The appearance of a new phase of QCD, Quarkyonic Matter in the limit of large number of colors is studied within Nambu-Jona-Lassinio effective chiral model coupled to the Polyakov loop. The interplay of this novel QCD phase with chiral symmetry restoration and color deconfinement is discussed. We find that at vanishing temperature and at large $N_c$, the quarkyonic transition occurs at densities only slightly lower than that expected for the chiral transition. This property is also shown to be valid at finite temperature if the temperature is less than that of deconfinement. The position and $N_c$-dependence of chiral critical end point is also discussed.
We discuss the formation of quarkyonic chiral spirals in the presence of a magnetic field. The explicit breaking of the rotational symmetry by the external magnetic field gives rise to an additional chiral spiral that varies along the field direction and rotates in the chiral space between pion and magnetic moment components.
We explore the inhomogeneous QCD phases at finite density and temperature using a (3+1)-dimensional Nambu-Jona-Lasinio (NJL) model in the large Nc limit with an additional attractive tensor-tensor interaction channel. For single modulated solutions, the problem reduces to solving the gap equation of a Chiral Gross-Neveu (NJL2) theory, whose minimum solution is a periodic array of chirally twisted kinks. At zero temperature, the minimum solution reduces to the quarkyonic chiral spiral found in quarkyonic matter. The connection between the quarkyonic matter and our (3+1)-dimensional NJL model is…
The nuclear matter, deconfined quark matter, and Quarkyonic matter in low temperature region are classified based on the 1/Nc expansion. The chiral symmetry in the Quarkyonic matter is investigated by taking into account condensations of chiral particle-hole pairs. It is argued that the chiral symmetry and parity are locally violated by the formation of chiral spirals, < psibar exp(2 i mu z gamma^0 gamma^z) psi >. An extension to multiple chiral spirals is also briefly discussed.
In this Addendum to our recent paper, Phys. Rev. D 77, 054027 (2008), we point out that a chiral restoration phase transition in a quarkyonic matter at low temperatures is of second order within a manifestly confining and chirally symmetric large $N_c$ model. This result is qualitatively different as compared to NJL and NJL-like models that are not confining and might have some implications for the existence or nonexistence of the critical end point in the QCD phase diagram.
We overview a possible mechanism for confining but chirally symmetric matter at low temperatures and large densities. As a new development we employ a diffused quark Fermi surface and show that such diffusion does not destroy possible existence of a confining but chirally symmetric matter at low temperatures and large density.
We study the phase diagram of strongly interacting matter including the inhomogeneous phase of Chiral Density Waves (CDW) within the Polyakov loop extended Nambu-Jona-Lasinio (PNJL) model. We discuss the phase structure taking into account density and flavour dependence of the Polyakov loop potential parameter and temperature dependence of the four-point coupling constant of the NJL model. It is shown that the CDW phase exists and that can be interpreted as a special realisation of quarkyonic matter. This fact is of particular interest because the existence of homogeneous quarkyonic matter is …
We point out a new configuration in the Witten-Sakai-Sugimoto model, allowing baryons in the pointlike approximation to coexist with fundamental quarks. The resulting phase is a holographic realization of quarkyonic matter, which is predicted to occur in QCD at a large number of colors, and possibly plays a role in real-world QCD as well. We find that holographic quarkyonic matter is chirally symmetric and that, for large baryon chemical potentials, it is energetically preferred over pure nuclear matter and over pure quark matter. The zero-temperature transition from nuclear matter to the quar…
We argue that in cold, dense quark matter, in the limit of a large number of colors the ground state is unstable with respect to creation of a complicated Quarkyonic Chiral Spiral (QCS) state, in which both chiral and translational symmetries are spontaneously broken. The entire Fermi surface is covered with patches of QCSs, whose number increases as the quark density does. The low energy excitations are gapless, given by Wess-Zumino-Novikov-Witten model plus transverse kinetic terms localized about different patches.
This work extends our previous study of isospin symmetric quarkyonic matter to quarkyonic neutron matter which might be relevant to the inner cores of neutron stars. The vector-isovector $ρ$ mesons are introduced to the model mainly to account for isospin density interactions, just like $ω$ meson for baryon density interactions. The modified Lagrangian still preserves approximate chiral symmetry which could be significantly broken at lower density. And new free parameters are fixed by adopting the experimental constraints on the symmetry energy and its slope at saturation density. Eventually, …
A new phase of dense QCD proposed in the limit of large number of colors, Quarkyonic Phase, is discussed in chiral approaches. The interplay between chiral symmetry breaking and confinement together with the $N_c$ dependence of the phase diagram are dealt with in the PNJL model. We also discuss a possible phase at finite density where chiral symmetry is spontaneously broken while its center remains unbroken. The quark number susceptibility exhibits a strong enhancement at the restoration point of the center symmetry rather than that of the chiral symmetry. This is reminiscent of the quarkyonic…
We study the interplay between the chiral and the deconfinement transitions, both at high temperature and high quark chemical potential, by a non local Nambu-Jona Lasinio model with the Polyakov loop in the mean field approximation and requiring neutrality of the ground state. We consider three forms of the effective potential of the Polyakov loop: two of them with a fixed deconfinement scale, cases I and II, and the third one with a $μ$ dependent scale, case III. In the cases I and II, at high chemical potential $μ$ and low temperature $T$ the main contribution to the free energy is due to th…
It has recently been suggested that at a reasonably large chemical potential a confining quarkyonic matter is formed that consists of the quark Fermi sea and confined hadrons on top of this Fermi sea. We study some properties of this matter. It is demonstrated that below the chiral restoration point there are gapless excitations of this matter through excitations of the Goldstone bosons. Above the chiral restoration point the single quarks are still removed from the spectrum of excitations and the only possible excitations are confined color-singlet hadrons with finite mass. Hence there appear…
We analyze the (1+1) dimensional QCD (QCD_2) at finite density to consider a number of qualitative issues: confinement in dense quark matter, the chiral symmetry breaking near the Fermi surface, the relation between chiral spirals and quark number density, and a possibility of the spontaneous flavor symmetry breaking. We argue that while the free energy is dominated by perturbative quarks, confined excitations at zero density can persist up to high density. So quark matter in QCD$_2$ is an example of Quarkyonic matter. The non-Abelian bosonization and associated charge-flavor-color separation …
We demonstrate an exact cancellation of the infrared divergences in the color-singlet quarkyonic matter with the 1/p^4 Coulomb-like confining interaction both in the chiral symmetry broken and restored regimes.
Chiral and deconfinement phase transitions at finite temperature $T$ and quark number chemical potential $μ$ are simultaneously studied in the quenched dynamical holographic QCD model within the Einstein-Dilaton-Maxwell framework. By calculating the corresponding order parameters, i.e., the chiral condensate and Polyakov loop, it is shown that the transition lines of these two phase transitions are separated in the $T-μ$ plane. The deconfinement phase transition is shown to be always of crossover type and the transition line depends weakly on the baryon number density. Differently, the chiral …
We consider the formation of chiral density waves in Quarkyonic matter, which is a phase where cold, dense quarks experience confining forces. We model confinement following Gribov and Zwanziger, taking the gluon propagator, in Coulomb gauge and momentum space, as 1/(p^2)^2. We assume that the number of colors, N, is large, and that the quark chemical potential, mu, is much larger than renormalization mass scale, Lambda_QCD. To leading order in 1/N and Lambda_QCD/mu, a gauge theory with Nf flavors of massless quarks in 3+1 dimensions naturally reduces to a gauge theory in 1+1 dimensions, with …
Large-N_c QCD matter at intermediate baryon density and low temperatures has been conjectured to be in the so-called quarkyonic phase, i.e., to have a quark Fermi surface and on top of it a confined spectrum of excitations. It has been suggested that the presence of the quark Fermi surface leads to a homogeneous phase with restored chiral symmetry, which is unstable towards creating condensates breaking both the chiral and translational symmetry. Motivated by these exotic features, we investigate properties of cold baryonic matter in the single flavor Sakai-Sugimoto model searching for a holog…
We present a field theoretical description of quarkyonic matter consisting of quark, nucleon and ghost fields coupling to mesonic degrees of freedom. The ghosts are present to cancel over-counting of nucleon states that are Pauli blocked by the quark Fermi sea. Such a theory becomes an effective field theory of nucleons at low baryon density, and as such will reproduce nucleonic matter phenomenology. This theory can accommodate chiral symmetry restoration and the dynamical generation of a shell of nucleons at the Fermi surface. It is valid for finite temperature and density. In such a theory, …
A mini-review of non-uniform phases in quark matter is presented, with particular attention to the pion condensation, also known as chiral density waves or chiral spirals. The phase diagram of strongly-interacting matter may involve such a phase, placed on the quarkyonic island between the baryonic phase and the chirally-restored quark-gluon plasma.
We discuss phases in dense hadronic and quark matter from chiral model approaches. Within PNJL models the phase diagram for various number of colors $N_c$ is studied. How phases are constrained in quantum field theories are also discussed along with the anomaly matching. An exotic phase with unbroken center symmetry of chiral group has a characteristic feature in the thermodynamics, which can be interpreted as one realization of the quarkyonic phase in QCD for $N_c=3$.
The phase diagram at finite temperature and density is investigated in the framework of the Polyakov linear sigma model (PLSM) with three light quark flavors in the mean field approximation. It is found that in the PLSM, the three phase transitions, i.e, the chiral restoration of $u,d$ quarks, the chiral restoration of $s$ quark, and the deconfinement phase transition are independent. There exists two-flavor quarkyonic phase at low density and three-flavor quarkyonic phase at high density. The critical end point (CEP) which separating the crossover from the first-order line in the PLSM model i…
We show that the magnitude of the order parameters in Polyakov-Nambu-Jona-Lasinio (PNJL) model, given by the quark condensate and the Polyakov loop, can be used as a criterium to clearly identify, without ambiguities, phases and boundaries of the strongly interacting matter, namely, the broken/restored chiral symmetry, and confinement/deconfinement regions. This structure is represented by the projection of the order parameters in the temperature-chemical potential plane, which allows a clear identification of pattern changes in the phase diagram. Such a criterium also enables the emergence of…
We review theoretical approaches to explore the phase diagram of nuclear and quark matter at high baryon density. We first look over the basic properties of quantum chromodynamics (QCD) and address how to describe various states of QCD matter. In our discussions on nuclear matter we cover the relativistic mean-field model, the chiral perturbation theory, and the approximation based on the large-Nc limit where Nc is the number of colors. We then explain the liquid-gas phase transition and the inhomogeneous meson condensation in nuclear matter with emphasis put on the relevance to quark matter. …
The Chiral Dilaton Model, where baryons arise as non-topological solitons built from the interaction of quarks and chiral mesons, shows in the high density low temperature regime a two phase scenario in the nuclear matter phase diagram. Dense soliton matter described by the Wigner-Seitz approximation generates a periodic potential in terms of the sigma and pion fields that leads to the formation of a band structure. The analysis up to three times nuclear matter density shows that soliton matter undergoes two separate phase transitions: a delocalization of the baryon number density leading to $…
We investigate the phase structure of the Nambu--Jona-Lasinio model at zero temperature, allowing for a two-dimensional spatial dependence of the chiral condensate. Applying the mean-field approximation, we consider various periodic structures with rectangular and hexagonal geometries, and minimize the corresponding free energy. We find that these two-dimensional chiral crystals are favored over homogeneous phases in a certain window in the region where the phase transition would take place when the analysis was restricted to homogeneous condensates. It turns out, however, that in this regime …
The chiral condensate, which is constant in vacuum, may become spatially modulated at moderately high densities where in the traditional picture of the QCD phase diagram a first-order chiral phase transition occurs. We review the current status of this idea, which originally dates back to Migdal's pion condensation, but recently received new momentum through studies on the nature of the chiral critical point and by the conjecture of a quarkyonic-matter phase. We discuss how these nonuniform phases emerge in generalized Ginzburg-Landau analyses as well as in specific calculations, both within e…
It is possible that at low temperatures and large density there exists a confining matter with restored chiral symmetry, just after the dense nuclear matter with broken chiral symmetry. Such a phase has sofar been studied within a confining and chirally symmetric model assuming a rigid quark Fermi surface. In the confining quarkyonic matter, however, near the Fermi surface quarks group into color-singlet baryons. Interaction between quarks leads to a diffusion of the quark Fermi surface. Here we study effects of such diffusion and verify that it does not destroy a possible existence of a confi…
The quark-hadron phase transition at finite temperature and baryon chemical potential is investigated in an extended NJL model with scalar-vector eight-point interaction by comparing the pressure of symmetric nuclear matter with that of the quark matter. As a result, the extended NJL phase diagram is obtained in the temperature-baryon chemical potential plane and the effects of the scalar-vector coupling constant G_{sv}^q on the chiral phase transition are summarized. It is shown that a quarkyonic-like phase in which the chiral symmetry is restored but the elementary excitation modes are nucle…
In this talk I discuss three recent developments in the theoretical understanding of the phase diagram of the strong interaction. The first topic deals with the comparison of model calculations of the quark-hadron transition at vanishing quark chemical potential with state-of-the-art lattice QCD results. In the second relates to the size of a possible 'quarkyonic phase'. The third deals with the occurence of inhomogeneous chiral phases.
We study effective models of chiral fields and Polyakov loop expected to describe the dynamics responsible for the phase structure of two-flavor QCD at finite temperature and density. We consider chiral sector described either using linear sigma model or Nambu-Jona-Lasinio model and study the phase diagram and determine the location of the critical point as a function of the explicit chiral symmetry breaking (i.e. the bare quark mass $m_q$). We also discuss the possible emergence of the quarkyonic phase in this model.
Finite-Temperature Axion-Admixed Neutron Stars in a Quarkyonic Crossover Framework
Institute of Physics, Sachivalaya Marg, Bhubaneswar-751005, India（印度布巴内斯瓦尔物理研究所）；Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India（印度孟买霍米巴巴哈国立研究所）；Department of Physics, Indira Gandhi Institute of Technology, Sarang, Dhenkanal, Odisha-759146, India（印度奥迪沙邦德赫卡纳尔萨拉格英迪拉甘地理工学院物理系）
The spontaneous breaking of chiral symmetry is examined by chiral effective theories, such as the linear sigma model and the Nambu Jona-Lasinio (NJL) model. Indicating that sufficiently large contribution of the UA(1) anomaly can break chiral symmetry spontaneously, we discuss such anomaly driven symmetry breaking and its implication. We derive a mass relation among the SU(3) flavor singlet mesons, eta0 and sigma0, in the linear sigma model to be satisfied for the anomaly driven symmetry breaking in the chiral limit, and find that it is also supported in the NJL model. With the explicit breaki…
We study two-color QCD with two flavors of Wilson fermion as a function of quark chemical potential mu and temperature T, for two different lattice spacings and two different quark masses. We find that the quarkyonic region, where the behaviour of the quark number density and the diquark condensate are described by a Fermi sphere of almost free quarks distorted by a BCS gap, extends to larger chemical potentials with decreasing lattice spacing or quark mass. In both cases, the quark number density also approaches its non-interacting value. The pressure at low temperature is found to approach t…
Casher's argument, which is believed to be quite general, states that in the confining regime chiral symmetry is necessarily broken. In the large-N_c limit and at moderate and low temperatures QCD is confining up to arbitrary large densities, and there should appear a quarkyonic matter. It has been demonstrated, within a manifestly confining and chirally symmetric model, which is a 3+1 dimensional generalization of the 't Hooft model, that, at zero temperature and at a density exceeding a critical one, the chiral symmetry is restored while quarks remain confined in color-singlet hadrons. This …
Lattice QCD simulations with chirally symmetric quarks have recently established approximate $SU(2)_{CS}$ and $SU(2N_F)$ symmetries of the quantum effective action in a temperature range above the chiral crossover $T_\mathrm{ch}$, in which color-electric interactions between quarks dominate the dynamics. We show that such an intermediate temperature range between the chirally broken and plasma regimes is fully consistent with published screening mass spectra, which demonstrate the breakdown of thermal perturbation theory at the crossover between the partonic and the chiral spin symmetric regim…
We consider the possibility that color deconfinement and chiral symmetry restoration do not coincide in dense baryonic matter at low temperature. As a consequence, a state of massive "constituent" quarks would exist as an intermediate phase between confined nuclear matter and the plasma of deconfined massless quarks and gluons. We discuss the properties of this state and its relation to the recently proposed quarkyonic matter.
We point out that adding higher dimension operators to the Nambu-Jona-Lasinio model can stabilize chiral symmetry breaking and resolve the issue raised by Kleinert and Van den Bossche that chiral symmetry breaking cannot occur for $N_c \le N_c^{\rm cr}$ due to large quantum fluctuations of the composite fields.
The implications of chiral symmetry breaking and SU(3) symmetry breaking have been studied in the chiral constituent quark model ($χ$CQM). The role of hidden strangeness component has been investigated for the scalar matrix elements of the nucleon with an emphasis on the meson-nucleon sigma terms. The $χ$CQM is able to give a qualitative and quantitative description of the "quark sea" generation through chiral symmetry breaking. The significant contribution of the strangeness is consistent with the recent available experimental observations.
In this contribution the role of quantum fluctuations for the QCD phase diagram is discussed. This concerns in particular the importance of the matter back-reaction to the gluonic sector. The impact of these fluctuations on the location of the confinement/deconfinement and the chiral transition lines as well as their interrelation are investigated. Consequences of our findings for the size of a possible quarkyonic phase and location of a critical endpoint in the phase diagram are drawn.
We examine flavor SU(3) breaking effects on meson-baryon scattering amplitudes in the chiral unitary model. It turns out that the SU(3) breaking, which appears in the leading quark mass term in the chiral expansion, can not explain the channel dependence of the subtraction parameters of the model, which are crucial to reproduce the observed scattering amplitudes and resonance properties.
We explore QCD phase diagram by constructing a holographic QCD model using the Einstein-Maxwell-Scalar system. The chiral transition is investigated by adding a probe scalar and confinement transition is studied by adding a probe string into the system. By interpreting the black hole phase transition in the bulk spacetime as the quarkyonic transition in the dual QCD theory and introducing the bypass mechanism for deconfinement transition, we give an explanation why chiral symmetry breaking and deconfinement transition lines coincide with each other despite their different physical origins.
We review how a classification into representations of color and flavor can be used to understand the possible patterns of symmetry breaking for color superconductivity in dense quark matter. In particular, we show how for three flavors, color-flavor locking is precisely analogous to the usual pattern of chiral symmetry breaking in the QCD vacuum.
We investigate the pressure of the pion, which should be equal to zero to ensure the stability of the pion, within the framework of the chiral quark model beyond the chiral limit. The pressure of the pion turns out to vanish nontrivially by the Gell-Mann-Oakes-Renner relation within the present framework. It implies that the stability of the pion might be deeply rooted in spontaneous chiral symmetry breaking. We also discuss physical quantities relevant to the energy-momentum tensor operator.
N* masses in the spin-1/2 and spin-3/2 sectors are computed using two non-perturbative methods: lattice QCD and QCD sum rules. States with both positive and negative parity are isolated via parity projection methods. The basic pattern of the mass splittings is consistent with experiments. The mass splitting within the same parity pair is directly linked to the chiral symmetry breaking QCD.
Nonperturbative Wilson coefficients associated with the leading chiral-symmetry-breaking operators in the operator product expansion of the pseudoscalar QCD correlation function are derived. Implementation of the new, instanton-induced operators enables the corresponding spectral sum rule to reproduce the small pion mass scale, thereby reconciling it with Goldstone's theorem. The same operators suppress the contributions of pionic resonances. Several predictions and structural insights from the new sum rule are discussed.
In this paper, the deconfinement and chiral restoration transitions in strong magnetic field is realized at zero temperature in the Polyakov Nambu$-$Jona-Lasinio model. We provide the thermodynamic treatment to mimic the deconfinement phase transition at zero temperature together with the entangled scalar and vector interactions coupled with the Polyakov loop. The magnetic catalysis is found by a rising behavior of the critical chemical potential for the first-order deconfinement phase transition. While the magnetic catalysis on the chiral restoration could convert to inverse magnetic catalysi…
We study the relation between the continuum threshold as function of the temperature $s_0(T)$ within finite energy sum rules and the trace of the Polyakov loop $Φ$ in the framework of a nonlocal SU(2) chiral quark model, establishing a contact between both deconfinement order parameters at finite temperature $T$ and chemical potential $μ$. In our analysis, we also include the order parameter for the chiral symmetry restoration, the chiral quark condensate. We found that $s_0$ and $Φ$ providing us the same information for the deconfinement transition, both for the zero and finite chemical poten…
We study $SU(N_c)$ lattice gauge theories with $N_f$ flavors of massless staggered fermions in the presence of quark chemical potential $μ$. A recent exact result that in the strong coupling limit (vanishing inverse gauge coupling $β$) and for sufficiently large $μ$ the theory is in a chiral symmetric phase is here extended into the finite gauge coupling region. A cluster expansion combining a fermion spacelike hopping expansion and a strong coupling plaquette expansion is shown to converge for sufficiently large $μ$ and small $β$ at any temperature $T$. All expectations of chirally non-invari…
In this paper we carry out a low-temperature scan of the phase diagram of dense two-color QCD with $N_f=2$ quarks. The study is conducted using lattice simulation with rooted staggered quarks. At small chemical potential we observe the hadronic phase, where the theory is in a confining state, chiral symmetry is broken, the baryon density is zero and there is no diquark condensate. At the critical point $μ= m_π/2$ we observe the expected second order transition to Bose-Einstein condensation of scalar diquarks. In this phase the system is still in confinement in conjunction with non-zero baryon …
We compare two order parameters for the deconfinement transition, induced by thermal and density effects, commonly used in the literature, namely the thermal and density evolution of the continuum threshold $s_{0}$, within the frame of the QCD sum rules, and the trace of the Polyakov loop $Φ$ in the framework of a nonlocal $SU(2)$ chiral quark model. We include in our discussion the evolution of the chiral quark condensate, the parameter that characterizes the chiral symmetry restoration. We found that essentially both order parameters, $s_{0}$ and $Φ$, provide the same information for the dec…
A key question to QCD is what mechanism generates the hadron mass in the light quark sector, where both confinement and chiral symmetry breaking are in the game. Are confinement and chiral symmetry breaking in the vacuum uniquely interconnected? Can hadrons survive chiral symmetry restoration? If yes, what happens with their mass and what symmetries beyond the chiral symmetry are there? We review our recent insights. In particular, in a dynamical lattice simulation we artificially restore chiral symmetry by removing the low-lying Dirac modes of the valence quark propagators, which is a well de…
A quantitative study of the effects of dynamical chiral symmetry breaking on the mass generation of the low-lying hadrons in a dynamical lattice QCD simulation is presented. The evolution of light hadron masses upon increasing the number of low-lying Dirac operator eigenmodes in the quark propagators is confronted with the hadron masses obtained upon removal of such low-lying eigenmodes from standard full quark propagators. The low-lying chiral symmetry breaking modes provide roughly two third of the nucleon and $ρ$ masses, while the $a_1$ mass is affected to a much smaller degree.
The masses of hadrons in the vacuum, where the chiral symmetry is restored, and in the medium are in general different even when the changes in the order parameters of chiral symmetry are the same. Here, we first discuss the relation between the hadron masses and the chiral symmetry breaking in approaches based on operator product expansion (OPE). We then discuss what additional changes occur to the hadron masses when going from the chiral symmetry restored vacuum to nuclear medium and/or finite temperature. The work will highlight how we can identify the effects of chiral symmetry restoration…
