[Paper Review] QCD phase diagram at high temperature and density

Mei Huang|arXiv (Cornell University)|Jan 19, 2010

High-Energy Particle Collisions Research1 references3 citations

TL;DR

This paper reviews the QCD phase diagram at high temperature and density, focusing on the discovery of strongly interacting quark-gluon plasma (sQGP) at RHIC and the phase structure of gapless color superconductors at high baryon density. It identifies bulk viscosity over entropy density as a probe for locating the critical end point and clarifies instabilities—chromomagnetic, Sarma, and Higgs—that drive inhomogeneous phases in gapless color superconducting matter.

ABSTRACT

This article reviews recent progress of QCD phase structure, including color superconductor at high baryon density and strongly interacting quark-gluon plasma (sQGP) at high temperature created through relativistic heavy ion collision. A brief overview is given on the discovery of sQGP at RHIC. The possibility of locating the critical end point (CEP) from the property of bulk viscosity over entropy density is discussed. For the phase structure at high baryon density, the status of the unconventional color superconducting phase with mismatched pairing is reviewed. The chromomagnetic instability, Sarma instability and Higgs instability in the gapless color superconducting phase are clarified.

Motivation & Objective

• To summarize recent progress in understanding the QCD phase diagram under extreme conditions of high temperature and high baryon density.
• To review the experimental discovery and theoretical characterization of strongly interacting quark-gluon plasma (sQGP) at RHIC.
• To investigate the possibility of locating the critical end point (CEP) in the QCD phase diagram using the ratio of bulk viscosity to entropy density.
• To analyze the stability and phase structure of gapless color superconducting phases, particularly the role of chromomagnetic, Sarma, and Higgs instabilities.
• To clarify the emergence of inhomogeneous states such as plane-wave and striped phases due to these instabilities in dense quark matter.

Proposed method

• Utilizes hydrodynamic simulations and relativistic hydrodynamics to model the evolution of the quark-gluon plasma formed in relativistic heavy-ion collisions.
• Applies perturbative QCD and effective field theories to describe the sQGP regime, particularly analyzing the shear and bulk viscosity over entropy density ratios.
• Employs the AdS/CFT duality to establish a lower bound on shear viscosity, suggesting sQGP as a nearly perfect fluid.
• Analyzes the gapless color superconducting phase using Gorkov-Nambu formalism and nonlinear realization of the order parameter to study instabilities.
• Evaluates the role of Coulomb interaction and gradient energy in competing with Higgs instability to determine the preferred ground state structure.
• Compares free energies of candidate states—mixed phase, FF, LO, and multi-plane wave states—to identify the most stable configuration.

Experimental results

Research questions

• RQ1 Can the bulk viscosity over entropy density ratio serve as a signature to locate the critical end point (CEP) in the QCD phase diagram?
• RQ2 What instabilities arise in the gapless color superconducting phase, and how do they influence the spatial structure of the superconducting order parameter?
• RQ3 How do chromomagnetic, Sarma, and Higgs instabilities compete or coexist in dense quark matter with mismatched pairing?
• RQ4 Why do imbalanced ultracold atom systems exhibit phase separation instead of a LOFF state, and what does this imply for quark matter?
• RQ5 What is the role of the coherence length and momentum scale $k_{ ext{min}}$ in determining the stability of inhomogeneous superconducting phases?

Key findings

• The sQGP produced at RHIC exhibits a shear viscosity over entropy density ratio close to the lower bound $1/(4 au)$ predicted by AdS/CFT, indicating it is the most perfect fluid observed.
• Bulk viscosity over entropy density ($\zeta/s$) shows a sharp rise near first-order phase transitions and a cusp at the critical temperature for second-order transitions, suggesting it as a probe for the critical end point.
• In the gapless color superconducting phase, the phase part of the order parameter is unstable to chromomagnetic instabilities, favoring a plane-wave state.
• The magnitude part of the order parameter is subject to both Sarma and Higgs instabilities; while the Sarma instability can be mitigated by charge neutrality, the Higgs instability cannot be cured by Coulomb interaction.
• The Higgs instability leads to the formation of inhomogeneous states with a characteristic length scale comparable to the coherence length of the 2SC phase, indicating a preference for spatially modulated structures.
• Numerical analysis shows that $l \sim k_{\text{min}}^{-1}$, and when $l/\xi < 1$, phase separation becomes energetically favorable, supporting the emergence of inhomogeneous phases.