The QCD phase diagram

TL;DR

This work surveys the QCD phase diagram, integrating experimental evidence from heavy-ion collisions, lattice QCD results, and a spectrum of theoretical approaches (weak coupling, functional methods, and effective models) to map the thermodynamics of strongly interacting matter. It emphasizes a crossover transition at zero density with precise lattice EOS and transition temperature around $T_c\approx157$ MeV, while exploring the curvature of Tc at finite density and the ongoing search for a chiral critical endpoint. The analysis extends to multidimensional settings, including external magnetic fields and isospin, and to dense matter where color superconductivity and neutron-star physics become central. The synthesis highlights how current methods cohere into a coherent picture of QCD phases, while identifying key open questions—especially the existence and location of the critical point and the behavior in the chiral limit—that will guide future experimental and theoretical efforts with significant implications for astrophysics and heavy-ion phenomenology.

Abstract

Strongly interacting matter exhibits new phases under extreme conditions. Matter was exposed to such extremes not only in the Early Universe, but also today in the cores of neutron stars, as well as in laboratory experiments at a much smaller scale. We study the underlying theory, Quantum Chromodynamics (QCD) with the methods of statistical physics and explore the various phases we may encounter in experiment, such as the Quark Gluon Plasma. We briefly summarize the experimental evidence for the new forms of matter and review the theoretical efforts to embed these findings in the broader context of quantum field theory, with special attention to exact and broken symmetries and critical behaviour.

Figures (23)

• Figure 1: Data on the QCD phase diagram. The left panel shows the diagram in the temperature ($T$) -- baryon chemical potential ($\mu_B$) plane. We know from lattice simulations Aoki:2006we that on the temperature axis the transition is a cross-over. A cross-over line starts at $T\approx 157$ MeV Borsanyi:2010bpBazavov:2011nk and stretches into the bulk of the phase diagram Borsanyi:2020fev. The width of the band refers to the theoretical uncertainties not to the width of the transition. The data points on and beyond the cross-over line show the thermodynamic parameters of the chemical freeze-out Cleymans:1998fqVovchenko:2015idtBecattini:2016xctVovchenko:2018fmhSTAR:2017salAndronic:2017pugLysenko:2024hqp. The small feature at $T\approx18$ MeV is the liquid gas transition and the corresponding end-point, measured in low energy heavy ion collision experiments Elliott:2013pna. The right panel uses the density, normalized to the nuclear saturation density $n_0=0.17 \, {\rm fm}^{-3}$ as the first axis. It shows not the data, but where we can expect information from. (Picture presented by the Muses collaboration MUSES:2023hyz)
• Figure 2: Left: schematic spacetime evolution of the system created in a heavy ion collision. Right: initial position of the nucleons in the laboratory frame for different collision energies Du:2024wjm.
• Figure 3: Left: jet nuclear modification factor in p-Pb as well as peripheral and central Pb-Pb collisions at the LHC ALICE:2022wpn. Right: charmonium nuclear modification factor in Pb-Pb collisions for $1S$ and $2S$ states at CMS CMS:2017uuv and ALICE ALICE:2018rtz.
• Figure 4: Left: flow coefficients in semi-central Pb-Pb collisions at the LHC, compared to results from a hybrid formalism including a viscous hydrodynamics description of the QGP phase Schenke:2020mbo. Right: temperatures extracted from dilepton invariant mass spectra from NA60, STAR and HADES, compared to chemical freezeout temperatures and model expectations. Figure from Ref. Ahdida:2932302.
• Figure 5: Net proton cumulant ratios (top) and proton factorial cumulant ratios (bottom) as functions of the collision energies from the STAR collaboration STAR:2025zdq, together with non-critical baselines.