Color-flavor locked (CFL) quark matter at high densities is a color superconductor, which spontaneously breaks baryon number and chiral symmetry. Its low-energy thermodynamic and transport properties are therefore dominated by the H (superfluid) boson, and the octet of pseudoscalar pseudo-Goldstone bosons of which the neutral kaon is the lightest. We study the CFL-K^0 phase, in which the stress induced by the strange quark mass causes the kaons to condense, and there is an additional ultra-light "K^0" Goldstone boson arising from the spontaneous breaking of isospin. We compute the bulk viscosity of matter in the CFL-K^0 phase, which arises from the beta-equilibration processes K^0<->H+H and K^0+H<->H. We find that the bulk viscosity varies as T^7, unlike the CFL phase where it is exponentially Boltzmann-suppressed by the kaon's energy gap. However, in the temperature range of relevance for r-mode damping in compact stars, the bulk viscosity in the CFL-K^0 phase turns out to be even smaller than in the uncondensed CFL phase, which already has a bulk viscosity much smaller than all other known color-superconducting quark phases.
We calculate the bulk viscosity of color-superconducting quark matter in the color-flavor-locked (CFL) phase. We assume that the lightest bosons are the superfluid mode H and the kaons K0 and K+, and that there is no kaon condensate. We calculate the rate of strangeness-equilibrating processes that convert kaons into superfluid modes, and the resultant bulk viscosity. We find that for oscillations with a timescale of milliseconds, at temperatures T << 1 MeV, the CFL bulk viscosity is much less than that of unpaired quark matter, but at higher temperatures the bulk viscosity of CFL matter can b…
We study the behavior of Goldstone bosons in color-flavor-locked (CFL) quark matter at nonzero temperature. Chiral symmetry breaking in this phase of cold and dense matter gives rise to pseudo-Goldstone bosons, the lightest of these being the charged and neutral kaons K^+ and K^0. At zero temperature, Bose-Einstein condensation of the kaons occurs. Since all fermions are gapped, this kaon condensed CFL phase can, for energies below the fermionic energy gap, be described by an effective theory for the bosonic modes. We use this effective theory to investigate the melting of the condensate: we d…
We investigate the influence of charged kaon condensation in hadronic sector on the formation of the electron-free charge neutral quark matter of equipartition of three light flavors, i.e., a phenomenon called ``enforced electrical neutrality" of the color-flavor locked (CFL) phase. We employ the chiral quark model which is assumed to be applicable, "bottom-up," toward chiral restoration while accessible to kaon condensation in the hadronic sector. Approaching "bottom-up" the high density regime is more appropriate in addressing the properties of compact stars than approaching "top-down" from …
The structure of $K^-$-condensed hypernuclei, which may be produced in the laboratory in strangeness-conserving processes, is investigated using an effective chiral Lagrangian for the kaon-baryon interaction, combined with a nonrelativistic baryon-baryon interaction model. It is shown that a large number of negative strangeness is needed for the formation of highly dense and deeply bound state with kaon condensates and that part of the strangeness should be carried by hyperons mixed in the nucleus. The properties of kaon-condensed hypernuclei such as the ground state energy and particle compos…
We study weak interactions involving Goldstone bosons in the neutral kaon condensed phase of color flavor locked quark matter. We calculate the rates for the dominant processes that contribute to the neutrino mean free p ath and to neutrino production. A light $K^+$ state, with a mass $\tilde{m}_{K^+} \propto (Δ/μ) (Δ/m_s)(m_d-m_u)$, where $μ$ and $Δ$ are the quark chemical potential and superconducting gap respectively, is shown to play an important role. We identify unique characteristics of weak interaction rates in this novel phase and discuss how they might influence neutrino emission in …
We calculate the kaonic contribution to the shear viscosity of quark matter in the kaon-condensed color-flavor locked phase (CFL-K0). This contribution comes from a light pseudo-Goldstone boson which arises from the spontaneous breaking of the flavor symmetry by the kaon condensate. The other contribution, from the exactly massless superfluid 'phonon", has been calculated previously. We specialize to a particular form of the interaction lagrangian, parameterized by a single coupling. We find that if we make reasonable guesses for the values of the parameters of the effective theory, the kaons …
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 …
Using the Callan-Klebanov bound state model for hyperons simulated on crystal lattice to describe strange baryonic matter, we argue that to ${\cal O} (1)$ in the large $N_c$ counting to which the theory is robust, hyperons can figure only when -- or after -- kaons condense in compact-star matter. We also discuss how the skyrmion-half-skyrmion topological transition affects the equation of state (EoS) of dense baryonic matter. The observations made in this note open wide the issue of how to theoretically access the EoS of compact stars.
The cooling of neutron stars by URCA processes in the kaon-condensed neutron star matter for various forms of nuclear symmetry energy is investigated. The kaon-nucleon interactions are described by a chiral lagrangian. Nuclear matter energy is parametrized in terms of the isoscalar contribution and the nuclear symmetry energy in the isovector sector. High density behaviour of nuclear symmetry energy plays an essential role in determining the composition of the kaon-condensed neutron star matter which in turn affects the cooling properties. We find that the symmetry energy which decreases at hi…
A new formulation is presented to treat thermal and quantum fluctuations around the kaon condensate on the basis of chiral symmetry; separating the zero-mode from the beginning and using the path-integral method, we can formulate the inclusion of fluctuations in a transparent way. Nucleons as well as kaons are treated in a self-consistent way to the one-loop order. The effects of the Goldstone mode, stemming from the breakdown of V- spin symmetry in the condensed phase, are figured out. A procedure is discussed to renormalize the divergent integrals properly up to the one-loop order. Consequen…
We show that at asymptotically high densities the ``color-flavor-locked + neutral kaon condensate'' phase of QCD develops a {\it charged} kaon condensate through the Coleman-Weinberg mechanism. At densities achievable in neutron stars a charged kaon condensate forms only for some (natural) values of the low energy constants describing the low-lying excitations of the ground state.
We explore the effects of a microscopic nuclear three-body force on the threshold baryon density for kaon condensation in chemical equilibrium neutron star matter and on the composition of the kaon condensed phase in the framework of the Brueckner-Hartree-Fock approach. Our results show that the nuclear three-body force affects strongly the high-density behavior of nuclear symmetry energy and consequently reduces considerably the critical density for kaon condensation provided that the proton strangeness content is not very large. The dependence of the threshold density on the symmetry energy …
We study the weak interaction rates involving Goldstone bosons in the Color Flavor Locked (CFL) quark matter. Neutrino mean free path and the rate of energy loss due to neutrino emission in a thermal plasma of CFL pions and kaons is calculated. We find that in addition to neutrino scattering off thermal mesons, novel Cherenkov like processes wherein mesons are either emitted or absorbed contribute to the neutrino opacity. Lack of Lorentz invariance in the medium and loss of rotational invariance for processes involving mesons moving relative to the medium allow for novel processes such as $π^0…
We consider three-flavor chiral perturbation theory ($χ$PT) at zero temperature and nonzero isospin ($μ_{I}$) and strange ($μ_{S}$) chemical potentials. The effective potential is calculated to next-to-leading order (NLO) in the $π^{\pm}$-condensed phase, the $K^{\pm}$-condensed phase, and the $K^0/\bar{K}^0$-condensed phase. It is shown that the transitions from the vacuum phase to these phases are second order and take place when, $|μ_I|=m_π$, $|{1\over2}μ_I+μ_S|=m_K$, and $|-{1\over2}μ_I+μ_S|=m_K$, respectively at tree level and remains unchanged at NLO. The transition between the two conde…
Previous work on high-density QCD suggests that the ground state configuration in the presence of a non-zero neutrino chemical potential consists of CFL matter plus a homogenous condensate of neutral and positive kaons. We consider here the stability of this homogenous configuration toward the production of a charge-separated mixed phase, and find that the system is indeed stable against the production of such a heterogenous configuration. We identify the critical value of the fine structure constant which would allow for phase separation. We also derive dispersion relations for the low-lying …
We study the equation of state (EOS) of kaon-condensed matter including the effects of temperature and trapped neutrinos. It is found that the order of the phase transition to a kaon-condensed phase, and whether or not Gibbs' rules for phase equilibrium can be satisfied in the case of a first order transition, depend sensitively on the choice of the kaon-nucleon interaction. The main effect of finite temperature, for any value of the lepton fraction, is to mute the effects of a first order transition, so that the thermodynamics becomes similar to that of a second order transition. Above a crit…
We point out that the problem of kaon condensation in dense hadronic matter can be addressed in perturbative QCD. Indeed, perturbative calculations suggest that negative kaons are condensed in high density quark matter if the electroweak interaction is taken into account. This observation sheds new light on the proposal that the low density hyperon and high density quark phase of QCD are continuously connected.
A unified treatment of normal nuclear matter described by Walecka's mean field theory and kaon condensed matter described by chiral perturbation theory is proposed in terms of mean fields of an effective chiral Lagrangian. The BR scaling is found to play a key role in making the link between the ground state properties of nuclear matter and the fluctuation into the strangeness-flavor direction. A simple prediction for kaon condensation is presented.
The core of neutron-star matter is supposed to be at a much higher density than the normal nuclear matter density for which various possibilities have been suggested such as, for example, meson or hyperon condensation and/or deconfined quark or color-superconducting matter. In this work, we explore the implication on hadron physics of a dense compact object that has three "phases", nuclear matter at the outer layer, kaon condensed nuclear matter in the middle and strange quark matter at the core. Using a drastically simplified but not unreasonable model, we develop the scenario where the diffe…
Possibility of kaon-condensed phase in hyperon-mixed matter is considered on the basis of chiral symmetry for kaon-baryon and kaon-kaon interactions, being combined with the relativistic mean-field theory for two-body baryon interaction. In addition, universal three-baryon repulsive force in the string-junction model and phenomenological three-nucleon attractive force are introduced. It is shown that softening of the equation of state stemming from both kaon condensation and mixing of hyperons is compensated with the repulsive effect of the three-baryon force and the relativistic effect for tw…
We calculate for the first time the surface tension and curvature coefficient of a first order phase transition between two possible phases of cold nuclear matter, a normal nuclear matter phase in equilibrium with a kaon condensed phase, at densities a few times the saturation density. We find the surface tension is proportional to the difference in energy density between the two phases squared. Furthermore, we show the consequences for the geometrical structures of the mixed phase region in a neutron star.
A schematic NJL-type model is employed to investigate kaon and pion condensation in deconfined quark matter in the color-flavor locked (CFL) phase, explicitly referring to quark degrees of freedom. To that end we allow for non-vanishing pseudoscalar diquark condensates in addition to the scalar ones which constitute the CFL phase. Color neutrality is ensured by the appropriate choice of color chemical potentials. The dependence of the free energy in the Goldstone condensed phases on quark masses and charge chemical potentials is found to be in good qualitative -- in most cases also quantitativ…
The properties of the pseudoscalar Goldstone bosons in the color-flavor locked phase at moderate densities are studied within a model of the Nambu--Jona-Lasinio type. The Goldstone bosons are constructed explicitly by solving the Bethe-Salpeter equation for quark-quark scattering in random phase approximation. Main focus of our investigations are (i) the weak decay constant in the chiral limit, (ii) the masses of the flavored (pseudo-) Goldstone bosons for non-zero but equal quark masses, (iii) their masses and effective chemical potentials for non-equal quark masses, and (iv) the onset of kao…
We present simulations of the evolution of a proto-neutron star in which kaon-condensed matter might exist, including the effects of finite temperature and trapped neutrinos. The phase transition from pure nucleonic matter to the kaon condensate phase is described using Gibbs' rules for phase equilibrium, which permit the existence of a mixed phase. A general property of neutron stars containing kaon condensates, as well as other forms of strangeness, is that the maximum mass for cold, neutrino-free matter can be less than the maximum mass for matter containing trapped neutrinos or which has a…
We describe a class of relativistic models incorporating finite density of matter in which spontaneous breakdown of continuous symmetries leads to a lesser number of Nambu-Goldstone bosons than that required by the Goldstone theorem. This class, in particular, describes the dynamics of the kaon condensate in the color-flavor locked phase of high density QCD. We describe the spectrum of low energy excitations in this dynamics and show that, despite the presence of a condensate and gapless excitations, this system is not a superfluid.
We investigate the composition and the equation of state of the kaon condensed phase in neutrino-free and neutrino-trapped star matter within the framework of the Brueckner-Hartree-Fock approach with three-body forces. We find that neutrino trapping shifts the onset density of kaon condensation to a larger baryon density, and reduces considerably the kaon abundance. As a consequence, when kaons are allowed, the equation of state of neutrino-trapped star matter becomes stiffer than the one of neutrino free matter. The effects of different three-body forces are compared and discussed. Neutrino t…
Possible coexistence and/or competition of kaon condensation with hyperons are investigated in hyperonic matter, where hyperons are mixed in the ground state of neutron-star matter. The formulation is based on the effective chiral Lagrangian for the kaon-baryon interaction and the nonrelativistic baryon-baryon interaction model. First, the onset condition of the s-wave kaon condensation realized from hyperonic matter is reexamined. It is shown that the usual assumption of the continuous phase transition is not always kept valid in the presence of the negatively charged hyperons. Second, the eq…
We discuss the equation of state of neutron stars in the dense interior considering hyperons and the possible onset of kaon condensation within the relativistic mean field model. We find that hyperons are favoured in dense matter and that their appearance make the existence of a kaon condensed phase quite unlikely. Implications for the recent measurements of kaons in heavy ion collisions at subthreshold energy are also given.
Non-uniform structures of mixed phases at the first-order phase transition to charged kaon condensation are studied using a density functional theory within the relativistic mean field model. Including electric field effects and applying the Gibbs conditions in a proper way, we numerically determine density profiles of nucleons, electrons and condensed kaons. Importance of charge screening effects is elucidated and thereby we show that the Maxwell construction is effectively justified. Surface effect is also studied to figure out its effect on the density profiles.
Coexistence of kaon condensation and hyperons, which may be realized in neutron stars, is investigated on the basis of the relativistic mean-field theory combined with the effective chiral Lagrangian. It is shown that kaon-condensed phase in hyperon-mixed matter is plausible, but it leads to significant softening of the equation of state (EOS).We discuss indispensable effects which make the EOS stiffer so as to be consistent with recent neutron-star observations.
The equation of state and the properties of neutron stars are studied for a phase transition to a charged kaon condensate. We study the mixed phase by using Gibbs condition with comparison to the hitherto applied Maxwell construction. Implications for kaon condensation and for the mass-radius relation of condensed neutron stars are examined.
We study the role of Coulomb and surface effects on the phase transition from dense nuclear matter to a mixed phase of nuclear and kaon-condensed matter. We calculate corrections to the bulk calculation of the equation of state (EOS) and the critical density for the transition by solving explicitly for spherical, cylindrical, and planar structures. The importance of Debye screening in the determination of the charged particle profiles is studied in some detail. We find that the surface and Coulomb contributions to the energy density are small, but that they play an important role in the determ…
We investigate the possibility of kaon condensation in the dense interior of neutron stars through the s--wave interaction of kaons with nucleons. We include nucleon--nucleon interactions by using simple parametrizations of realistic forces, and include electrons and muons in $β$--equilibrium. The conditions under which kaon condensed cores undergo a transition to quark matter containing strange quarks are also established. The critical density for kaon condensation lies in the range (2.3--5.0)$~ρ_0$, where $ρ_0=0.16$~fm$^{-3}$ is the equilibrium density of nuclear matter. For too large a valu…
We explore the possibility of three phases in the core of neutron star in a form of triple layers. From the center, strange quark matter, kaon condensed nuclear matter and nuclear matter form a triple layer. We discuss how the phase of strange quark matter is smoothly connected to kaon condensed nuclear matter phase. We also demonstrate that the compact star with triple layered structure can be a model compatible with the 1.97-solar-mass object PSR J1614-2230 recently observed.
We analyze various aspects of pion and kaon condensation in the framework of chiral perturbation theory. Considering a system at vanishing temperature and varying the isospin chemical potential and the strange quark chemical potential we reproduce known results about the phase transition to the pion condensation phase and to the kaon condensation phase. However, we obtain mesonic mixings and masses in the condensed phases that are in disagreement with the results reported in previous works. Our findings are obtained both by a theory group analysis and by direct calculation by means of the same…
We perform a field-theoretical computation of hadron production in large systems at the QCD confinement phase transition associated with restoration of the Z(3) global symmetry. This occurs from the decay of a condensate for the Polyakov loop. From the effective potential for the Polyakov loop, its mass just below the confinement temperature T_c is in between the vacuum masses of the pion and that of the kaon. Therefore, due to phase-space restrictions the number of produced kaons is roughly an order of magnitude smaller than that of produced pions, in agreement with recent results from collis…
In a previous article, the 4D half-skyrmion (or 5D dyonic salt) structure of dense baryonic matter described in crystalline configuration in the large $N_c$ limit was shown to impact nontrivially on how anti-kaons behave in compressed nuclear matter with a possible implication on an "ice-9" phenomenon of deeply bound kaonic matter and condensed kaons in compact stars. We extend the analysis to make a further prediction on the scaling properties of hadrons that have a surprising effect on the nuclear tensor forces, the symmetry energy and hence on the phase structure at high density. We treat t…
Hydrodynamics of superfluids can be described by formally dividing the fluid into a normal fluid and a superfluid part. In color-flavor locked quark matter, at least one superfluid component is present due to spontaneous breaking of baryon number conservation, and an additional one due to the breaking of strangeness arises once one takes into account kaon condensation. We show how such a two-component description emerges from an underlying scalar field theory which can be viewed as an effective theory for kaons. Furthermore, the occurring hydrodynamic quantities in the low-temperature limit ar…
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 bulk viscosities of two color-superconducting phases, the color-flavor locked (CFL) phase and the 2SC phase, are computed and compared to the result for unpaired quark matter. In the case of the CFL phase, processes involving kaons and the superfluid mode give the largest contribution to the bulk viscosity since all fermionic modes are gapped. In the case of the 2SC phase, ungapped fermionic modes are present and the process u+d <-> u+s provides the dominant contribution. In both cases, the bulk viscosity can become larger than that of the unpaired phase for sufficiently large temperatures…
Cooling of Isolated Neutron Stars with Hyperon-mixed Kaon-Condensation Matter
The University of Manchester（曼彻斯特大学）；Indian Institute of Technology, Roorkee（印度理工学院鲁尔基分校）；RIKEN（理化学研究所）；Chiba Institute of Technology（千叶工业大学）；Kurume Institute of Technology（久留米工业大学）
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 (CFL) 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 …
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.
We study the effect of a non-zero strange quark mass on the color-flavor-locked (CFL) phase of high density quark matter. We have previously shown that for a strange quark mass $m_s\sim m_u^{1/3}Δ^{2/3}$ the CFL state becomes unstable toward the formation of a neutral kaon condensate. Recently, several authors discovered that for $m_s\sim (2Δp_F)^{1/2}$ the CFL state contains gapless fermions, and that the gapless modes lead to an instability in current-current correlation functions. Using an effective theory of the CFL state we demonstrate that this instability is resolved by the formation of…
At nuclear matter density, electrically neutral strongly interacting matter in weak equilibrium is made of neutrons, protons and electrons. At sufficiently high density, such matter is made of up, down and strange quarks in the color-flavor locked phase, with no electrons. As a function of increasing density (or, perhaps, increasing depth in a compact star) other phases may intervene between these two phases which are guaranteed to be present. The simplest possibility, however, is a single first order phase transition between CFL and nuclear matter. Such a transition, in space, could take plac…
We compute free energy of quark matter at asymptotically high baryon number density in the presence of non zero strange quark mass including dynamics of pseudo Nambu-Goldstone bosons due to chiral symmetry breaking, extending previously existing analysis based on perturbative expansion in $m_s^2/4μΔ.$ We demonstrate that the CFL$K^0$ state has lower free energy than the symmetric CFL state for $0<m_s^2/4μΔ<2/3$. We also calculate the spectrum of the fermionic quasiparticle excitations about the kaon condensed ground state in the regime $m_s^2/4μΔ\sim 1$ and find that $(m_s^2/4μΔ)_{crit}=2/3$ f…
The r-mode instability in rotating compact stars is used to constrain the phase of matter at high density. The color-flavor-locked phase with kaon condensation (CFL-K0) and without (CFL) is considered in the temperature range 10^8K < T <10^{11} K. While the bulk viscosity in either phase is only effective at damping the r-mode at temperatures T > 10^{11} K, the shear viscosity in the CFL-K0 phase is the only effective damping agent all the way down to temperatures T > 10^8 K characteristic of cooling neutron stars. However, it cannot keep the star from becoming unstable to gravitational wave e…
We study the phase diagram of dense quark matter with an emphasis on the role of the strange quark mass. Our approach is based on two effective field theories (EFTs). The first is an EFT that describes quark quasi-particles near the Fermi surface. This EFT is valid at energies small compared to the chemical potential. The second is an EFT for the Goldstone modes in the paired phase. We find that in response to a non-zero strange quark mass the CFL phase first undergoes a transition to a kaon condensed phase, and then to a gapless phase with a non-zero Goldstone boson current.
The bulk viscosity in quark matter is sufficiently high to reduce the effective pressure below the corresponding vapor pressure during density perturbations in neutron stars and strange stars. This leads to mechanical instability where the quark matter breaks apart into fragments comparable to cavitation scenarios discussed for ultra-relativistic heavy-ion collisions. Similar phenomena may take place in kaon-condensed stellar cores. Possible applications to compact star phenomenology include a new mechanism for damping oscillations and instabilities, triggering of phase transitions, changes in…
Transition from baryonic matter to color-flavor-locked quark matter is described in terms of skyrmion matter changing into half-skyrmion matter. The intermediate phase between the density $n_p$ at which a skyrmion turns into two half skyrmions and the chiral transition density $n_c^{χSR}$ at which hadronic matter changes over to quark matter corresponds to a chiral symmetry restored phase characterized by a vanishing quark condensate and a {\em non-vanishing} pion decay constant. When hidden local fields are incorporated, the vector manifestation of Harada-Yamawaki HLS theory implies that as d…
The hadronic matter described as a skyrmion matter embedded in an FCC crystal is found to turn into a half-skyrmion matter with vanishing (in the chiral limit) quark condensate and {\em non-vanishing} pion decay constant at a density $n_{1/2S}$ lower than or at the critical density $n_c^{χSR}$ at which hadronic matter changes over to a chiral symmetry restored phase with deconfined quarks. When hidden local gauge fields and dilaton scalars -- one "soft" and one "hard" -- are incorporated, this phase is characterized by $a=1$, $f_π\neq 0$ with the hidden gauge coupling $g\neq 0$ but $\ll 1$. Wh…
