L. Ya. Glozman, V. K. Sazonov, R. F. Wagenbrunn
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.
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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.
Here we overview a possible mechanism for confining but chirally symmetric matter at low temperatures and large densities.
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.
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…
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 $…
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…
We discuss the phase structure of quantum chromodynamics (QCD) with two colors and two flavors of light quarks. This is motivated by the increasing interest in the QCD phase diagram as follows: (1) The QCD critical point search has been under intensive dispute and its location and existence suffer from uncertainty of effective U(1)_A symmetry restoration. (2) A new phase called quarkyonic matter is drawing theoretical and experimental attention but it is not clear whether it can coexist with diquark condensation. We point out that two-color QCD is nontrivial enough to contain essential ingredi…
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.
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.
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…
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 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.
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 …
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 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, …
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, …
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 …
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 …
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…
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…
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…
Suppression of dynamical momentum-space shell by chiral symmetry
该研究采用宇称双重态模型分析致密核物质，对比夸克核物质与重子夸克物质，发现纯强子物质在远高于核饱和密度下自由能最低，证明夸克自由度出现与手征对称性恢复未必同步。
Effects of tensor spin polarization on the chiral restoration and deconfinement phase transitions
本文在PNJL模型中研究张量自旋极化对手征恢复和退禁闭相变的影响，发现其显著影响手征相变温度及禁闭相的各向异性压力，并与手征对称性密切相关。
It has recently been suggested that the observed structure of parity doublets, seen in the spectrum of highly excited baryons, may be due to the effective restoration of chiral symmetry for these states. This chiral symmetry restoration high in the spectrum is consistent with the concept of quark-hadron duality. Moreover, if QCD dynamics implies the linear Regge trajectories for highly excited baryons, then the MacDowell symmetry requires the parity doubling to appear, which shows that linear Regge trajectories and chiral symmetry restoration are well compatible. On the contrary, in the low-en…
It is argued that an appearance of the near parity doublets in the upper part of the light baryon spectrum is an evidence for the chiral symmetry restoration in the regime where a typical momentum of quarks is around the chiral symmetry restoration scale. At high enough baryon excitation energy the nontrivial gap solution, which signals the chiral symmetry breaking regime, disappears and the chiral symmetry should be restored. Thus one observes a phase transition in the upper part of the light baryon spectrum. The average kinetic energy of the constituent quarks in this region is just around t…
Chiral symmetry restoration high in the hadron spectra is expected but it remains to be confirmed both in lattice QCD computations and in experiments. Recently, a theorem was derived, relating chiral symmetry restoration high in the hadron spectra to the spontaneous generation of the dynamical quark mass in QCD. We refine the theorem in the case of static-light mesons. Utilizing chiral quark model computations and lattice QCD results for the spectrum of mesons composed by a static antiquark and a light quark, we explore chiral symmetry restoration in the spectrum and the quark running mass m(k…
The imposition of Dirichlet boundary conditions in lattice computations obstructs the formation of a chiral condensate. We use chiral perturbation theory and meson models to address the effect of a Dirichlet boundary on chiral symmetry breaking. While pions are the longest-range modes in QCD, the restoration of chiral symmetry due to a boundary is shown not to depend upon the pion Compton wavelength but rather on that of the sigma meson. Power-law finite size corrections are exposed, and require prohibitively large lattices to overcome. We further speculate on the frustration of the chiral con…
We compare axial charges of excited nucleons, as predicted by the chiral symmetry restoration picture, with the traditional, moderately successful for the ground-state baryons SU(6) symmetry. The axial charges of excited nucleons can (and will) be measured in lattice QCD simulations, and comparison of the lattice results with the two different symmetry schemes will give an insight on the origins of the excited hadron masses as well as on interrelations of chiral symmetry and confinement.
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.
Color-superconducting quarkyonic matter
本研究探讨了颜色超导性在夸克性物质中的作用，通过引入配对间隙的动量依赖性，扩展了夸克性框架，为中子星中平滑的夸克-强子转变提供了新的研究工具。
We analyze the restoration pattern of the members of the scalar and pseudoscalar meson nonets under chiral $O(4)$ and $U(1)_A$ symmetries. For that purpose, we exploit QCD Ward Identities (WI), which allow one to relate susceptibilities with quark condensates, as well as susceptibility differences with meson vertices. In addition, we consider the low-energy realization of QCD provided by $U(3)$ Chiral Perturbation Theory (ChPT) at finite temperature to perform a full analysis of the different correlators involved. Our analysis suggests $U(1)_A$ partner restoration if chiral symmetry partners a…
Hadron-quark transition and chiral symmetry restoration at high density
该研究提出含重子有效体积与手征动力学的强子-夸克混合唯象模型，发现中间密度存在混合相，类一阶夸克相变可引发强手征对称性恢复且声速在高密度处有大峰值。
We overview two interconnected topics: possible effective restoration of chiral symmetry in highly excited hadrons and possible existence of confined but chirally symmetric matter at low temperatures and high densities.
We present results on both the restoration of the spontaneously broken chiral symmetry and the effective restoration of the anomalously broken U(1)_A symmetry in finite temperature QCD at zero chemical potential using lattice QCD. We employ domain wall fermions on lattices with fixed temporal extent N_τ= 8 and spatial extent N_σ= 16 in a temperature range of T = 139 - 195 MeV, corresponding to lattice spacings of a \approx 0.12 - 0.18 fm. In these calculations, we include two degenerate light quarks and a strange quark at fixed pion mass m_π= 200 MeV. The strange quark mass is set near its phy…
It is shown that in the large $N_c$ limit the light baryon spectrum exhibits the chiral restoration phase transition at high enough excitation energy. Such a phase transition is evidenced by the systematical parity doublets observed in the upper part of $N$ and $Δ$ spectra.
Quark saturation in the QCD phase diagram
本研究通过IdylliQ模型的汤川假设确定夸克相空间密度达1时的夸克物质起始阈值，分析不同温度下各强子及共振态的贡献，划定参数不确定性范围，为QCD相图中夸克物质的可能存在区域提供估算。
Restoration of chiral and $U(1)_A$ symmetries in excited hadrons is reviewed. Implications of the OPE as well as of the semiclassical expansion for this phenomenon are discussed. A solvable model of the 't Hooft type in 3+1 dimensions is presented, which demonstrates a fast restoration of both chiral and $U(1)_A$ symmetries at larger spins and radial excitations.
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 $N_c=3$.
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…
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 propose that in QCD with dynamical quarks, colour deconfinement occurs when an external field induced by the chiral condensate strongly aligns the Polyakov loop. This effect sets in at the chiral symmetry restoration temperature T-chi and thus makes deconfinement and chiral symmetry restoration coincide. The predicted singular behaviour of Polyakov loop susceptibilities at T-chi is shown to be supported by finite temperature lattice calculations.
We present and analyze a new set of Ward Identities which shed light on the distinction between different patterns of chiral symmetry restoration in QCD, namely $O(4)$ vs $O(4)\times U(1)_A$. The degeneracy of chiral partners for all scalar and pseudoscalar meson nonet members are studied through their corresponding correlators. Around chiral symmetry degeneration of $O(4)$ partners, our analysis predicts that $U(1)_A$ partners are also degenerated. Our analysis also leads to $I=1/2$ scalar-pseudoscalar partner degeneration at exact chiral restoration, and supports ideal mixing between the $η$…
The evidence, theoretical justification and implications of chiral symmetry restoration in excited hadrons are presented.
We review the relationship between the pion decay constant $f_π$, the chiral symmetry restoration temperature $T_c$ and the phenomenology of low energy chiral symmetry breaking in view of the recent confirmation of the existence of a sigma meson with a mass of 600-700 MeV.
A fast restoration of chiral symmetry in excited mesons is demonstrated. A minimal "realistic" chirally symmetric confining model is used, where the only interaction between quarks is the linear instantaneous Lorentz-vector confining potential. Chiral symmetry breaking is generated via the nonperturbative resummation of valence quarks self-energy loops and the meson bound states are obtained from the Bethe-Salpeter equation. The excited mesons fall into approximate chiral multiplets and lie on the approximately linear radial and angular Regge trajectories, though a significant deviation from t…
We study the spectrum of heavy-light mesons within a model with linear instantaneous confining potential. The single-quark Green function and spontaneous breaking of chiral symmetry are obtained from the Schwinger-Dyson (gap) equation. For the meson spectrum we derive a Bethe-Salpeter equation (BSE). We solve thiss equation numerically in the heavy-light limit and obtain effective restoration of chiral and $U(1)_A$ symmetries at large spins.
We analyze the chiral phase transition of the Nambu--Jona-Lasinio model in the cold and dense region on the lattice developing the Grassmann version of the anisotropic tensor renormalization group algorithm. The model is formulated with the Kogut--Susskind fermion action. We use the chiral condensate as an order parameter to investigate the restoration of the chiral symmetry. The first-order chiral phase transition is clearly observed in the dense region at vanishing temperature with $μ/T\sim O(10^3)$ on a large volume of $V=1024^4$. We also present the results for the equation of state.
Chiral symmetry restoration at finite temperature in a model with manifest confinement
本文利用一个手征对称且明显禁闭的可解夸克模型，论证禁闭在零温诱导手征对称性破缺，但在临界温度Tch处发生手征恢复相变，从而解释格点QCD中高温禁闭但手征对称区域的存在。
The evidence and the theoretical justification of chiral symmetry restoration in high-lying hadrons is presented.
In this article we study restoration of chiral symmetry at finite temperature for quark matter with a chiral chemical potential, $μ_5$, by means of a nonlocal Nambu-Jona-Lasinio model. This model allows to introduce in the simplest way possible a Euclidean momentum, $p_E$, dependent quark mass function which decays (neglecting logarithms) as $1/p_E^2$ for large $p_E$, in agreement with asymptotic behaviour expected in QCD in presence of a nonperturbative quark condensate. We focus on the critical temperature for chiral symmetry restoration in the chiral limit, $T_c$, versus $μ_5$, as well as o…
Complex poles of the unitarized pi-pi scattering amplitude in nuclear matter are studied. Partial restoration of chiral symmetry is modeled by the decrease of in-medium pion decay constant f*_{pi}. For large chiral restoration (f*_{pi}/f_{pi} << 1), 2nd sheet poles in the scalar (sigma) and the vector (rho) mesons are both dictated by the Lambert W function and show universal softening as f*_{pi} decreases. In-medium pi-pi cross section receives substantial contribution from the soft mode and exhibits a large enhancement in low-energy region. Fate of this universality for small chiral restorat…
The chiral phase transition at high temperature and/or density is interpreted in terms of Georgi's vector limit. We discuss three cases as possible support for this scenario: Quark-number susceptibility, cool kaons in heavy-ion process and an instanton-molecule picture for chiral restoration. Both the notion of ``mended symmetry" and the Georgi vector limit are suggested to be relevant in nuclear physics of dense matter.
The light-quark correlator in the axial-vector channel is used, in conjunction with finite energy QCD sum rules at finite temperature, in order to (a) establish a relation between chiral-symmetry restoration and deconfinement, and (b) determine the temperature behavior of the $a_1(1260)$ width and coupling. Results indicate that deconfinement takes place at a slightly lower temperature than chiral-symmetry restoration, although this difference is not significant given the accuracy of the method. The behaviour of the $a_1(1260)$ parameters is consistent with quark-gluon deconfinement, as the wi…
In the mean-field approximation we study the chiral soliton within the linear sigma model in a thermal vacuum. The chiral soliton equations with different boundary conditions are solved at finite temperatures and densities. The solitons are discussed before and after the chiral restoration. We find that the system has soliton solutions even after the chiral restoration and they are very different from those before the chiral restoration, which indicates that the quarks are still bounded after the chiral restoration.
We review recent theoretical progress in low-mass dilepton production at CERN-SpS energies. Various hadronic approaches to calculate the vector correlator in hot/dense hadronic matter are discussed and confronted with each other. Possible consequences for the nature of chiral restoration are indicated.
Chiral symmetry imposes some constrains on hadron correlation functions in dense medium. These constraints imply a certain general structure of the two- and three-point correlation functions of chiral partners and lead to the effect of mixing arising from the interaction of the long-ranged nuclear pions with corresponding interpolating currents. It reflects the phenomena of partial restoration of chiral symmetry. We consider soft pion corrections for quark condensates and several possible pairs of chiral partners for both mesons and nucleons and analyse their mixing patterns. We explored both …
Spectral enhancement near the 2m_π threshold in the I=J=0 channel in nuclei is shown to be a distinct signal of the partial restoration of chiral symmetry. The relevance of this phenomenon with the possible detection of 2π^{0} and 2γin hadron-nucleus and photo-nucleus reactions is discussed.
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 report on recent work relating the medium effects observed in dilepton spectra in heavy-ion collisions to potential signals of chiral symmetry restoration. The key connection remains the approach to spectral function degeneracy between the vector-isovector channel with its chiral partner, the axialvector-isovector channel. Several approaches are discussed to elaborate this connection, namely QCD and Weinberg sum rules with input for chiral order parameters from lattice QCD, and chiral hadronic theory to directly evaluate the medium effects of the axialvector channel and the pertinent pion d…
Reduction of (pseudo-)Critical Temperatures of Chiral Restoration and Deconfinement Phase Transitions in a Magnetized PNJL Model
该研究在Pauli-Villars正则化PNJL模型中引入随磁场变化的Polyakov loop标度参数，解释逆磁催化并降低手征恢复与退禁闭相变的临界温度。
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