Phase Diagram Of Quark Matter Research Articles

Phase diagram of neutral quark matter in nonlocal chiral quark models

We consider the phase diagram of two-flavor quark matter under neutron star constraints for two nonlocal, covariant quark models within the mean-field approximation. In the first case (Model I) the nonlocality arises from the regularization procedure, motivated by the instanton liquid model, whereas in the second one (Model II) a separable approximation of the one-gluon exchange interaction is applied. We find that Model II predicts a larger quark mass gap and a chiral symmetry breaking (CSB) phase transition line which extends 15--20% further into the phase diagram spanned by temperature ($T$) and chemical potential ($\ensuremath{\mu}$). The corresponding critical temperature at $\ensuremath{\mu}=0$, ${T}_{c}(0)\ensuremath{\simeq}140\text{ }\text{ }\mathrm{MeV}$, is in better accordance to recent lattice QCD results than the prediction of the standard local NJL model, which exceeds 200 MeV. For both Model I and Model II we have considered various coupling strengths in the scalar diquark channel, showing that different low-temperature quark matter phases can occur at intermediate densities: a normal quark matter (NQM) phase, a two-flavor superconducting (2SC) quark matter phase and a mixed 2SC-NQM phase. Although in most cases there is also a gapless 2SC phase, this occurs in general in a small region at nonzero temperatures, thus its effect should be negligible for compact star applications.

Phase diagram of three-flavor quark matter under compact star constraints

The phase diagram of three-flavor quark matter under compact star constraints is investigated within a Nambu--Jona-Lasinio model. Global color and electric charge neutrality is imposed for $\ensuremath{\beta}$-equilibrated superconducting quark matter. The constituent quark masses and the diquark condensates are determined self-consistently in the plane of temperature and quark chemical potential. Both strong and intermediate diquark coupling strengths are considered. We show that in both cases, gapless superconducting phases do not occur at temperatures relevant for compact star evolution, i.e., below $T\ensuremath{\sim}50\text{ }\text{ }\mathrm{MeV}$. The stability and structure of isothermal quark star configurations are evaluated. For intermediate coupling, quark stars are composed of a mixed phase of normal (NQ) and two-flavor superconducting (2SC) quark matter up to a maximum mass of $1.21\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. At higher central densities, a phase transition to the three-flavor color flavor locked (CFL) phase occurs and the configurations become unstable. For the strong diquark coupling we find stable stars in the 2SC phase, with masses up to $1.33\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. A second family of more compact configurations (twins) with a CFL quark matter core and a 2SC shell is also found to be stable. The twins have masses in the range $1.30\dots{}1.33\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. We consider also hot isothermal configurations at temperature $T=40\text{ }\text{ }\mathrm{MeV}$. When the hot maximum mass configuration cools down, due to emission of photons and neutrinos, a mass defect of $0.1\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ occurs and two final state configurations are possible.

Density dependence of quark masses and stability of color-flavor locked phases

Considering the density dependence of quark masses, we investigate the color-flavor-locked matter and its stability relative to the ( unpaired ) strange quark matter. We find that, when the current mass of strange quark $m_s$ is small, the strange quark matter remains stable for the moderate baryon densities. When $m_s$ is large, the gapless phase of the color-flavor-locked matter is found to be difficult to be stable. A schematic phase diagram of three-flavor quark matter is presented, in which the color-flavor-locked phase region is suppressed in comparison with the previous results.

Phase diagram of neutral quark matter: Self-consistent treatment of quark masses

We study the phase diagram of dense, locally neutral three-flavor quark matter within the framework of the Nambu--Jona-Lasinio model. In the analysis, dynamically generated quark masses are taken into account self-consistently. The phase diagram in the plane of temperature and quark chemical potential is presented. The results for two qualitatively different regimes, intermediate and strong diquark coupling strength, are presented. It is shown that the role of gapless phases diminishes with increasing diquark coupling strength.

Gapless phases of colour-superconducting matter

We discuss gapless colour superconductivity for neutral quark matter in β equilibrium at zero as well as at nonzero temperature. Basic properties of gapless superconductors are reviewed. The current progress and the remaining problems in the understanding of the phase diagram of strange quark matter are discussed.

Heating (gapless) color-flavor locked quark matter

We explore the phase diagram of neutral quark matter at high baryon density as a function of the temperature T and the strange quark mass Ms. At T=0, there is a sharp distinction between the insulating color-flavor locked (CFL) phase, which occurs where Ms^2/mu < 2 Delta, and the metallic gapless CFL phase, which occurs at larger Ms^2/mu. Here, mu is the chemical potential for quark number and Delta is the gap in the CFL phase. We find this distinction blurred at nonzero T, as the CFL phase undergoes an insulator-to-metal crossover when it is heated. We present an analytic treatment of this crossover. At higher temperatures, we map out the phase transition lines at which the gap parameters Delta_1, Delta_2 and Delta_3 describing ds-pairing, us-pairing and ud-pairing respectively, go to zero in an NJL model. For small values of Ms^2/mu, we find that Delta_2 vanishes first, then Delta_1, then Delta_3. We find agreement with a previous Ginzburg-Landau analysis of the form of these transitions and find quantitative agreement with results obtained in full QCD at asymptotic density for ratios of coefficients in the Ginzburg-Landau potential. At larger Ms^2/mu, we find that Delta_1 vanishes first, then Delta_2, then Delta_3. Hence, we find a "doubly critical'' point in the (Ms^2/mu,T)-plane at which two lines of second order phase transitions (Delta_1->0 and Delta_2->0) cross. Because we do not make any small-Ms approximation, if we choose a relatively strong coupling leading to large gap parameters, we are able to pursue the analysis of the phase diagram all the way up to such large values of Ms that there are no strange quarks present.

Phase diagram of dense neutral three-flavor quark matter

We study the phase diagram of dense, locally neutral three-flavor quark matter as a function of the strange quark mass, the quark chemical potential, and the temperature, employing a general nine-parameter ansatz for the gap matrix. At zero temperature and small values of the strange quark mass, the ground state of matter corresponds to the color–flavor-locked (CFL) phase. At some critical value of the strange quark mass, this is replaced by the recently proposed gapless CFL (gCFL) phase. We also find several other phases, for instance, a metallic CFL (mCFL) phase, a so-called uSC phase where all colors of up quarks are paired, as well as the standard two-flavor color-superconducting (2SC) phase and the gapless 2SC (g2SC) phase.

Color-flavor locked phase of dense quark matter with nonzero strangeness chemical potential

We study the effects of a nonzero strangeness chemical potential ${\ensuremath{\mu}}_{S}$ on the color-flavor locked phase of dense quark matter. It is found that, depending on the value of ${\ensuremath{\mu}}_{S},$ both the antikaon and kaon condensations may occur in color-flavor locked quark matter. The consequences of these condensations for the phase diagram of dense quark matter are investigated.

Diquark condensation effects on hot quark star configurations

The equation of state for quark matter is derived for a nonlocal, chiral quark model within the mean field approximation. We investigate the effects of a variation of the formfactors of the interaction on the phase diagram of quark matter. Special emphasis is on the occurrence of a diquark condensate which signals a phase transition to color superconductivity and its effects on the equation of state under the condition of β-equilibrium and charge neutrality. We calculate the quark star configurations by solving the Tolman–Oppenheimer–Volkoff equations and obtain for the transition from a hot, normal quark matter core of a protoneutron star to a cool diquark condensed one a release of binding energy of the order of Δ Mc 2∼10 53 erg. We find that this energy could not serve as an engine for explosive phenomena since the phase transition is not first order. Contrary to naive expectations the mass defect increases when for a given temperature we neglect the possibility of diquark condensation.

Thermodynamics of the three-flavor Nambu–Jona-Lasinio model: Chiral symmetry breaking and color superconductivity

Employing an extended three flavor version of the NJL model we discuss in detail the phase diagram of quark matter. The presence of quark as well as of diquark condensates gives raise to a rich structure of the phase diagram. We study in detail the chiral phase transition and the color superconductivity as well as color flavor locking as a function of the temperature and chemical potentials of the system.

Opening the crystalline color superconductivity window

Cold dense quark matter is in a crystalline color superconducting phase wherever pairing occurs between species of quarks with chemical potentials whose difference \delta\mu lies within an appropriate window. If the interaction between quarks is modeled as point-like, this window is rather narrow. We show that when the interaction between quarks is modeled as single-gluon exchange, the window widens by about a factor of ten at accessible densities and by much larger factors at higher density. This striking enhancement reflects the increasingly (1+1)-dimensional nature of the physics at weaker and weaker coupling. Our results indicate that crystalline color superconductivity is a generic feature of the phase diagram of cold dense quark matter, occurring wherever one finds quark matter which is not in the color-flavor locked phase. If it occurs within the cores of compact stars, a crystalline color superconducting region may provide a new locus for glitch phenomena.

Chiral symmetry breaking, color superconductivity and quark matter phase diagram: a variational approach

We discuss in this note simultaneous existence of chiral symmetry breaking and color superconductivity at finite temperature and density in a Nambu–Jona–Lasinio type model. The methodology involves an explicit construction of a variational ground state and minimisation of the thermodynamic potential. There exist nontrivial solutions to the gap equations at finite densities with both quark–antiquark as well as diquark condensates for the “ground” state. However, such a phase is thermodynamically unstable with the pressure being negative in this region. We also compute the equation of state, and obtain the structure of the phase diagram in the model.

Nuclear-matter-quark-matter phase diagram with strangeness.

A phenomenological equation of state of strongly interacting matter, including strange degrees of freedom, is presented. It is shown that the hyperon and kaon interactions must be included, in order to obtain a reasonable description of the deconfinement transition at high baryon densities. The consequences of kaon condensation on the nuclear-matter---quark-matter phase diagram are explored. The relative particle abundances obtained in an isentropic expansion of a blob of quark-gluon plasma are presented for different initial conditions. Implications for ultrarelativistic heavy-ion collisions are briefly discussed.