Surface effects in strange-quark matter play an important role for certain observables which have been proposed in order to identify strange stars, and color superconductivity can strongly modify these effects. We study the surface of color superconducting strange-quark matter by solving the Hartree-Fock-Bogoliubov equations for finite systems ("strangelets") within the MIT bag model, supplemented with a pairing interaction. Due to the bag-model boundary condition, the strange-quark density is suppressed at the surface. This leads to a positive surface charge, concentrated in a layer of ~1 fm below the surface, even in the color-flavor locked (CFL) phase. However, since in the CFL phase all quarks are paired, this positive charge is compensated by a negative charge, which turns out to be situated in a layer of a few tens of fm below the surface, and the total charge of CFL strangelets is zero. We also study the surface and curvature contributions to the total energy. Due to the strong pairing, the energy as a function of the mass number is very well reproduced by a liquid-drop type formula with curvature term.
Finite lumps of color-flavor locked strange quark matter (CFL-strangelets) are significantly more stable than strangelets without color-flavor locking for wide ranges of parameters, increasing the likelihood of strangelet metastability, or even absolute stability beyond some minimum baryon number $A_{min}$. Whereas bulk CFL strange quark matter is electrically neutral, CFL-strangelets are positively charged, with $Z\approx 0.3 A^{2/3}$. This is quite different from ``ordinary'' strangelets and may provide a possible test of color-flavor locking if strangelets are detected in upcoming cosmic-ra…
We study effects of two-flavor color superconductivity on the structure of strange dwarfs, which are stellar objects with similar masses and radii with ordinary white dwarfs but stabilized by the strange quark matter core. We find that unpaired quark matter is a good approximation to the core of strange dwarfs.
It is shown that extremely strong electric fields may be generated at the surface of strange quark matter in the color-flavor locked phase because of the surface effects. Some properties of strange stars made of this matter are briefly discussed.
It is possible that a system composed of up, down and strange quarks consists the true ground state of nuclear matter at high densities and low temperatures. This exotic plasma, called strange quark matter (SQM), seems to be even more favorable energetically if quarks are in a superconducting state, the so-called color-flavor locked state. Here are presented calculations made on the basis of the MIT bag model considering the influence of finite temperature on the allowed parameters characterizing the system for stability of bulk SQM (the so-called stability windows) and also for strangelets, s…
Under the combination effect of the recommencement heating due to spin-down of strange stars and the heat perseveration due to weak conduct heat of the crust, the Cooper pair breaking and formation(PBF) in color superconduction quark matter arises. We investigated the cooling of the strange stars with a crust in color superconductivity phase including both decomfinement heating and PBF process. We find that deconfinement heating can delay the thermal evolution of strange stars and the PBF process suppresses the early temperature rise of the stars. The cooling strange stars behave within the br…
The dispersion relation and damping rate of longitudinal color plasmons in finite strange quark matter (strangelets) are evaluated in the limits of weak coupling, low temperature, and long wavelength. The property of the QCD vacuum surrounding a strangelet makes the frequency of the plasmons nearly the same as the color plasma frequency of bulk matter. The plasmons are damped by their coupling with individual excitations of particle-hole pairs of quarks, of which the energy levels are discretized by the boundary. For strangelets of macroscopic size, the lifetime of the plasmons is found to be …
R-mode instabilities in rapidly rotating quark matter stars (strange stars) lead to specific signatures in the evolution of pulsars with periods below 2.5 msec, and may explain the apparent lack of very rapid pulsars. Existing data seem consistent with pulsars being strange stars with a normal quark matter phase surrounded by an insulating nuclear crust. In contrast, quark stars in a color-flavor-locked (CFL) phase are ruled out. Two-flavor color superconductivity (2SC) is marginally inconsistent with pulsar data.
At ultra-high density, matter is expected to form a degenerate Fermi gas of quarks in which there is a condensate of Cooper pairs of quarks near the Fermi surface: color superconductivity. In these proceedings I review some of the underlying physics, and discuss outstanding questions about the phase structure of ultra-dense quark matter.
The cooling of a young bare strange star is studied numerically by solving the equations of energy conservation and heat transport for both normal and superconducting strange quark matter inside the star. We show that the thermal luminosity from the strange star surface, due to both photon emission and e+e- pair production, may be orders of magnitude higher than the Eddington limit, for about one day for normal quark matter but possibly for up to a hundred years for superconducting quark matter, while the maximum of the photon spectrum is in hard X-rays with a mean energy of ~ 100 keV or even …
We present a non-relativistic quark molecular model (QMM) of the strange crypto-exotic pentaquark baryon spectrum motivated by the recent data showing narrow, resonance enhancements in electromagnetic and hadronic production of kaons. Our model assumes color octet bonded quark molecular clusters forming exotic color singlet pentaquark baryons. We develop explicit molecular pentaquark wavefunctions that exhibit color interchange and cluster fermion antisymmetry. Our color electro-dynamics (CED) inspired Hamiltonian, which includes confinement, one gluon exchange and color magnetic interactions,…
Electric and color neutral solutions, and the critical conditions for the formation of gapless color superconductors, are investigated in $K^0$ condensed color-flavor locked quark matter for nonzero strange quark mass. We show that as the strange quark mass increases, gapless modes for up-strange quark pairing occur first, followed by down-strange quark pairing. The behavior of the gaps, the dispersion relations, and the thermodynamic potential are all found as functions of the strange quark mass on the basis of a Nambu Jona-Lasinio type model. To a high degree of accuracy, they are presented …
The relative multiplicities for hadron production in different high energy collisions are in general well described by an ideal gas of all hadronic resonances, except that under certain conditions, strange particle rates are systematically reduced. We show that the suppression factor gamma_s, accounting for reduced strange particle rates in pp, pA and AA collisions at different collision energies, becomes a universal function when expressed in terms of the initial entropy density s_0 or the initial temperature T of the produced thermal medium. It is found that gamma_s increases from about 0.5 …
We analyze the color-flavor-locked phase of strange quark matter modelled by the three-flavor Nambu-Jona-Lasinio (NJL) framework with and without magnetic field and discuss some additional constraints on the stability scenario when a high magnetic field is applied. We compare the results obtained by employing the MIT Bag Model and discuss the pairing gap behavior and its influence on the equation of state.
The phase diagram of strongly interacting matter at non-zero temperature and baryon chemical potential is calculated within a 3-flavor NJL-type quark model with realistic quark masses. The model exhibits spontaneous chiral symmetry breaking as well as diquark condensation in the two-flavor color-superconducting phase and in the color-flavor locked phase. We investigate the color-flavor unlocking phase transition, taking into account self-consistently calculated effective quark masses. We find that it is mainly triggered by a first order phase transition with respect to the strange quark mass. …
The quark quasiparticle model is extended to study the properties of color-flavor locked strange quark matter at finite chemical potential and in a strong magnetic field. We present a self-consistent thermodynamic treatment by employing a chemical potential dependent bag function. It is found that the magnetized color-flavor-locked (MCFL) matter is more stable than other phases within a proper magnitude of magnetic field. The stability window is graphically shown for the MCFL matter compared with ordinate magnetized matter. The anisotropic structure of MCFL matter is dominated by the magnetic …
The structure of $(ΩΩ)_{0^+}$ dibaryon with strangeness $s=-6$ is studied in the extended chiral SU(3) quark model, in which vector meson exchange dominates the short range interaction. The resonating group method (RGM) is adopted, in which the $ΩΩ$ and $CC$ (hidden color) channels are involved. The color screening effect and the effects of mixing of scalar mesons on $(ΩΩ)_{0^+}$ are also investigated.
We study compact stars that contain quark matter. We look at the effect of color superconductivity in the quark matter on the nuclear-quark matter transition density, mass-radius relationship, and the density discontinuity at the boundary between nuclear and quark matter. We find that color superconducting quark matter will occur in compact stars at values of the bag constant where ordinary quark matter would not be allowed. We are able to construct ``hybrid'' stars with a color superconducting quark matter interior and nuclear matter surface, with masses in the range 1.3-1.6 M_solar and radii…
The gap caused by a strong electric field between the quark surface and nuclear crust of a strange star is studied in an improved model including gravity and pressure as well as electrostatic forces. The transition from gap to crust is followed in detail. The properties of the gap are investigated for a wide range of parameters assuming both color-flavor locked and non color-flavor locked strange star cores. The maximally allowed crust density is generally lower than that of neutron drip. Finite temperature is shown to increase the gap width, but the effect is significant only at extreme tempe…
Dibaryon candidates with strangeness S=-2,-3,-4,-5,-6 are studied in terms of the extended quark delocalization and color screening model. The results show that there are only a few promising low lying dibaryon states: The H and di-Omega may be marginally strong interaction stable but model uncertainties are too large to allow any definitive statement. The SIJ=-3,1/2,2 N-Omega state is 62 MeV lower than the N-Omega threshold and 24 MeV lower than the Lambda-Xi-pi threshold. It might appear as a narrow dibaryon resonance and be detectable in the RHIC detector through the reconstruction of the v…
In this work, the relative Underlying Event (UE) transverse multiplicity activity classifier ($R_{\rm {T}}$) is used to study the strange and multi-strange hadron production in proton-proton collisions. Our study with $R_{\rm {T}}$ would allow to disentangle these particles, which are originating from the soft and hard QCD processes. We have used the PYTHIA 8 Monte-Carlo (MC) with a different implementation of color reconnection and rope hadronization models to demonstrate the proton-proton collisions data at $\sqrt{s}$ = 13 TeV. The relative production of strange and multi-strange hadrons are…
The nonzero strange quark mass effect in different types of single flavor color superconductivity and the phase diagram in a magnetic field are studied. We have obtained simple analytical forms of the quasi-particle energies for an arbitrary mass and explored the mass correction to the pressure and the transition temperature. It is found that the mass reduces the pressure and transition temperature of strange quarks, but it doesn't change the ranking $P_n<P_{\rm A}<P_{\rm polar}<P_{\rm planar}<P_{\rm CSL}$ of the pressure for the four canonical single flavor phases. The phase diagram with magn…
The bulk viscosity in spin-one color-superconducting strange quark matter is calculated by taking into account the interplay between the nonleptonic and semi-leptonic week processes. In agreement with previous studies, it is found that the inclusion of the semi-leptonic processes may result in non-negligible corrections to the bulk viscosity in a narrow window of temperatures. The effect is generally more pronounced for pulsars with longer periods. Compared to the normal phase, however, this effect due to the semi-leptonic processes is less pronounced in spin-one color superconductors. Assumin…
We compare the mass-radius relationship of strange stars obtained in two theoretical frameworks describing the color-flavor-locking state of dense quark matter: The semi-empirical MIT model and a self-consistent approach using the Nambu-Jona-Lasinio (NJL) model. In the simplest MIT model extended to include pairing, one can make the equation of state stiffer by increasing the gap parameter so that larger maximum masses for these objects can be reached. In the NJL model, however, such an effect is not possible. To increase the gap parameter within the NJL model to values comparable to those con…
This paper provides an overview of the possible role of Quantum Chromo Dynamics (QDC) for neutron stars and strange stars. The fundamental degrees of freedom of QCD are quarks, which may exist as unconfined (color superconducting) particles in the cores of neutron stars. There is also the theoretical possibility that a significantly large number of up, down, and strange quarks may settle down in a new state of matter known as strange quark matter, which, by hypothesis, could be more stable than atomic nuclei. In the latter case new classes of self-bound, color superconducting objects, ranging …
We explore the phase diagram of strongly interacting matter with massless u and d quarks as a function of the strange quark mass m_s and the chemical potential mu for baryon number. Neglecting electromagnetism, we describe the different baryonic and quark matter phases at zero temperature. For quark matter, we support our model-independent arguments with a quantitative analysis of a model which uses a four-fermion interaction abstracted from single-gluon exchange. For any finite m_s, at sufficiently large mu we find quark matter in a color-flavor locked state which leaves a global vector-like …
The strangeness content of hadronic matter is studied in a string-flip model that reproduces various aspects of the QCD-inspired phenomenology, such as quark clustering at low density and color deconfinement at high density, while avoiding long range van der Waals forces. Hadronic matter is modeled in terms of its quark constituents by taking into account its internal flavor (u,d,s) and color (red, blue, green) degrees of freedom. Variational Monte-Carlo simulations in three spatial dimensions are performed for the ground-state energy of the system. The onset of the transition to strange matte…
Fluctuations of the color superconducting order parameter in dense quark matter at finite temperatures are investigated in terms of the phenomenological Ginzburg - Landau approach. Our estimates show that fluctuations of the di-quark gap may strongly affect some of thermodynamic quantities even far below and above the critical temperature. If the critical temperature of the di-quark phase transition were rather high one could expect a manifestation of fluctuations of the di-quark gap in the course of heavy ion collisions.
We summarize masses and radii for a number of white dwarfs as deduced from a combination of proper motion studies, Hipparcos parallax distances, effective temperatures, and binary or spectroscopic masses. A puzzling feature of these data is that some stars appear to have radii which are significantly smaller than that expected for a standard electron-degenerate white-dwarf equations of state. We construct a projection of white-dwarf radii for fixed effective mass and conclude that there is at least marginal evidence for bimodality in the radius distribution forwhite dwarfs. We argue that if su…
Thermal fluctuations of the color superconducting order parameter in dense quark matter are investigated in terms of the phenomenological Ginzburg - Landau approach. Our estimates show that fluctuations of the di-quark gap may strongly affect some of thermodynamic quantities even far below and above the critical temperature. If the critical temperature $T_c$ of the di-quark phase transition were rather high ($\gsim (50÷70)$ MeV) one could expect a manifestation of fluctuations of the di-quark gap in the course of heavy ion collisions (above $T_c$). For $T_c \sim 50 $MeV color superconducting f…
Considering the confinement of massless $u$ and $d$ quarks and massive $s$ quarks in an axially symmetric quadrupole shaped deformable bag, the stability properties of color-singlet strangelets at finite temperatures are studied for the baryon number $A \leq$ 100. It is found that, in general, at each $A$ the energy of the strangelet is the lowest for the spherical shape. However, it is interesting to find shell structures for the deformed shapes at some new $A$ values, not found for the spherical shape. This should be of relevance for the experimental search of strangelets. The color projecte…
We calculate the neutrino mean free path in color superconducting quark matter, and employ it to study the cooling of matter via neutrino diffusion in the superconducting phase as compared to a free quark phase. The cooling process slows when quark matter undergoes a second order phase transition to a superconducting phase at the critical temperature $T_c$. Cooling subsequently accelerates as the temperature decreases below $T_c$. This will directly impact the early evolution of a newly born neutron star should its core contain quark matter. Consequently, there may be observable changes in the…
The role of the strange quark mass for the phase structure of QCD at non-vanishing densities is studied by employing a recently developed self-consistent truncation scheme for the Dyson-Schwinger equations of the quark propagators in Landau gauge. Hereby the medium modification of the effective quark interaction by the polarization of gluons is implemented. Taking into account this effect results in significantly smaller dynamical quark masses at the Fermi surface. Due to this reduction the color-flavor locked phase is always the preferred color-superconducting phase at zero temperature and fo…
Compact astrophysical objects are a window for the study of strongly interacting nuclear matter given the conditions in their interiors, which are not reproduced in a laboratory environment. Much has been debated about their composition with possibilities ranging from a simple mixture of mostly protons and neutrons to deconfined quark matter. Recent observations on the mass of two pulsars, PSR J1614-2230 and PSR J0348+0432, have posed a great restriction on their composition, since the equation of state must be hard enough to support masses of about at least two solar masses. The onset of quar…
We solve Schwinger-Dyson (SD) equation for the color superconducting (CS) gap in nonlocal gauge which justifies the ladder approximation in subleading order calculation. The gap prefactor increases about 1.6 times to the leading order gap determined in Landau gauge.
We calculate the antibaryon-to-baryon ratios, anti-p/p, anti-Lambda/Lambda, anti-Xi/Xi, and anti-Omega/Omega for Au+Au collisions at RHIC (sqrt{s}_{NN}=200 GeV). The effects of strong color fields associated with an enhanced strangeness and diquark production probability and with an effective decrease of formation times are investigated. Antibaryon-to-baryon ratios increase with the color field strength. The ratios also increase with the strangeness content |S|. The netbaryon number at midrapidity considerably increases with the color field strength while the netproton number remains roughly t…
We review the status of research on the cooling of compact stars, with emphasis on the influence of color superconducting quark matter phases. Although a consistent microscopic approach is not yet available, severe constraints on the phase structure of matter at high densities come from recent mass and cooling observations of compact stars.
We consider the effect of a six-fermion interaction of the {'}t Hooft form in the quark-quark channel on the ground state of matter at finite density. The coupling constant for this new term is varied within the limits suggested by naturalness. The flavor-mixing effects of the additional term destabilize the color-flavor-locked (CFL) and, to a lesser extent, the two-color superconducting (2SC) phases of quark matter, especially for positive values of the coupling. For some values of the coupling, the critical density for the CFL phase is nearly larger than the maximum density in the neutron st…
We study numerically the thermal emission of $e^+e^-$ pairs from a bare strange star heated by energy input onto its surface; heating starts at some moment, and is steady afterwards. The thermal luminosity in $e^+e^-$ pairs increases to some constant value. The rise time and the steady thermal luminosity are evaluated. Both normal and colour superconducting states of strange quark matter are considered. The results are used to test the magnetar model of soft gamma-ray repeaters where the bursting activity is explained by fast decay of superstrong magnetic fields and heating of the strange star…
Using generalized Nielsen identities a formal proof is given that the fermionic quasiparticle dispersion relations in a color superconductor are gauge independent. This turns out to involve gluonic tadpoles which are calculated to one-loop order in a two-flavor color superconductor. Regarding the appearance of gluon tadpoles, we argue that in QCD the color superconducting phase is automatically color neutral.
Realistic nonstrange hybrid compact stars with color superconducting quark matter in their interior are constructed. It is shown that a positively charged two-flavor color superconducting phase could naturally appear in the core of a hybrid star as one of the components of a globally neutral mixed phase. The negatively charged normal quark phase is the other component of the mixed phase. The quark core of the star is surrounded by another mixed phase made of hadronic and normal quark matter. The two mixed phases are separated by a sharp interface. Finally, the lowest density regions of the sta…
We investigate the consequences of enforcing local color neutrality on the color superconducting phases of quark matter by utilizing the Nambu-Jona-Lasinio model supplemented by diquark and the t'Hooft six-fermion interactions. In neutrino free matter at zero temperature, color neutrality guarantees that the number densities of u, d, and s quarks in the Color-Flavor-Locked (CFL) phase will be equal even with physical current quark masses. Electric charge neutrality follows as a consequence and without the presence of electrons. In contrast, electric charge neutrality in the less symmetric 2-fl…
We discuss the possibility that the recent detection of 511 keV gamma rays from the galactic bulge, as observed by INTEGRAL, can be naturally explained by the supermassive very dense droplets (strangelets) of dark matter. These droplets are assumed to be made of ordinary light quarks (or antiquarks) condensed in non-hadronic color superconducting phase. The droplets can carry electrons (or positrons) in the bulk or/and on the surface. The e^+e^- annihilation events take place due to the collisions of electrons from the visible matter with positrons from dark matter droplets which may result in…
Based upon the analogy to the electroweak phase diagram, I propose that in QCD there might be a critical line for a superfluid transition, in the plane of chemical potential and temperature. The order parameter has the quantum numbers of the H-dibaryon, but the transition is driven by color superconductivity in strange quark matter.
Lack of Lorentz invariance of QCD at finite quark chemical potential in general implies the need of Lorentz non-invariant condensates for the self-consistent description of the color-superconducting ground state. Moreover, the spontaneous breakdown of color SU(3) in this state naturally leads to the existence of SU(3) non-invariant non-superconducting expectation values. We illustrate these observations by analyzing the properties of an effective 2-flavor Nambu-Jona-Lasinio type Lagrangian and discuss the possibility of color-superconducting states with effectively gapless fermionic excitation…
The most strange dibaryon $ΩΩ$ with quantum numbers $S=-6$, $I=0$, and $J^{P}=0^{+},~1^{-},~2^{+},~3^{-}$ is reanalyzed in the framework of quark delocalization color screening model (QDCSM) and chiral quark model (ChQM). The $ΩΩ$ dibaryon with $J^{P}=0^{+}$ is bound, and the one with other quantum numbers $J^{P}=1^{-},~2^{+},~3^{-}$ are all unbound in our calculation. The low-energy scattering phase shifts, the scattering length, and the effective range of the $ΩΩ$ dibaryon with $J^{P}=0^{+}$ also support the existence of such strange dibaryon. This dibaryon is showed to be a shallow bound st…
We review the basic properties of the currCFL-K^0 phase in dense quark matter. At asymptotically large densities, three-flavor quark matter is in the color-flavor locked (CFL) state. The currCFL-K^0 state is a way to respond to ``stress'' on the quark Cooper pairing, imposed at more moderate densities by the strange quark mass and the conditions of electric and color neutrality. We show how a kaon supercurrent is incorporated in a purely fermionic formalism, and show that the net current vanishes due to cancellation of fermion and charge-conjugate fermion contributions.
The phase diagram of a three-flavor Polyakov-loop Nambu-Jona-Lasinio model is analyzed for the case of isospin symmetric matter with color superconducting phases. The coexistence of chiral symmetry breaking and two-flavor color superconductivity (2SC phase) and a thermodynamic instability due to the implementation of a color neutrality constraint is observed. It is suggested to use a universal hadronization pressure to estimate the phase border between hadronic and quark-gluon plasma phases. Trajectories of constant entropy per baryon are analyzed for conditions appropriate for heavy-ion colli…
We discuss a Nambu--Jona-Lasinio (NJL) type quantum field theoretical approach to the quark matter equation of state with color superconductivity and construct hybrid star models on this basis. It has recently been demonstrated that with increasing baryon density, the different quark flavors may occur sequentially, starting with down-quarks only, before the second light quark flavor and at highest densities also the strange quark flavor appears. We find that color superconducting phases are favorable over non-superconducting ones which entails consequences for thermodynamic and transport prope…
Final-state interaction and screening have a great influence on $q \bar q$ production cross sections, which are important quantities in many problems in quark-gluon plasma physics. They lead to an enhancement of the cross section for a $q \bar q$ color-singlet state and a suppression for a color-octet state. The effects are large near the production threshold. The presence of screening gives rise to resonances for $q\bar q$ production just above the threshold at specific plasma temperatures. These resonances, especially $c\bar c$ and $b \bar b$ resonances, may be utilized to search for the qua…
We discuss gapless color superconductivity for neutral quark matter in beta 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.
We study the interplay of the chiral and the color superconducting phase transitions in an extended Nambu--Jona-Lasinio model with a multi-quark interaction that produces the nonlinear chiral-diquark coupling. We observe that this nonlinear coupling adds up coherently with the ω^2 interaction to produce the chiral-color superconductivity coexistence phase or cancel each other depending on its sign. We discuss that large coexistence region in the phase diagram is consistent with the quark-diquark picture for the nucleon whereas its smallness is the prerequisite for the applicability of the Ginz…
The gap parameter for color superconductivity is expected to be a gauge invariant quantity, at least on the appropriate mass shell. Computing the gap to subleading order in the QCD coupling constant, g, we show that the prefactor of the exponential in 1/g is gauge dependent off the mass shell, and independent of gauge on the mass shell.
When nuclear matter reaches a high enough density, we expect that the nucleons will overlap so much as to lose their separate identities, and merge into quark matter. In this talk I will review some theoretical expectations and speculations about quark matter, focusing on the phenomenon of quark pair condensation (color superconductivity) and its application to compact stars.
We consider color superconductivity with two flavors of massless quarks which form Cooper pairs with total spin zero. We solve the gap equation for the color-superconducting gap parameter to subleading order in the QCD coupling constant $g$ at zero temperature. At this order in $g$, there is also a previously neglected contribution from the real part of the quark self-energy to the gap equation. Including this contribution leads to a reduction of the color-superconducting gap parameter $\f_0$ by a factor $b_0'=\exp \big[ -(\p ^2+4)/8 \big]\simeq 0.177$. On the other hand, the BCS relation $T_c…
We investigate the phase diagram of color superconducting quark matter with strange quarks (2SC+s quark matter) in beta equliibrium at zero as well as finite temperatures within a Nambu-Jona-Lasinio model. The variational method as used here allows us to investigate simultaneous formation of condensates in quark--antiquark as well as in diquark channels. Color and electric charge neutrality conditions are imposed in the calculation of the thermodynamic potential. Medium dependance of strange quark mass plays a sensitve role in maintaining charge neutrality conditions. At zero temperature the s…
The properties of plasmons, Nambu-Goldstone bosons and gapless Carlson-Goldman collective modes in color-flavor locked phase of color superconducting dense quark matter at finite temperature are reviewed. A possibility of a kaon condensation with an abnormal number of the NG bosons is also discussed.
The first lecture provides an introduction to the physics of color superconductivity in cold dense quark matter. The main color superconducting phases are briefly described and their properties are listed. The second lecture covers recent developments in studies of color superconducting phases in neutral and beta-equilibrated matter. The properties of gapless color superconducting phases are discussed.
We examine electrically and color neutral quark matter in beta-equilibrium focusing on the possibility of mixed phases between different color superconducting phases. To that end we apply the Gibbs criterion to ensure phase equilibrium and discuss the external conditions under which these mixed phases can occur. Neglecting surface and Coulomb effects we find a rich structure of different mixed phases with up to four components, including 2SC and CFL matter as well as more ``exotic'' components, like a phase with us- and ds-pairing but without ud-pairing. Preliminary estimates indicate, however…
