Color Superconductivity Research Articles

Pairing fluctuation effects in a strongly coupled color superfluid/superconductor

We investigate the effects of pairing fluctuations in fermionic superfluids/superconductors where pairing occurs among three species (colors) of fermions. Such color superfluids/superconductors can be realized in three-component atomic Fermi gases and in dense quark matter. The superfluidity/superconductivity is characterized by a three-component order parameter which denotes the pairing among the three colors of fermions. Due to the SU$(3)$ symmetry of the Hamiltonian, one color does not participate pairing. This branch of fermionic excitation is gapless in the naive BCS mean-field description. In this paper, we adopt a pairing-fluctuation theory to investigate the pairing fluctuation effects on the unpaired color in strongly coupled atomic color superfluids and quark color superconductors. At low temperature, a large pairing gap of the paired colors suppresses the pairing fluctuation effects for the unpaired color, and the spectral density of the unpaired color shows a single Fermi-liquid peak, which indicates the naive mean-field picture remains valid. As the temperature is increased, the spectral density of the unpaired color generally exhibits a three-peak structure: the Fermi-liquid peak remains but get suppressed, and two pseudogap-like peaks appears. At and above the superfluid transition temperature, the Fermi-liquid peak disappears completely and the all three colors exhibits pseudogap-like spectral density. The coexistence of Fermi liquid and pseudogap behavior is generic for both atomic color superfluids and quark color superconductors.

Quark deconfinement in protoneutron star cores: Effect of color superconductivity within the MIT bag model

We analyze the effect of color superconductivity in the transition from hot hadron matter to quark matter in the presence of a gas of trapped electron neutrinos. To describe the strongly interacting matter we adopt a two-phase picture in which the hadronic phase is described by means of a non-linear Walecka model and just deconfined matter through the MIT bag model including color superconductivity. We impose flavor conservation during the transition in such a way that just deconfined quark matter is transitorily out of equilibrium with respect to weak interactions. Our results show that color superconductivity facilitates the transition for temperatures below Tc. This effect may be strong if the superconducting gap is large enough. As in the previous work, we find that the trapped neutrinos increase the critical density for deconfinement; however, if the just deconfined phase is color superconducting this effect is weaker than if deconfined matter is unpaired. We also explore the effect of different parametrizations of the hadronic equation of state (GM1 and NL3) and the effect of hyperons in the hadronic phase. We compare our results with those previously obtained employing the Nambu–Jona–Lasinio model in the description of just deconfined matter and show that they are in excellent agreement if the bag constant B is properly chosen.

Non-equilibrium Beta Processes in Neutron Stars Containing Color-Superconductivity Quark Cores

The effect of quark color-superconductivity on the reactions rate and emissivity of nonequilibrium beta processes is investigated. We calculate the implied reduction factors for the direct Urca processes, with three flavors of quarks all pairing with the same gap. The numerical results show that the color-superconductivity dramatically suppress the Durca reaction rate and emissivity, and the reduction is also related to the chemical departure from beta equilibrium. For small chemical departure, the reduction factor almost only depends on the gap. Until the departure reaches a certain value, it enhances the reaction rate and emissivity rapidly. Furthermore, the chemical departure may be the cause of the breaking of quark Cooper pairs formed between different flavors of quarks. These results may be used in the cooling simulation of neutron stars, which contain a color-superconductivity quark core in the non-equilibrium state.

Dyson-Schwinger approach to color superconductivity at finite temperature and density

We investigate the phases of dense QCD matter at finite temperature with Dyson-Schwinger equations for the quark propagator for N_f=2+1 flavors. For the gluon propagator we take a fit to quenched lattice data and add quark-loop effects perturbatively in a hard-thermal-loop--hard-dense-loop approximation. We consider 2SC and CFL-like pairing with chiral up and down quarks and massive strange quarks and present results for the condensates and the phase diagram. We find a dominant CFL phase at chemical potentials larger than 500-600 MeV. At lower values of the chemical potential we find a 2SC phase, which also exists in a small band at higher temperatures for larger chemical potentials. With values of 20-30 MeV, the critical temperatures to the normal phase turn out to be quite small.

ONE-DIMENSIONAL SUPERSYMMETRIC ALGEBRAS IN COLOR SUPERCONDUCTORS AND REISSNER–NORDSTRÖM–ANTI-DE SITTER GRAVITATIONAL SYSTEMS

We study two fermionic systems that have an underlying supersymmetric structure, namely a color superconductor and Dirac fermion in a Reissner–Nordström–anti-de Sitter gravitational background. In the chiral limit of the color superconductor, the localized fermionic zero modes around the vortex form an N = 2 with zero central charge d = 1 quantum algebra, with all the operators being Fredholm. We compute the Witten index of this algebra and we find an unbroken supersymmetry. The fermionic gravitational system in the chiral limit too, has two underlying unbroken N = 2, d = 1 supersymmetric algebras. The unbroken supersymmetry in the later is guaranteed by the existence of fermionic quasinormal modes in the Reissner–Nordström–anti-de Sitter background. In this case the operators are not Fredholm and regularized indices are deployed.

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

Abelian and non‐Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non‐Abelian gauge theory of the strong interactions between quarks and gluons, is non‐perturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real‐time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real‐time evolution of heavy‐ion collisions, first in simpler model gauge theories and ultimately in QCD.

Quark–hadron matter at finite temperature and density in a two-color PNJL model

Quark-hadron matter at finite temperature and density is studied using a two-flavor, color SU(2) (P)NJL model. The hadronic effective Lagrangian, derived by bosonization of the quark fields and renormalized using the Eguchi method, emerges in the form of an extended linear sigma model with meson and diquark-baryon fields. Chiral and diquark condensates are studied as functions of temperature and baryon density. Masses of mesons and diquark-baryons are calculated with and without the Polyakov loop effect. We investigate the equation of state of quark-hadron matter by taking into account the contributions of mesons and diquark-baryons in addition to the quark quasiparticles.

Time-dependent ginzburg-landau equations for rotating two-flavor color superconductors

Time-dependent ginzburg-landau equations for rotating two-flavor color superconductors

Non-Abelian statistics of vortices with non-Abelian Dirac fermions

We extend our previous analysis on the exchange statistics of vortices having a single Dirac fermion trapped in each core to the case where vortices trap two Dirac fermions with U(2) symmetry. Such a system of vortices with non-Abelian Dirac fermions appears in color superconductors at extremely high densities and in supersymmetric QCD. We show that the exchange of two vortices having doublet Dirac fermions in each core is expressed by non-Abelian representations of a braid group, which is explicitly verified in the matrix representation of the exchange operators when the number of vortices is up to four. We find that the result contains the matrices previously obtained for the vortices with a single Dirac fermion in each core as a special case. The whole braid group does not immediately imply non-Abelian statistics of identical particles because it also contains exchanges between vortices with different numbers of Dirac fermions. However, we find that it does contain, as its subgroup, genuine non-Abelian statistics for the exchange of the identical particles, that is, vortices with the same number of Dirac fermions. This result is surprising compared with conventional understanding because all Dirac fermions are defined locally at each vortex, unlike the case of Majorana fermions for which Dirac fermions are defined nonlocally by Majorana fermions located at two spatially separated vortices.

Four-fermion interaction in relativistic heavy ion collisions

A (nearly) perfect liquid discovered in experiments with ultrarelativistic heavy ion collisions is investigated by studying the quark ensembles with four-fermion interaction considered as a fundamental theoretical approach. A comparative analysis of several quantum liquid models is performed, allowing one to conclude that the presence of gas-liquid phase transition is a characteristic feature of those models. The problem of the instability of the quark droplets with the small number of quarks, related with a possible formation of a chiral soliton, is discussed. A mixed phase of vacuum and baryon matter, as a possible scenario of its stability, is studied. Some aspects of the color superconductivity are considered. In addition, a recently proposed nontrivial thermodynamic state, called the fermion condensate, is studied. An analysis of unexpected opportunity to link the bare and effective coupling constants is performed within the framework of a simple model. It is pointed out that a simple subtraction procedure leads to the finite result without a typical logarithmic singularity for the observed coupling constant as a function of the transferred energy.

Neutrality of a magnetized two-flavor quark superconductor

We investigate the effect of electric and color charge neutrality on the two-flavor color superconducting (2SC) phase of cold and dense quark matter in presence of constant external magnetic fields and at moderate baryon densities. Within the framework of the Nambu-Jona-Lasinio (NJL) model, we study the inter-dependent evolution of the quark's BCS gap and constituent mass with increasing density and magnetic field. While confirming previous results derived for the highly magnetized 2SC phase with color neutrality alone, we obtain new results as a consequence of imposing charge neutrality. In the charge neutral gapless 2SC phase (g2SC), a large magnetic field drives the color superconducting phase transition to a crossover, while the chiral phase transition is first order. At larger diquark-to-scalar coupling ratio $G_D/G_S$, where the 2SC phase is preferred, we see hints of the Clogston-Chandrasekhar limit at a very large value of the magnetic field ($B\sim 10^{19}$G), but this limit is strongly affected by Shubnikov de Haas-van Alphen oscillations of the gap, indicating the transition to a domain-like state.

Maximum mass of a hybrid star having a mixed-phase region based on constraints set by the pulsar PSR J1614-2230

Recent observation of pulsar PSR J1614-2230 with a mass of about two solar masses poses a severe constraint on the equations of state (EOSs) of matter describing stars under extreme conditions. Neutron stars (NSs) can reach the mass limit set by PSR J1614-2230, but stars having hyperons or quark stars (QSs) having boson condensates, with softer EOSs, can barely reach such limit and are ruled out. QSs with pure strange matter cannot attain such high mass unless the effect of strong coupling constants or color superconductivity are considered. In this work I calculate the upper mass limit for a hybrid star (HS) having a quark-hadron mixed phase. The hadronic matter (having hyperons) EOS is described by relativistic mean field theory and the quark matter EOS is modeled according to the Massachusetts Institute of Technology bag model. The intermediate mixed phase is constructed using the Glendenning prescription. A HS with a mixed phase cannot reach the mass limit set by PSR J1614-2230 unless one assumes a density-dependent bag constant. However, for such case the mixed-phase region is small. The maximum mass of a mixed hybrid star obtained with such a mixed-phase region is $2.01{M}_{\ensuremath{\bigodot}}$. A stiffer hadronic EOS can raise the maximum mass of a mixed HS to $2.1$ ${M}_{\ensuremath{\bigodot}}$.

Towards the phase diagram of dense two-color matter

We study two-color QCD with two flavors of Wilson fermion as a function of quark chemical potential $\ensuremath{\mu}$ and temperature $T$. We find evidence of a superfluid phase at intermediate $\ensuremath{\mu}$ and low $T$ where the quark number density and diquark condensate are both very well described by a Fermi sphere of nearly free quarks disrupted by a BCS condensate. Our results suggest that the quark contribution to the energy density is negative (and balanced by a positive gauge contribution), although this result is highly sensitive to details of the energy renormalization. We also find evidence that the chiral condensate in this region vanishes in the massless limit. This region gives way to a region of deconfined quark matter at higher $T$ and $\ensuremath{\mu}$, with the deconfinement temperature, determined from the renormalized Polyakov loop, decreasing only very slowly with increasing chemical potential. The quark number susceptibility ${\ensuremath{\chi}}_{q}$ does not exhibit any qualitative change at the deconfinement transition. We argue that this is because ${\ensuremath{\chi}}_{q}$ is not an appropriate measure of deconfinement for two-color QCD at high density.

Color Superconductors, Fermions in Reissner-Nordström-anti-de Sitter Spacetimes and Zero Central Charge Supersymmetry

Two fermionic systems that have an underlying supersymmetric structure are studied, a color superconductor model and Dirac fermion in a Reissner-Nordström-anti-de Sitter gravitational background. In the chiral limit of both systems, an N = 2 with zero central charge d = 1 quantum algebra, underlies both systems.

COOLING OF COMPACT STARS WITH COLOR SUPERCONDUCTING PHASE IN QUARK-HADRON MIXED PHASE

We present a new scenario for the cooling of compact stars considering the central source of Cassiopeia A (Cas A). The Cas A observation shows that the central source is a compact star that has high effective temperature, and it is consistent with the cooling without exotic phases. The observation also gives the mass range of $M \geqslant 1.5 M_\odot$, which may conflict with the current plausible cooling scenario of compact stars. There are some cooled compact stars such as Vela or 3C58, which can be barely explained by the minimal cooling scenario, which includes the neutrino emission by nucleon superfluidity (PBF). Therefore, we invoke the exotic cooling processes, where a heavier star cools faster than lighter one. However, the scenario seems to be inconsistent with the observation of Cas A. Therefore, we present a new cooling scenario to explain the observation of Cas A by constructing models that include a quark color superconducting (CSC) phase with a large energy gap; this phase appears at ultrahigh density region and reduces neutrino emissivity. In our model, a compact star has CSC quark core with a low neutrino emissivity surrounded by high emissivity region made by normal quarks. We present cooling curves obtained from the evolutionary calculations of compact stars: while heavier stars cool slowly, and lighter ones indicate the opposite tendency without considering nucleon superfluidity. Furthermore, we show that our scenario is consistent with the recent observations of the effective temperature of Cas A during the last 10 years, including nucleon superfluidity.

Nucleation rate of colour superconducting droplets in protoneutron stars

We analyse the nucleation of quark matter droplets under protoneutron star conditions. We adopt a two-phase framework in which the hadronic phase is described through a nonlinear Walecka model and the just deconfined matter by the MIT bag model including colour superconductivity. Surface tension and curvature energy are calculated self-consistently within the multiple reflection expansion formalism. We impose flavour conservation during the transition, which means that the just deconfined quark droplet is transiently out of equilibrium with respect to weak interactions. Our results show that trapped neutrinos slightly increase the critical density for deconfinement and that colour superconductivity significantly decreases such density at low temperatures. We also show that the nucleation rate is negligible for droplets larger than 100–200 fm and is huge for smaller droplets provided that the temperature is low enough. We compare our results with previous calculations using the Nambu–Jona–Lasinio model with colour superconductivity and the MIT bag model without colour superconductivity. We conclude that the deconfinement transition should be triggered instantaneously when a density slightly larger than the bulk transition density is reached at some layer of a protoneutron star. Since colour superconductivity lowers the transition density at low temperatures, the transition is likely to occur after significant cooling in a massive enough protoneutron star.

(NON-)ALIGNED GAUGES AND GLOBAL GAUGE SYMMETRY BREAKING

The concept of (global) gauge symmetry breaking plays an important role in many areas of physics. Since the corresponding symmetry is a gauge symmetry, its breaking is actually gauge-dependent. Thus, it is possible to design gauges which restore the symmetry as good as possible. Such gauge constructions will be detailed here, illustrated with the use of lattice gauge theory. Their use will be discussed for the cases of the Higgs effect, high-baryon density color superconductors, and BRST symmetry.

Stability of colour-flavour locked quark matter with three massive quark flavours

We investigate the role of the dynamical masses of up, down, and strange quarks on the stability of electrically and colour neutral Colour-Flavour Locked (CFL) quark matter in chemical equilibrium. We derive a condition for the stability of such matter in terms of the chemical potentials of quarks and electrons, the quark masses, as well as the pairing gap. The free energy density of CFL quark matter is analyzed for a broad range of dynamical quark masses. A comparison with ordinary (non-CFL) quark matter shows that low strange quark masses favor colour superconductivity. Stability of the CFL phase can also be achieved, however, for larger values of the quark chemical potential and larger values of the dynamical strange quark mass, provided the differences between the quark masses are not too big.

Spontaneous magnetization through non-Abelian vortex formation in rotating dense quark matter

When a color superconductor of high density QCD is rotating, superfluid vortices are inevitably created along the rotation axis. In the color-flavor locked phase realized at the asymptotically large chemical potential, there appear non-Abelian vortices carrying both circulations of superfluid and color magnetic fluxes. A family of solutions has a degeneracy characterized by the Nambu-Goldtone modes CP2, associated with the color-flavor locked symmetry spontaneously broken in the vicinity of the vortex. In this paper, we study electromagnetic coupling of the non-Abelian vortices and find that the degeneracy is removed with the induced effective potential. We obtain one stable vortex solution and a family of metastable vortex solutions, both of which carry ordinary magnetic fluxes in addition to color magnetic fluxes. We discuss quantum mechanical decay of the metastable vortices by quantum tunneling, and compare the effective potential with the other known potentials, the quantum mechanically induced potential and the potential induced by the strange quark mass.

Superfluid Phase Transition and Strong-Coupling Effects in an Ultracold Fermi Gas with Mass Imbalance

We investigate the superfluid phase transition and effects of mass imbalance in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an cold Fermi gas. We point out that the Gaussian fluctuation theory developed by Nozi\`eres and Schmitt-Rink and the $T$-matrix theory, that are now widely used to study strong-coupling physics of cold Fermi gases, give unphysical results in the presence of mass imbalance. To overcome this problem, we extend the $T$-matrix theory to include higher-order pairing fluctuations. Using this, we examine how the mass imbalance affects the superfluid phase transition. Since the mass imbalance is an important key in various Fermi superfluids, such as $^{40}$K-$^6$Li Fermi gas mixture, exciton condensate, and color superconductivity in a dense quark matter, our results would be useful for the study of these recently developing superfluid systems.