark mass (panel on the right), the critical point turns into a critical line, which is the boundary of a surface of hadron-quark phase coexistence (part of it is cut away to show the structure). This critical line meets the chiral critical line at the tricritical point $(T^*,\mu_{ B}^*)$, which is the end point of a triple line in QCD. The shape of this phase diagram is not expected to change in $N_f=1+1+1$. However, $T_{co}$, $\mu_{ B}^1$, and $(T^E,\mu_{ B}^E)$ could shift.
• Figure 5: The phase diagram for $N_f=1+1+1$ QCD in the space of $T$ and $\mu_{ I}$ as $\Delta m$ is varied. For $\Delta m=0$ lattice computations indicate that the critical line between the hadron and $\pi$C phases is nearly vertical, until the cross over between the hadron and quark phases is reached. Beyond this the critical line is either horizontal or rises slowly. For any finite $\Delta m$ the transition turns into a crossover. Since this whole volume has an extended symmetry, an isolated critical line is allowed; this is the edge of a first order surface for a hidden parameter, as explained in the text.