The phase diagram of a two-flavor Polyakov loop Nambu-Jona-Lasinio model is analyzed imposing the constraint of color charge neutrality. Main effects of this constraint are a shrinking of the chiral symmetry breaking (chiSB) domain in the T-mu plane, a shift of the critical point to lower temperatures and a coexistence of chiSB and two-flavor superconducting phases. The effects can be understood in view of the presence of a nonvanishing color chemical potential mu_8, which is necessary to compensate the color charge density rho_8 induced by the nonvanishing Polyakov-loop mean field phi_3.
We discuss a gauge-invariant prescription to take the mean-field approximation self-consistently in the PNJL model (Nambu--Jona-Lasinio model with the Polyakov loop). We first address the problem of non-vanishing color density in normal quark matter, which is an artifact arising from gauge-fixed treatment of the Polyakov loop mean-fields. We then confirm that the gauge average incorporated in our prescription resolves this problem and ensures color neutrality. We point out that the proposed method has an advantage in computing the expectation value of any function of the Polyakov loop matrix. …
We study the phase diagram and the pion modes in the electrically neutral two flavor PNJL model. One of the main result of this paper is that when electrical neutrality is required, pions do not condense in the ground state of the model: the isospin chemical potential $μ_I = -μ_e/2$ is always smaller than the value required for pion condensation to occur. Moreover we investigate on the pions and $σ$ mass spectra. We find that the qualitative behavior of the masses resembles that obtained in the NJL model. We close this paper by studying the intriguing possibility that a bound state with the qu…
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…
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 con…
We discuss the isentropic trajectories on the QCD phase diagram in the temperature and the quark chemical potential plane using the Nambu--Jona-Lasinio model with the Polyakov loop coupling (PNJL model). We impose a constraint on the strange quark chemical potential so that the strange quark density is zero, which is the case in the ultra relativistic heavy-ion collisions. We compare our numerical results with the truncated estimates by the Taylor expansion in terms of the chemical potential to quantify the reliability of the expansion used in the lattice QCD simulation. We finally discuss the…
We study how the charge neutrality affects the phase structure of three-flavor PNJL model. We point out that, within the conventional PNJL model at finite density the color neutrality is missing because the Wilson line serves as an external ``colored'' field coupled to dynamical quarks. In this paper we heuristically assume that the model may still be applicable. To get color neutrality one has then to allow non vanishing color chemical potentials. We study how the quark matter phase diagram in $(T,m_s^2/μ)$-plane is affected by imposing neutrality and by including the Polyakov loop dynamics. …
We elucidate how the color neutrality is harmed in the Polyakov Nambu-Jona Lasinio (PNJL) model at finite density within the adopted mean field approximation. Also we point out how usual assumption about the diagonal form of the Wilson loop may fail in the presence of the diquark condensate on several grounds.
We revisit the issue of color neutrality in effective model descriptions of dense quark matter based on global color symmetry. While the equilibrium thermodynamics of such models is now well understood, we examine the collective modes, focusing on the fluctuations of the order parameter. We point out that the constraint of color neutrality must be carefully generalized in order to obtain physically consistent and well-defined results. Particularly important is that the collective modes associated with order parameter fluctuations couple to charge density fluctuations in the neutral medium. We …
By referring to the underlying physics behind the color charge neutrality condition in quark matter, we discuss how this condition should be properly imposed in NJL-type models in a phenomenologically meaningful way. In particular, we show that the standard assumption regarding the use of two color chemical potentials, chosen in a very special way, is not justified in general. When used uncritically, such an approach leads to wrong or unphysical conclusions.
The role of neutrality constraints for the phase structure of QCD at non-vanishing chemical potentials is studied within a self-consistent truncation scheme for the Dyson-Schwinger equation of the quark propagator in Landau gauge. We find the (approximate) color-flavor-locked phase to be energetically preferred at all potentially relevant densities and for physical values of the quark masses. We furthermore observe the impossibility to define this phase by residual global symmetries and discuss the role of chemical potentials.
We investigate the effects of realistic quark masses and local color neutrality on quark pairing in the three-flavor Polyakov--Nambu--Jona-Lasinio model. While prior studies have indicated the presence of light flavor quark (2SC) or symmetric color-flavor-locked (CFL) pairing at low temperatures, we find that in the absence of a local color neutrality constraint the inclusion of the Polyakov loop gives rise to phases in which all quark colors and flavors pair, but with unequal magnitudes. We study this asymmetric color-flavor-locked (ACFL) phase, which can exist even for equal mass quarks, ide…
We investigate the issue of charge neutrality of the CFL$K^0$ phase of dense quark matter using the low energy effective theory of high density QCD. We show that the local electric and color charge neutrality of the ground state in a homogeneous color superconducting medium follows from its dynamics. We also consider the situation of a spatially inhomogeneous medium, such as may be found in a neutron star core. We find that spatial inhomogeneity results in the generation of electric fields, and positrons/electrons may be present in the ground state. We estimate the concentration of charged lep…
The effect of Polyakov loop on the QCD phase diagram at high density is studied within the Nambu-Jona Lasinio model with Polyakov loop (PNJL model). We point out that the color neutrality is missing in the standard PNJL model at finite density. Moreover, we discuss how the color-flavor locked (CFL) phase is to be distorted by the inclusion of Polyakov loop.
We investigate the Mott effect for heavy quarkonia due to Debye screening of the heavy quark potential in a plasma of massless quarks and antiquarks. The influence of residual color correlation is investigated by coupling the light quark sector to a temporal gauge field driven by the Polyakov loop potential. This leads to an increase of the Mott dissociation temperatures for quarkonia states which stabilizes in particular the excited states, but has marginal effect on the ground states. The temperature dependence of binding energies suggests that the dissciation of the charmonium (bottomonium)…
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 …
Considering cold, dense quark matter with two massless quark flavors, we demonstrate how, in a self-consistent calculation in the framework of QCD, the condensation of Cooper pairs induces a non-vanishing background color field. This background color field has precisely the right magnitude to cancel tadpole contributions and thus ensures overall color neutrality of the two-flavor color superconductor.
It is generally believed that when Cooper pairing occurs between two different species of fermions, their Fermi surfaces become locked together so that the resultant state remains 'neutral', with equal number densities of the two species, even when subjected to a chemical potential that couples to the difference in number densities. This belief is based on mean-field calculations in models with a zero-range interaction, where the anomalous self-energy is independent of energy and momentum. Following up on an early report of a deviation from neutrality in a Dyson-Schwinger calculation of color-…
The thermodynamic behavior of the two-flavor($N_f=$2) three-color ($N_c=3$) Polyakov-loop-extended Nambu-Jona-Lasinio model at the finite chemical potential is investigated. New lattice gluon data for gluon thermodynamics are used defining the effective potential within polynomial and logarithmic forms of its approximation. We study the effects of using different sets of data and different forms of the potential on thermodynamic properties of hot and dense matter. It is found that the PNJL thermodynamics depends stronger on the form of the effective potential than on the used lattice data set.…
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 t…
A formal proof is given that the fermionic quasiparticle dispersion laws in a color superconductor are gauge independent. It is shown that the gluon (photon) field acquires a non-vanishing expectation value in a color superconductor, which is related to color (electric) neutrality.
We investigate the phase structure of two-color QCD at both real and imaginary chemical potentials mu, performing lattice simulations and analyzing the data with the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. Lattice QCD simulations are done on an 8^3 times 4 lattice with the clover-improved two-flavor Wilson fermion action and the renormalization-group improved Iwasaki gauge action. We test the analytic continuation of physical quantities from imaginary mu to real mu by comparing lattice QCD results calculated at real mu with the result of analytic function the coefficients of w…
We improve the McLerran-Venugopalan model for the gluon distribution functions in very large nuclei by imposing the condition that the nucleons should be color neutral. We find that enforcing color neutrality cures the infrared divergences in the transverse coordinates which are present in the McLerran-Venugopalan model. Since we obtain well-defined expressions for the distribution functions, we are able to draw unambiguous conclusions about various features of the model. In particular, we show that the gluon distribution functions in the absence of quantum corrections behave as 1/x to all ord…
We compute the equation of state of hadronic matter at finite temperature with zero net baryon density by the Nambu-Jona-Lasinio model for interacting quarks in uniform background temporal color gauge fields. In the low temperature confining phase, unphysical thermal quark-antiquark excitations which would appear in the mean field approximation, are eliminated by enforcing vanishing expectation value of the "Polyakov-loop" of the background gauge field, while in the high temperature confining phase this expectation value is taken as close to unity allowing thermal excitations of free quarks an…
We investigate the vacuum realignment for chiral symmetry breaking and color superconductivity at finite density in Nambu-Jona-Lasinio model in a variational method. The treatment allows us to investigate simultaneous formation of condensates in quark antiquark as well as in diquark channels. The methodology involves an explicit construction of a variational ground state and minimisation of the thermodynamic potential. Color and electric charge neutrality conditions are imposed through introduction of appropriate chemical potentials. Color and flavor dependent condensate functions are determin…
We investigate the effects of the dynamical formation of the chiral condensates on color superconducting phases under the electric and color neutrality constraints at vanishing temperature. We shall show that the phase appearing next to the color-flavor-locked (CFL) phase down in density depends on the strength of the diquark coupling. In particular, the gapless CFL (gCFL) phase is realized only in a weak coupling regime. We give a qualitative argument on why the gCFL phase in the weak coupling region is replaced by some other phases in the strong coupling, once the competition between dynamic…
The effect of electric and color neutrality on 2-flavor color superconductivity has been investigated. It has been found that the effect of the charge neutrality on a 2-flavor quark system is very different from that on a 3-flavor system. The BCS diquark pair in 2-flavor color superconducting phase has been largely reduced by the large Fermi momentum of electron, the diquark condensate first increases with the increasing of quark's chemical potential $μ$,then decreases rapidly and finally disappears at about $μ=535MeV$, at which the thermodynamic potential equals to that in the neutral normal …
We study quark-hadron phase transition at finite temperature with zero net baryon density by the Nambu-Jona-Lasinio model for interacting quarks in uniform background temporal color gauge fields. At low temperatures, unphysical thermal quark-antiquark excitations which would appear in the mean field approximation, are eliminated by en- forcing vanishing expectation value of the Polyakov-loop of the background gauge field, while at high temperatures this expectation value is taken as unity allowing thermal excitations of free quarks and antiquarks. Mesonic excitations in the low temperature pha…
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 demonstrate that quark matter in the color-flavor locked phase of QCD is rigorously electrically neutral, despite the unequal quark masses, and even in the presence of an electron chemical potential. As long as the strange quark mass and the electron chemical potential do not preclude the color-flavor locked phase, quark matter is automatically neutral. No electrons are required and none are admitted.
The mesonic excitations and s-wave pi--pi scattering lengths at finite temperature are studied in the two-flavor Polyakov--Nambu--Jona-Lasinio (PNJL) model. The masses of pi-meson and sigma-meson, pion-decay constant, the pion-quark coupling strength, and the scattering lengths $a_{0}$ and $a_{2}$ at finite temperature are calculated in the PNJL model with two forms of Polyakov-loop effective potential. The obtained results are almost independent of the choice of the effective potentials. The calculated results in the PNJL model are also compared with those in the conventional Nambu--Jona-Lasi…
We apply Ginzburg-Landau theory to determine BCS pairing in a strongly-coupled uniform superfluid of three-flavor massless quarks in flavor equilibrium. We elucidate the phase diagram near the critical temperature in the space of the parameters characterizing the thermodynamic potential terms of fourth order in the pairing gap. Within the color and flavor antisymmetric channel with zero total angular momentum, the phase diagram contains an isoscalar (IS) color-antitriplet phase and a color-flavor-locked (CFL) phase, reached by a second order transition from the normal state, as well as states …
We investigate properties of strongly interacting matter in a schematic model, based on the combined degrees of freedom of a non-interacting hadronic phase and a non-interacting deconfined phase. It is found that in a finite system both phases contribute to the thermodynamic state due to fluctuations and that signatures of critical behviour like the divergence of statistical quantities are damped. The constraint of color-neutrality leads to a volume-dependent shift of the effective critical temperature, which follows a scaling law, independent of the baryochemical potential. According to the m…
We have studied the vector meson spectral function (VMSF) in a hot and dense medium within an effective QCD model namely the Nambu-Jona-Lasinio (NJL) and its Polyakov Loop extended version (PNJL) with and without the effect of isoscalar vector interaction (IVI). The effect of the IVI has been taken into account using the ring approximation. We obtained the dilepton production rate (DPR) using the VMSF and observed that at moderate temperature it is enhanced in the PNJL model as compared to the NJL and Born rate due to the suppression of color degrees of freedom.
We recently argued that as the density of quark matter decreases, there is a continuous transition from the color-flavor-locked (CFL) phase to a gapless "gCFL" phase. The reason is the growing importance of the strange quark mass, and the constraint of electric/color neutrality. In this paper we discuss mixed phases that achieve neutrality by charge seperation, and might offer an alternative to the gCFL phase. We find that none of the obvious mixtures is favored relative to gCFL.
The color neutrality of hadrons is interpreted as an expression of conformal symmetry of strong interaction, the latter being signaled through the detected "walking" at low transferred momenta, $\lim_{Q^2\to 0}α_s(Q^2)/π\to 1 $, of the strong coupling toward a fixed value ($α_s $ "freezing" ). The fact is that conformal symmetry admits quarks and gluons to reside on the compactified $AdS_5$ boundary, whose topology is $S^1\times S^3$, a closed space that can bear exclusively color-charge neutral configurations, precisely as required by color confinement. The compactification radius, once emplo…
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…
We study properties of two-color QCD at imaginary chemical potential ($μ$) from the viewpoint of the Roberge-Weiss (RW) periodicity, the charge conjugation and the pseudo-reality. At $μ=\pm iπT/2$, where $T$ is temperature, the system is symmetric under the combination of the charge conjugation ${\cal C}$ and the ${\mathbb Z}_{2}$ transformation. The symmetry, called ${\cal C} {\mathbb Z}_{2}$ symmetry, is preserved at lower $T$ but broken at higher $T$. The Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model has the same properties as two-color QCD for ${\cal C} {\mathbb Z}_{2}$ symmetry …
The diquark condensate susceptibility in neutral color superconductor at moderate baryon density is calculated in the frame of two flavor Nambu-Jona-Lasinio model. When color chemical potential is introduced to keep charge neutrality, the diquark condensate susceptibility is negative in the directions without diquark condensate in color space, which may be regarded as a signal of the instability of the conventional ground state with only diquark condensate in the color 3 direction.
The color neutral two-flavor superconducting (2SC) phase of cold and dense quark matter is studied in the presence of constant magnetic fields and at moderate baryon densities. In the first part of the paper, a two-flavor effective Nambu--Jona-Lasinio model consisting of a chiral symmetry breaking mass gap sigma_{B}, a color superconducting mass gap Delta_{B} and a color neutrality coefficient mu_{8} is introduced in the presence of a rotated U(1) magnetic field B. To study the phenomenon of magnetic catalysis in the presence of strong magnetic fields, the gap equations corresponding to sigma_…
A quark-meson-diquark plasma is considered within the PNJL model for dynamical chiral symmetry breaking and restoration in quark matter. Based on a generalized Beth-Uhlenbeck approach to mesons and diquarks we present the thermodynamics of this system including the Mott dissociation of mesons and diquarks at finite temperature. A striking result is the suppression of the diquark abundance below the chiral restoration temperature by the coupling to the Polyakov loop, because of their color degree of freedom. This is understood in close analogy to the suppression of quark distributions by the sa…
We propose a QCD-like theory with the ZNc symmetry. The flavor-dependent twisted boundary condition (TBC) is imposed on Nc degenerate flavor quarksin the SU(Nc) gauge theory. The QCD-like theory is useful to understand the mechanism of color confinement. Dynamics of the QCD-like theory is studied by imposing the TBC on the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model. The TBC model is applied to two- and three-color cases. The ZNc symmetry is preserved below some temperature Tc, but spontaneously broken above Tc. The color confinement below Tc preserves the flavor symmetry. Above Tc,…
We investigate the effect of a magnetic field on cold dense three-flavor quark matter using an effective model with four-Fermi interactions with electric and color neutrality taken into account. The gap parameters Delta_1, Delta_2, and Delta_3 representing respectively the predominant pairing between down and strange (d-s) quarks, strange and up (s-u) quarks, and up and down (u-d) quarks, show the de Haas-van Alphen effect, i.e. oscillatory behavior as a function of the modified magnetic field B that can penetrate the color superconducting medium. Without applying electric and color neutrality…
Enforcing color and electric charge neutrality conditions on the three-flavor color superconducting matter, I derive the explicit form of the quark propagators and the gluon self-energies for the gapless and the ordinary color-flavor-locked phases.
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…
We discuss a hybrid equation of state (EoS) that fulfills constraints for mass-radius relationships and cooling of compact stars. The quark matter EoS is obtained from a Polyakov-loop Nambu--Jona-Lasinio (PNJL) model with color superconductivity, and the hadronic one from a relativistic mean-field (RMF) model with density-dependent couplings (DD-RMF). For the construction of the phase transition regions we employ here for simplicity a Maxwell construction. We present the phase diagram for symmetric matter which exhibits two remarkable features: (1) a "nose"-like structure of the hadronic-to-qu…
We investigate the chiral symmetry breaking and color superconductivity in color and electric charge neutral quark matter including strange quarks (2SC+s quark matter) in a Nambu-Jona-Lasinio model using a variational method. The methodology involves an explicit construction of a variational ground state and minimisation of the thermodynamic potential. Simultaneous existence of a mass gap and a superconducting gap is seen in a small window of quark chemical potential within the model when charge neutrality conditions are not imposed. Enforcing color and electric charge neutrality conditions gi…
We improve the McLerran-Venugopalan model by introducing a charge-density correlation function which is consistent with the observation that nucleons carry no net color charge. The infrared divergence in the transverse coordinates that was present in the McLerran-Venugoplan model is eliminated by the enforcement of color neutrality.
Employing constraints derived from the microscopic theory of the strong interaction, we estimate the zero-temperature phase structure of dense isospin-asymmetric matter with two quark flavors. We find indications that strong-interaction matter along trajectories relevant for astrophysical applications undergoes a first-order phase transition from a color-superconducting phase to an ungapped quark-matter phase when the density is increased. Such a phase transition is found to be absent in isospin-symmetric matter. Moreover, by taking into account constraints from $β$-equilibrium, charge neutral…
In the presence of nonzero strange quark mass $m_s$, we investigate color neutrality in the $K^0$ condensed phase of color-flavor locked quark matter. By treating the $m_s$ effects on both kaon condensate and Fermi-surface phenomenon self-consistently, we develop a new treatment to evaluate color neutral solutions within the model-independent framework. It is pointed out that, in the general sense, the expectation values of gluon fields obtained from dynamics of Goldstone bosons solely are not identified with the factual color chemical potentials.
Thermal color superconducting phase transitions in high density three-flavor quark matter are investigated in the Ginzburg-Landau approach. Effects of nonzero strange quark mass, electric and color charge neutrality, and direct instantons are considered. Weak coupling calculations show that an interplay between the mass and electric neutrality effects near the critical temperature gives rise to three successive second-order phase transitions as the temperature increases: a modified color-flavor locked (mCFL) phase (ud, ds, and us pairings) -> a ``dSC'' phase (ud and ds pairings) -> an isoscala…
The color superconductivity was studied with an adaptation of the Nambu and Jona-Lasinio model (NJL). This one was coupled to a Polyakov loop, to form the PNJL model. A $μ$-dependent Polyakov loop potential was considered. An objective of the presented works was to describe the analytical calculations required to establish the equations to be solved, in all of the treated cases. They concerned the normal quark phase, the 2-flavor color-superconducting and the color-flavor-locked phases, in an SU(3)f X SU(3)c description. The calculations were performed according to the temperature T, the chemi…
We study a spin-1 single flavor color superconducting phase which results from a color-spin locking (CSL) interaction in two-flavor quark matter. This phase is particularly interesting for compact star cooling applications since the CSL phase may survive under charge neutrality constraints implying a mismatch between up- and down-quark chemical potentials which can destroy the scalar diquark condensate. CSL gaps are evaluated within an NJL model and they are found to be consistent with cooling phenomenology if a density dependent coupling constant is used.
I investigate some of the inert phases in three-flavor, spin-zero color-superconducting quark matter: the CFL phase (the analogue of the B phase in superfluid $^3\rm He$), the A and A* phases, and the 2SC and sSC phases. I compute the pressure of these phases with and without the neutrality condition. It is shown that the 2SC phase is identical to the A* phase up to a color rotation. The CFL phase is the energetically favored phase except for a small region of intermediate densities where the 2SC/A* phase is favored.
We consider an extended Nambu--Jona-Lasinio model including both (q \bar q)- and (qq)-interactions with two light-quark flavors in the presence of a single (quark density) chemical potential. In the color superconducting phase of the quark matter the color SU(3) symmetry is spontaneously broken down to SU(2). If the usual counting of Goldstone bosons would apply, five Nambu-Goldstone (NG) bosons corresponding to the five broken color generators should appear in the mass spectrum. Unlike that expectation, we find only three gapless diquark excitations of quark matter. One of them is an SU(2)-si…
We investigate the combined effect of the repulsive vector interaction and the positive electric chemical potential on the chiral phase transition by considering neutral color superconductivity (CSC). The chiral condensate, diquark condensate and quark number densities are solved in both two-flavor and two-plus-one-flavor Nambu-Jona-Lasinio(NJL) models with the so called Kobayashi-Maskawa-'t Hooft term under the charge neutrality constraint. We demonstrate that multiple chiral critical-point structures always exist in the NJL model within the self-consistent mean-field approximation and the nu…
This article focuses on the two-flavor color superconducting phase at moderate baryon density. In order to simultaneously investigate the chiral phase transition and the color superconducting phase transition, the Nambu-Gorkov formalism is extended to treat the quark-antiquark and diquark condensates on an equal footing. The competition between the chiral condensate and the diquark condensate is analyzed. The cold dense charge neutral two-flavor quark system is investigated in detail. Under the local charge neutrality condition, the ground state of two-flavor quark matter is sensitive to the c…
We investigate the effect of the electric-charge neutrality in $β$ equilibrium on the chiral phase transition by solving the chiral and diquark condensates in the two-flavor Nambu--Jona-Lasinio model. We demonstrate that the electric-charge neutrality plays a similar role as the repulsive vector interaction; they both weaken the first-order chiral phase transition in the high-density and low-temperature region. The first-order chiral phase transition is not affected, however, at finite temperatures where the diquark condensate melts. In this way the chiral phase transition could be second-orde…
