The phase diagram of dense quark matter with chiral imbalance is considered with the conditions of electric neutrality and $β$-equilibrium. It has been shown recently that chiral imbalance can generate charged pion condensation in dense quark matter, so it was interesting to verify that this phenomenon takes place in realistic physical scenarios such as electrically neutral matter in $β$-equilibrium, because a window of pion condensation at dense quark matter phase diagram (without chiral imbalance) predicted earlier was closed by the consideration of these conditions at the physical current quark mass. In this paper it has been shown that the charged pion condensation is generated by chiral imbalance in the dense electric neutral quark/baryonic matter in $β$-equilibrium, i. e. matter in neutron stars. It has been also demonstrated that pion condensation is inevitable phenomenon in dense quark matter with chiral imbalance if there is non-zero chiral imbalance in two forms, chiral and chiral isospin one. It seems that in this case pion condensation phase can be hardly avoided by any physical constraint on isopin imbalance and that this conclusion can be probably generalized from neutron star matter to the matter produced in heavy ion collisions or in neutron star mergers. The chiral limit and the physical piont (physical pion mass) has been considered and it was shown that the appearance of pion condensation is not much affected by the consideration of non-zero current quark mass.
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 …
We study pion condensation and the phase structure in a two-flavor Nambu-Jona-Lasinio model in the presence of baryon chemical potential $μ$ and isospin chemical potential $μ_I$at zero and finite temperature. There is a competition between the chiral condensate and a Bose-Einstein condensate of charged pions. In the chiral limit, the chiral condensate vanishes for any finite value of the isospin chemical potential, while there is a charged pion condensate that depends on the chemical potentials and the temperature. At the physical point, the chiral condensate is always nonzero, while the charg…
After the first predictions in seventies that in dense nuclear matter, for example, in neutron stars there could be pion condensation phenomenon, it was shown that at least s-wave pion condensation is unlikely to occur in such a medium in different approaches including NJL model consideration with neutrality and $β$-equilibrium condition. Then it has been found a condition that can promote this phenomenon in dense baryonic matter, it is chiral imbalance, so now it is interesting if this generation can survive rather strict requirement of electric neutrality and $β$-equilibrium. Here in this pa…
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.
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 study aspects of the pion condensation in two-flavor neutral quark matter using the Nambu--Jona-Lasinio model of QCD at finite density. We investigate the role of electric charge neutrality, and explicit symmetry breaking via quark mass, both of which control the onset of the charged pion $(π^c)$ condensation. We show that the equality between the electric chemical potential and the in-medium pion mass, $μ_{e}=M_{π^-}$, as a threshold, persists even for a composite pion system in the medium, provided the transition to the pion condensed phase is of the second order. Moreover, we find that t…
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…
In this paper the phase structure of dense quark matter has been investigated in the presence of baryon, isospin and chiral isospin chemical potentials in the framework of (3+1)-dimensional Nambu--Jona-Lasinio model with two quark flavors. It has been shown that in the large-$N_{c}$ limit ($N_{c}$ is the number of colors of quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation one. The key conclusion of our studies is the fact that chiral isospin chemical potential generates charged pion condensation in dense quark matter wit…
The possibility of the pion condensation phenomenon in cold and electrically neutral dense baryonic matter is investigated in $β$-equilibrium. For simplicity, the consideration is performed in the framework of a NJL model with two quark flavors at zero current quark mass and for rather small values of the baryon chemical potential, where the diquark condensation might be ignored. Two sets of model parameters are used. For the first one, the pion condensed phase with finite baryon density is realized. In this phase both electrons and the pion condensate take part in the neutralization of the qu…
We study the consequences of antineutrino trapping in hot quark matter for quark star configurations with possible diquark condensation. Due to the conditions of charge neutrality and beta-equilibrium the flavor asymmetry increases with the number density of trapped antineutrinos such that above a critical value of the antineutrino chemical potential of 30 MeV diquark condensation is inhibited. When the quark star cools a two-phase structure occurs: a superconducting quark matter core surrounded by a shell of normal quark matter. Below the critical temperature of about 1 MeV, the antineutrino …
The equation of state for quark matter is derived for a nonlocal, chiral quark model within the mean field approximation.We investigate the effects of a variation of the formfactors of the interaction on the phase diagram of quark matter. Special emphasis is on the occurrence of a diquark condensate which signals a phase transition to color superconductivity and its effects on the equation of state under the condition of beta- equilibrium and charge neutrality. We calculate the quark star configurations by solving the Tolman- Oppenheimer- Volkoff equations and obtain for the transition from a …
The phase structure of dense quark matter in the two color case has been investigated with nonzero baryon $μ_B$, isospin $μ_I$ and chiral isospin $μ_{I5}$ chemical potentials. %in the framework of Nambu--Jona-Lasinio model with quark-antiquark and quark-quark interaction channels. It has been shown in the mean-field approximation that there exist three dualities, one of them between phases with spontaneous chiral symmetry breaking and condensation of charged pions, found in the three color case. The other two dual symmetries between the phase with condensation of charged pions and the phase wi…
Pion stars consisting of Bose-Einstein condensed charged pions have recently been proposed as a new class of compact stars. We use the two-particle irreducible effective action to leading order in the $1/N$-expansion to describe charged and neutrals pions as well as the sigma particle. Tuning the parameters in the Lagrangian correctly, the onset of Bose-Einstein condesation of charged pions is exactly at $μ_I=m_π$, where $μ_I$ is the isospin chemical potential. We calculate the pressure, energy density, and equation of state, which are used as input to the Tolman-Oppenheimer-Volkov equations. …
In this paper the influence of chiral chemical potential $μ_5$ on the phenomenon of diquark condensation and phase structure of dense quark matter altogether is contemplated in the framework of effective two-color and two-flavor Nambu--Jona-Lasinio model. We show that the duality relations, found $μ_5=0$, are also valid for any value of $μ_5\neq0$. Hence the dualities seem to be a real fundamental feature of the phase diagram of two color quark matter, and besides they are a very powerful tool of studying the phase structure. In terms of dualities and the influence on the phase diagram chiral …
At very high densities, QCD is in the color-flavor locked phase, which is a color-superconducting phase. The diquark condensates break chiral symmetry in the same way as it is broken in vacuum QCD and gives rise to an octet of pseudo-Goldstone bosons and a superfluid mode. The lightest of these are the charged and neutral kaons. For energies below the superconducting gap, the kaons are described by an $O(2)\times O(2)$-symmetric effective scalar field theory with chemical potentials. We use this effective theory to study Bose-condensation of kaons and their properties as functions of the tempe…
In this paper the phase structure of the dense quark matter has been investigated in the presence of baryon $μ_B$, isospin $μ_I$, chiral $μ_{5}$ and chiral isospin $μ_{I5}$ chemical potentials in the framework of Nambu--Jona-Lasinio model. It has been shown that in the large-$N_{c}$ limit ($N_{c}$ is the number of quark colours) there exist three duality correspondences in the model. The first duality is between the chiral symmetry breaking and the charged pion condensation phenomena. And there are two new dualities that hold only for chiral symmetry breaking and charged pion condensation phen…
Isospin asymmetry is the well-known property of dense quark matter, which exists in the compact stars and is produced in heavy ion collisions. On the other hand, the chiral imbalance between left- and right-handed quarks is another highly anticipated phenomenon that could occur in the dense quark matter. To investigate quark matter under these conditions, we take into account baryon -- $μ_B$, isospin -- $μ_I$ and chiral isospin -- $μ_{I5}$ chemical potentials and study QCD phase portrait using NJL$_4$ model generalized to two massive quarks that could condense into the pion condensation. We ha…
Dilepton Production as a Probe of Pion Condensation in Hot and Dense QCD Matter
University of Wrocław（弗罗茨瓦夫大学）；West University of Timişoara（蒂米什瓦拉西大学）；Aliah University（阿利亚大学）；Polish Academy of Sciences PAN（波兰科学院）；Hiroshima University（广岛大学）
In this short review we tried to give an outline of investigations of charged pion condensation (PC) in dense baryonic (quark) matter in the framework of effective Nambu--Jona-Lasinio (NJL) type models. The possibility of charged PC phase in dense quark matter with isospin asymmetry is investigated. First, it is demonstrated that this phase can be realized in the framework of massless NJL model. But the existence of this phase is enormously fragile to the values of current quark mass %.Then, and we show that charged PC phase is forbidden in electrically neutral dense quark matter with $β$-equi…
We offer a diagrammatic derivation of the effective masses of the axial flavor excitations in the electrical and color neutral CFL phase of QCD. In particular we concentrate on the excitations with the quantum numbers of the kaons: we show how their effective chemical potentials, responsible of their Bose-Einstein condensation and found previously on the basis of pure symmetry arguments, arise at the microscopic level by loop effects. We perform also the numerical evaluation of the relevant loops in the whole CFL regime $M_s^2/2μΔ\leqslant 1$, showing the existence of the enhancement of the ka…
We discuss possible inhomogeneous phases in two regions of the QCD phase diagram: We begin with color superconducting quark matter at moderately high densities, which is an imbalanced Fermi system due to the finite strange quark mass and neutrality constraints. Within an NJL-type toy model we find that this situation could lead to the formation of a soliton lattice. Similar solutions also exist in the context of the chiral phase transition. As an interesting result, the first-order transition line in the phase diagram of homogeneous phases gets replaced by an inhomogeneous phase which is borde…
Hot and dense quark matter with isospin and chiral imbalances is investigated in the framework of the (3+1)-dimensional Nambu--Jona-Lasinio model (NJL) in the large-$N_c$ limit ($N_c$ is the number of quark colors). Its phase structure is considered in terms of baryon -- $μ_B$, isospin -- $μ_I$ and chiral isospin -- $μ_{I5}$ chemical potentials. It is shown in the paper that (i) in the chiral limit there is a duality between chiral symmetry breaking (CSB) and charged pion condensation (PC) phenomena. (ii) At the physical point, i.e. at nonzero bare quark mass $m_0$, and temperature this dualit…
We study the turbulent regime of chiral (magneto)hydrodynamics for charged and neutral matter with chirality imbalance. We find that the chiral magnetohydrodynamics for charged plasmas possesses a unique scaling symmetry, only without fluid helicity under the local charge neutrality. We also find a different type of unique scaling symmetry in the chiral hydrodynamics for neutral matter with fluid helicity in the inertial range. We show that these symmetries dictate the self-similar inverse cascade of the magnetic and kinetic energies. Our results imply the possible inverse energy cascade in co…
We study the phase structures of charge neutral quark matter under the beta-equilibrium for a wide range of the quark-quark coupling strength within a four-Fermion model. A comprehensive and unified picture for the phase transitions from weak to strong coupling is presented. We first develop a technique to deal with the gap equation and neutrality constraints without recourse to numerical derivatives, and show that the off-diagonal color densities automatically vanish with the standard assumption for the diquark condensates. The following are shown by the numerical analyses: (i) The thermally-…
We study pion and kaon condensation using three-flavor chiral perturbation theory at finite isospin and strangeness quark chemical potentials μI and μS . The phase diagram consists of a vacuum phase and three distinct Bose condensed phases with condensates of charged pions as well as charged and neutral kaons. Adding electromagnetic interactions, a phase with a charged condensate becomes a Higgs phase and the resulting phase diagram is modified due to the electromagnetic mass splittings of the mesons. The results for the pion-condensed phase are applied to calculate mass-radius relation of pio…
It has been shown in [32,33] in the framework of Nambu--Jona-Lasinio model with the assumption of spatially homogeneous condensates that in the large-$N_{c}$ limit ($N_{c}$ is the number of quark colours) there exist three dual symmetries of the thermodynamic potential, which describes dense quark matter with chiral and isospin imbalances. The main duality is between the chiral symmetry breaking and the charged pion condensation phenomena. There have been a lot of studies and hints that the ground state could be characterized by spatially inhomogeneous condensates, so the question arises if du…
Recently it has been found that quantum chromodynamics (QCD) phase diagram possesses a duality between chiral symmetry breaking and pion condensation. For the first time this was revealed in the QCD motivated toy model. Then it was demonstrated in effective models as well and new additional dualities being found. We briefly recap the main features of this story and then discuss its applications as a tool to explore the QCD phase structure. The most appealing application is the possibility of getting the results on the QCD phase diagram at large baryon density. Taking the idea from large $1/N_{…
The equation of state for quark matter is derived for a nonlocal, chiral quark model within the mean field approximation. We investigate the effects of a variation of the form factors of the interaction on the phase diagram of quark matter under the condition of beta-equilibrium and charge neutrality. Special emphasis is on the occurrence of a diquark condensate which signals a phase transition to color superconductivity and its effects on the equation of state. We calculate the quark star configurations by solving the Tolman- Oppenheimer- Volkoff equations and obtain for the transition from a…
We present results for pseudo-critical temperatures of QCD chiral crossovers at zero and non-zero values of baryon ($B$), strangeness ($S$), electric charge ($Q$), and isospin ($I$) chemical potentials $μ_{X=B,Q,S,I}$. The results were obtained using lattice QCD calculations carried out with two degenerate up and down dynamical quarks and a dynamical strange quark, with quark masses corresponding to physical values of pion and kaon masses in the continuum limit. By parameterizing pseudo-critical temperatures as $ T_c(μ_X) = T_c(0) \left[ 1 -κ_2^{X}(μ_{X}/T_c(0))^2 -κ_4^{X}(μ_{X}/T_c(0))^4 \rig…
