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On the Phase Diagram of QCD

M. A. Halasz, A. D. Jackson, R. E. Shrock, M. A. Stephanov, J. J. M. Verbaarschot

TL;DR

The paper maps the QCD phase structure for two massless quarks in the $T$-$$ plane, arguing that a tricritical point governs the connection between the low-temperature, first-order chiral transition and the high-temperature, second-order chiral transition. It combines lattice-informed insight, universality arguments, and a random matrix model to describe chiral restoration, deriving universal critical behavior (3D Ising on wing lines, O(4) on the $=0$ line) and quantitative tricritical coordinates. The random matrix approach provides tractable, semi-analytic predictions for the location and geometry of the transition lines, including a triple line and spinodal boundaries, and yields rough mappings to physical scales (e.g., $T_c o160$ MeV, $ _1 o1200$ MeV). Overall, the work highlights universal features of the QCD phase diagram that could inform interpretations of heavy-ion collision experiments and guide future lattice studies at finite density.

Abstract

We analyze the phase diagram of QCD with two massless quark flavors in the space of temperature, T, and chemical potential of the baryon charge, mu, using available experimental knowledge of QCD, insights gained from various models, as well as general and model independent arguments including continuity, universality, and thermodynamic relations. A random matrix model is used to describe the chiral symmetry restoration phase transition at finite T and mu. In agreement with general arguments, this model predicts a tricritical point in the T mu plane. Certain critical properties at such a point are universal and can be relevant to heavy ion collision experiments.

On the Phase Diagram of QCD

TL;DR

The paper maps the QCD phase structure for two massless quarks in the - plane, arguing that a tricritical point governs the connection between the low-temperature, first-order chiral transition and the high-temperature, second-order chiral transition. It combines lattice-informed insight, universality arguments, and a random matrix model to describe chiral restoration, deriving universal critical behavior (3D Ising on wing lines, O(4) on the line) and quantitative tricritical coordinates. The random matrix approach provides tractable, semi-analytic predictions for the location and geometry of the transition lines, including a triple line and spinodal boundaries, and yields rough mappings to physical scales (e.g., MeV, MeV). Overall, the work highlights universal features of the QCD phase diagram that could inform interpretations of heavy-ion collision experiments and guide future lattice studies at finite density.

Abstract

We analyze the phase diagram of QCD with two massless quark flavors in the space of temperature, T, and chemical potential of the baryon charge, mu, using available experimental knowledge of QCD, insights gained from various models, as well as general and model independent arguments including continuity, universality, and thermodynamic relations. A random matrix model is used to describe the chiral symmetry restoration phase transition at finite T and mu. In agreement with general arguments, this model predicts a tricritical point in the T mu plane. Certain critical properties at such a point are universal and can be relevant to heavy ion collision experiments.

Paper Structure

This paper contains 6 sections, 34 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Definitions
  3. Zero Temperature
  4. Finite $T$ and $\mu$
  5. Universal properties of the tricritical point
  6. A random matrix model at finite $T$ and $\mu$

Figures (2)

  • Figure 1: Schematic dependence of the baryon charge density on the chemical potential at $T=0$ (a) in QCD ($\mu_0\approx m_N-16$ MeV) and (b) in QCD+ ($\mu_0\approx m_N-8$ MeV).
  • Figure :