Color Superconductivity Research Articles

Roles of axial anomaly on neutral quark matter with color superconducting phase

We investigate the effects of the axial-anomaly term with a chiral-diquark coupling on the phase diagram within a two-plus-one-flavor Nambu-Jona-Lasinio model under the charge-neutrality and $\ensuremath{\beta}$-equilibrium constraints. We find that when such constraints are imposed, the new anomaly term plays a quite similar role as the vector interaction does on the phase diagram, which the present authors clarified in a previous work. Thus, there appear several types of phase structures with multiple critical points at low temperature $T$, although the phase diagrams with intermediate-$T$ critical point(s) are never realized without these constraints even within the same model Lagrangian. This drastic change is attributed to an enhanced interplay between the chiral and diquark condensates due to the anomaly term at finite temperature; the $u\mathrm{\text{\ensuremath{-}}}d$ diquark coupling is strengthened by the relatively large chiral condensate of the strange quark through the anomaly term, which in turn definitely leads to the abnormal behavior of the diquark condensate at finite $T$, inherent to the asymmetric quark matter. We note that the critical point from which the crossover region extends to zero temperature appears only when the strength of the vector interaction is larger than a critical value. We also show that the chromomagnetic instability of the neutral asymmetric homogenous two-flavor color-superconducting phase is suppressed and can be even completely cured by the enhanced diquark coupling due to the anomaly term and/or by the vector interaction.

Realizing analogues of color superconductivity with ultracold alkali atoms

A degenerate three-component Fermi gas of atoms with identical attractive interactions is expected to exhibit superfluidity and magnetic order at low temperature and, for sufficiently strong pairwise interactions, become a Fermi liquid of weakly interacting trimers. The phase diagram of this system is analogous to that of quark matter at low temperature, motivating strong interest in its investigation. We describe how a three-component gas below the superfluid critical temperature can be prepared in an optical lattice. To realize an SU(3)-symmetric system, we show how pairwise interactions in the three-component atomic system can be made equal by applying radiofrequency and microwave radiation. Finally, motivated by the aim to make more accurate models of quark matter, which have color, flavor and spin degrees of freedom, we discuss how an atomic system with SU(2)⊗SU(3) symmetry can be achieved by confining a three-component Fermi gas in the p-orbital band of an optical lattice potential.

Towards a holographic model of color superconductivity

In this paper, we discuss the basic elements that should appear in a gravitational system that is dual to a confining gauge theory displaying color superconductivity at large baryon density. We consider a simple system with these minimal elements and show that for a range of parameters, the phase structure of this model as a function of temperature and baryon chemical potential exhibits phases that can be identified with confined, deconfined and color superconducting phases in the dual field theory. We find that the critical temperature at which the superconducting phase disappears is remarkably small (relative to the chemical potential). This small number arises from the dynamics and is unrelated to any small parameter in the model that we study. We discuss similar models that exhibit flavor superconductivity.

NON-UNIFORM CHIRAL AND 2SC COLOR SUPERCONDUCTING PHASES, TAKING INTO ACCOUNT THE NONZERO CURRENT QUARK MASS

We have shown that the possibility of the existence of the mixed phase of the non-uniform chiral (NCh) and the color superconducting (2SC) ground state depends significantly on the choice of the parameters and type of the regularization scheme. Our calculations indicate that irrespective of the choice of regularization type, in a moderate baryon density region, there is a local minimum of a system corresponding to the NCh/2SC related phase. In the 3d cutoff regularization scheme, the mixed region of the NCh and the 2SC phases exists for a broad set of NJL model parameters. However, in the Schwinger regularization scheme, if parameters are set to the vacuum values of fπ, mπ and [Formula: see text], then the mixed region of the NCh and the 2SC phases does not exist.

Condensation of Embedded Monopoles in SU(2) Gauge Theory

Extending the Restricted Chromo dynamics (RCD) and exploring the role of quark monopoles (i.e. embedded monopoles) in restoration of chiral symmetry in SU(2) gauge theory, it has been shown that these monopoles play very important part in confining properties including color superconductivity.

Ginzburg-Landau phase diagram for dense matter with axial anomaly, strange quark mass, and meson condensation

We discuss the phase structure of dense matter, in particular, the nature of the transition between hadronic and quark matter. Calculations within a Ginzburg-Landau approach show that the axial anomaly can induce a critical point in this transition region. This is possible because in three-flavor quark matter with instanton effects a chiral condensate can be added to the color-flavor locked phase without changing the symmetries of the ground state. In (massless) two-flavor quark matter such a critical point is not possible since the corresponding color superconductor (2SC) does not break chiral symmetry. We study the effects of a nonzero but finite strange quark mass which interpolates between these two cases. Since at ultrahigh density the first reaction of the color-flavor locked phase to a nonzero strange quark mass is to develop a kaon condensate, we extend previous Ginzburg-Landau studies by including such a condensate. We discuss the fate of the critical point systematically and show that the continuity between hadronic and quark matter can be disrupted by the onset of a kaon condensate. Moreover, we identify the mass terms in the Ginzburg-Landau potential which are needed for the 2SC phase to occur in the phase diagram.

Supercoductivity in extended gauge theories

Extending the restricted quantum chromodynamics in SU(2) and SU(3) gauge theories by including quarks and gluons and also by reactivating the suppressed dynamical gauge degrees of freedom, the study of dyonic condensation, quark confinement and superconductivity (dual superconductivity as well as color superconductivity) has been undertaken in extended RCD. It has been shown that the global structure of the underlying gauge symmetry of this extended theory exhibits more information than the conventional QCD may do. It has also been shown that at sufficiently high baryon densities, when nucleons get converted into quark matter, the extended RCD is expected to be in one kind or other of the many different possible color superconductivity phases at low temperature.

Phase diagram of hot magnetized two-flavor color-superconducting quark matter

A two-flavor color superconducting (2SC) Nambu--Jona-Lasinio (NJL) model is introduced at finite temperature T, chemical potential mu and in the presence of a constant magnetic field eB. The effect of (T,mu,eB) on the formation of chiral and color symmetry breaking condensates is studied. The complete phase portrait of the model in T-mu, mu-eB, and T-eB phase spaces for various fixed eB, T, and mu is explored. A threshold magnetic field eB_t~ 0.5 GeV^2 is found above which the dynamics of the system is solely dominated by the lowest Landau level (LLL) and the effects of T and mu are partly compensated by eB.

Spin-one color superconductors: Collective modes and effective Lagrangian

We investigate the collective excitations in spin-one color superconductors. We classify the Nambu–Goldstone modes by the pattern of spontaneous symmetry breaking, and then use the Ginzburg–Landau theory to derive their dispersion relations. These soft modes play an important role for the low-energy dynamics of the system such as the transport phenomena and hence are relevant for late-stage evolution of neutron stars. In the case of the color-spin-locking phase, we use a functional technique to obtain the low-energy effective action for the physical Nambu–Goldstone bosons that survive after gauging the color symmetry.

Color Superconductivity in Supersymmetric Gauge Theories

The studies of superconductivity, dual superconductivity and color superconductivity have been undertaken through the breaking of supersymmetric gauge theories which automatically incorporate the condensation of monopoles and dyons leading to confining and superconducting phases. Constructing the total effective Lagrangian of N=2 SU(2) gauge theory with N f =2 quark multiplets and quark chemical potential at classical and quantum levels, it has been demonstrated that baryon number symmetry is spontaneously broken as a consequence of the SU(2) strong gauge dynamics and the color superconductivity dynamically takes space at the non-SUSY vacuum.

Role of two-flavor color superconductor pairing in a three-flavor Nambu–Jona-Lasinio model with axial anomaly

The phase diagram of strongly interacting matter is studied within a three-flavor Nambu--Jona-Lasinio model, which contains the coupling between chiral and diquark condensates through the axial anomaly. Our results show that it is essential to include the 2SC phase in the analysis. While this is expected for realistic strange quark masses, we find that even for equal up, down, and strange bare quark masses, 2SC pairing can be favored due to spontaneous flavor-symmetry breaking by the axial anomaly. This can lead to a rich phase structure, including BCS- and BEC-like 2SC and CFL phases and new endpoints. On the other hand, the low-temperature critical endpoint, which was found earlier in the same model without 2SC pairing, is almost removed from the phase diagram and cannot be reached from the low-density chirally broken phase without crossing a preceding first-order phase boundary. For physical quark masses no additional critical endpoint is found.

THE MASSIVE PULSAR PSR J1614–2230: LINKING QUANTUM CHROMODYNAMICS, GAMMA-RAY BURSTS, AND GRAVITATIONAL WAVE ASTRONOMY

The recent measurement of the Shapiro delay in the radio pulsar PSR J1614-2230 yielded a mass of 1.97 +/- 0.04 M_sun, making it the most massive pulsar known to date. Its mass is high enough that, even without an accompanying measurement of the stellar radius, it has a strong impact on our understanding of nuclear matter, gamma-ray bursts, and the generation of gravitational waves from coalescing neutron stars. This single high mass value indicates that a transition to quark matter in neutron-star cores can occur at densities comparable to the nuclear saturation density only if the quarks are strongly interacting and are color superconducting. We further show that a high maximum neutron-star mass is required if short duration gamma-ray bursts are powered by coalescing neutron stars and, therefore, this mechanism becomes viable in the light of the recent measurement. Finally, we argue that the low-frequency (<= 500 Hz) gravitational waves emitted during the final stages of neutron-star coalescence encode the properties of the equation of state because neutron stars consistent with this measurement cannot be centrally condensed. This will facilitate the measurement of the neutron star equation of state with Advanced LIGO/Virgo.

Nambu–Jona-Lasinio model description of weakly interacting Bose condensate and BEC-BCS crossover in dense QCD-like theories

QCD-like theories possess a positively definite fermion determinant at finite baryon chemical potential ${\ensuremath{\mu}}_{B}$ and the lattice simulation can be successfully performed. While the chiral perturbation theories are sufficient to describe the Bose condensate at low density, to describe the crossover from Bose-Einstein condensation (BEC) to BCS superfluidity at moderate density we should use some fermionic effective model of QCD, such as the Nambu--Jona-Lasinio model. In this paper, using two-color two-flavor QCD as an example, we examine how the Nambu--Jona-Lasinio model describes the weakly interacting Bose condensate at low density and the BEC-BCS crossover at moderate density. Near the quantum phase transition point ${\ensuremath{\mu}}_{B}={m}_{\ensuremath{\pi}}$ (${m}_{\ensuremath{\pi}}$ is the mass of pion/diquark multiplet), the Ginzburg-Landau free energy at the mean-field level can be reduced to the Gross-Pitaevskii free energy describing a weakly repulsive Bose condensate with a diquark-diquark scattering length identical to that predicted by the chiral perturbation theories. The Goldstone mode recovers the Bogoliubov excitation in weakly interacting Bose condensates. The results of in-medium chiral and diquark condensates predicted by chiral perturbation theories are analytically recovered. The BEC-BCS crossover and meson Mott transition at moderate baryon chemical potential as well as the beyond-mean-field corrections are studied. Part of our results can also be applied to real QCD at finite baryon or isospin chemical potential.

Superconductivity in Supersymmetric Theory in Restricted Chromodynamics

The study of superconductivity, dual superconductivity and color superconductivity has been undertaken through the breaking of super symmetric gauge theory in restricted chromo dynamics (RCD) which automatically incorporates the condensation of monopoles and dyons leading to confining and superconducting phases. Dyonic supermultiplets in N=1 super symmetry have been obtained quantum mechanically in RCD and it has been shown that dyon appears in RCD theory only through restricted part of the generalized potential and it is only this part of this potential which is responsible for quark confinement and the resulting superconductivity through the mechanism of dyonic condensation.

Bulk viscosity of spin-one color superconducting strange quark matter

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. Assuming that the critical temperature of the phase transition is much larger than 40 keV, the main effect of spin-one color superconductivity in a wide range of temperatures is an overall increase of the bulk viscosity with respect to the normal phase. The corresponding enhancement factor reaches up to about 9 in the polar and A-phases, about 25 in the planar phase and about 29 in the CSL phase. This factor is determined by the suppression of the nonleptonic rate in color-superconducting matter and, therefore, may be even larger if all quark quasiparticles happen to be gapped.

Phase Structure of Dense QCD

QCD phase structure and a new critical point at finite baryon density are discussed with special emphasis on the interplay between the dynamical chiral symmetry breaking and the color superconductivity. Results of a model independent Ginzburg-Landau approach and of a phenomenological Nambu−Jona-Lasinio model are presented. A theoretical connection between the hadron-quark phase transtion at finite baryon density and the boson-fermion mixture of ultracold atoms is also discussed.

Majorana Fermions in Non-Abelian QCD Vortices

We study the internal structure of a non-Abelian vortex in color superconductivity with respect to quark degrees of freedom. Stable non-Abelian vortices appear in the Color-FlavorLocked phase whose symmetry SU(3)C+L+R is further broken to SU(2)C+L+R ⊗ U(1)C+L+R in the vortex cores. Fermionic description of vortices is made possible by the Bogoliubov-de Gennes (B-dG) equation. Quark spectra in the vortex are obtained from the B-dG equation by treating the diquark gap having the vortex configuration as a background field. We find that there are massless modes (zero modes) well-localized around a vortex, in the triplet and singlet states of the unbroken symmetry SU(2)C+L+R. §1. Vortices in superconductors have internal structure At various scales in nature, there appear vortices, for instance, Cosmic strings in space, typhoons on Earth, water flow in a sink, and quantized vortices in superconductors and liquid Helium. The vortices that we discuss here appear at the shortest scales, the scale of strong interaction, in particular in the color-flavor locked (CFL) phase of color superconductivity in high density quark matter. All the vortices are essentially two-dimensional objects and are characterized by non-zero winding numbers of order parameters or velocity fields. However, vortices in superconductors are unique because they have non-trivial internal structure originating from their microscopic degrees of freedom. Although theoretical framework of this problem was established long time ago in the context of inhomogeneous superconductors, 1) it has been attracting people’s attention with renewed interests. One of the recent developments is the possibilities of “unconventional” superconductors where the order parameters have non-trivial symmetries. 2) It is argued that one can determine the symmetry-breaking pattern of the order parameters by looking at the vortex internal structure. In some cases called “topological” superconductors, there exists a zero-energy fermionic mode (“Majorana fermions”). On the other hand, we know several examples where massless modes are present around defects or nontrivial configuration. For instance, domain-wall fermions used in lattice QCD, fermion zero modes of the Dirac operator in the presence of instantons, and the edge modes in quantum Hall effects. Hence, it is quite a natural interest to investigate the internal structure of vortices. We have a novel type of vortices with non-Abelian symmetry, which is realized in the CFL phase of high-density quark matter. Thus, we study the internal structure of such non-Abelian vortices. 3)

QCD Critical Points and Their Associated Soft Modes

The mean-field level calculation shows that the QCD matter can have multiple critical points incorporating the color superconductivity under charge neutrality constraint due to the repulsive vector interaction; this actually implies that the QCD matter is very soft for a simultaneous formation of diquark and chiral condensates coupled with the baryonic density. Dynamical density fluctuations are analyzed as possible soft modes around the QCD critical point using dissipative relativistic fluid dynamics. It is found that the entropy fluctuation solely gets enhanced while the sound modes due to mechanical density fluctuations are strongly attenuated around the QCD CP, which may suggest a suppression or even total disappearance of Mach cone at the CP.

Hybrid Neutron Stars Based on a Modified PNJL Model

We discuss a three-flavor Nambu--Jona-Lasinio (NJL) type quantum field theoretical approach to the quark matter equation of state (EoS) with scalar diquark condensate, isoscalar vector mean field and Kobayashi-Maskawa-'t Hooft (KMT) determinant interaction. While often the diquark and vector meson couplings are considered as free parameters, we will fix them here to their values according to the Fierz transformation of a one-gluon exchange interaction. In order to estimate the effect of a possible change in the vacuum pressure of the gluon sector at finite baryon density we exploit a recent modification of the Polyakov-loop NJL (mPNJL) model which introduces a parametric density dependence of the Polyakov-loop potential also at T=0, thus being relevant for compact star physics. We use a Dirac-Brueckner-Hartree-Fock (DBHF) EoS for the hadronic matter phase and discuss results for mass-radius relationships following from a solution of the TOV equations for such a hybrid EoS in the context of observational constraints from selected objects.

Pulsar glitch recovery and the superfluidity coefficients of bulk nuclear matter

A two-component hydrodynamic model is constructed of the global superfluid flow induced by two-component Ekman pumping during the recovery stage of a glitch. The model successfully accounts for the quasi-exponential recovery observed in pulsars like Vela and the "overshoot" observed in pulsars like the Crab. By fitting the model to high-resolution timing data, three important constitutive coefficients in bulk nuclear matter can be extracted: the shear viscosity, the mutual friction parameter, and the charged fluid fraction. The fitted coefficients for the Crab and Vela are compared with theoretical predictions for several equations of state, including the color-flavor locked and two-flavor color superconductor phases of quark matter.