The phase diagram of dense QCD

TL;DR

This work surveys the dense QCD phase diagram, focusing on deconfinement, chiral restoration, and color superconductivity across temperature and density. It combines lattice QCD results, Ginzburg-Landau-Wilson analyses, and effective theories to map phase boundaries, critical points, and possible inhomogeneous and gluonic phases, emphasizing how order parameters like the Polyakov loop, chiral condensate, and diquark condensate govern transitions. Key contributions include the discussion of quarkyonic matter, various CSC patterns (CFL, 2SC, and spin-1 variants), and the role of the $U(1)_A$ anomaly in shaping the phase structure, as well as novel inhomogeneous and mixed-phase possibilities. The findings have implications for heavy-ion experiments, neutron-star physics, and beyond-QCD analogies in ultracold atoms, highlighting ongoing challenges such as the sign problem in lattice simulations at finite density and the elimination of instabilities in dense quark matter.

Abstract

Current status of theoretical researches on the QCD phase diagram at finite temperature and baryon chemical potential is reviewed with special emphasis on the origin of various phases and their symmetry breaking patterns. Topics include; quark deconfinement, chiral symmetry restoration, order of the phase transitions, QCD critical point(s), colour superconductivity, various inhomogeneous states and implications from QCD-like theories.

Figures (14)

• Figure 1: Conjectured QCD phase diagram with boundaries that define various states of QCD matter based on S$\chi$B patterns.
• Figure 2: Characteristic points on the QCD phase diagram. E represents so-called the QCD critical point. F is another critical point induced by the quark-hadron continuity. G is the critical point associated with the liquid-gas transition of nuclear matter. H refers to a region which looks like an approximate triple point. See the text for details.
• Figure 3: Schematic figure of the Columbia phase diagram in $3$-flavour QCD at $\mu_{\rm B}=0$ on the plane with the light and heavy quark masses. The $\mathrm{U}(1)_{\rm A}$ symmetry restoration is not taken into account. Near the left-bottom corner the chiral phase transition is of first order and turns to smooth crossover as $m_{\rm ud}$ and/or $m_{\rm s}$ increase. The right-top corner indicates the deconfinement phase transition in the pure gluonic dynamics.
• Figure 4: Determination of the pseudo-critical temperature $T_{\rm pc}$ for thermal QCD transition(s) from recent lattice QCD simulations. (1) $169(12)(4)\,\hbox{MeV}$ for $2+1$ flavours in the asqtad action with $N_t$ up to $8$ determined by $\chi_m/T^2$ (where $\chi_m$ is the chiral susceptibility) Bernard:2004je. (2) $192(7)(4)\,\hbox{MeV}$ for $2+1$ flavours in the p4fat3 staggered action with $N_t$ up to $6$ determined by $\chi_m$ and $\chi_L$ (where $\chi_L$ is the Polyakov loop susceptibility) Cheng:2006qk. (3) $151(3)(3)\,\hbox{MeV}$ and $176(3)(4)\,\hbox{MeV}$ for $2+1$ flavours in the stout-link improved staggered action with $N_t$ up to $10$ determined by $\chi_m/T^4$ and $\chi_L$ respectively Aoki:2006br. (4) $172(7)\,\hbox{MeV}$ for $2$ flavours in clover improved Wilson action with $N_t$ up to $6$ determined by $\chi_L$Maezawa:2007fd. (5) $152(3)(3)\,\hbox{MeV}$ and $170(4)(3)\,\hbox{MeV}$ for $2+1$ flavours in the stout-link improved staggered action with $N_t$ up to $12$ determined by $\chi_m/T^2$ and $\chi_L$ respectively Aoki:2009sc. (6) $185$--$195\,\hbox{MeV}$ for $2+1$ flavours in the asqtad and p4 actions with $N_t$ up to $8$ determined by $\chi_m$ and $\chi_L$Bazavov:2009zn. (7) $174(3)(6)\,\hbox{MeV}$ for $2$ flavours in the improved Wilson action with $N_t$ up to $12$ determined by $\chi_m$ and $\chi_L$Bornyakov:2009qh. (8) $171(10)(17)\,\hbox{MeV}$ for $2+1$ flavours in the domain-wall action with $N_t=8$ determined by $\chi_m/T^2$Cheng:2009be. (9) $147(2)(3)\,\hbox{MeV}$ and $165(5)(3)\,\hbox{MeV}$ for $2+1$ flavours in the stout-link improved staggered action with $N_t$ up to $16$ determined by $\chi_m/T^4$ and $\chi_s/T^2$ (where $\chi_s$ is the strange-quark susceptibility) Borsanyi:2010bp.
• Figure 5: Schematic evolution of the Columbia plot with increasing $\mu_{\rm B}$ in the standard scenario (left) and the exotic scenario (right).