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 appears a gap in the excitation spectrum of the quarkyonic matter that should be crucially important for its properties above the chiral restoration point. This gap is of a new type and is not related with the condensation of the fermionic system into a quasibosonic system. It is only due to such properties as confinement and manifest chiral symmetry at the same time.
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 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 results from simulations of Two Color QCD with two Wilson quark flavors in the presence of a quark chemical potential mu at two different lattice spacings. The equation of state, conformal anomaly, superfluid order parameter and Polyakov line are all discussed. Our results suggest that the transition from hadronic to quark matter, and that from confined to deconfined matter occur at distinct values of mu, consistent with the existence of a quarkyonic phase in this model.
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.
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 calculate the Bremsstrahlung photon spectrum emitted from dynamically evolving quarkyonic matter, and compare this spectrum with that of a high chemical potential quark-gluon plasma as well as to a hadron gas. We find that the transverse momentum distribution and the harmonic coefficient is markedly different in the three cases. The transverse momentum distribution of quarkyonic matter can be fit with an exponential, but is markedly steeper than the distribution expected for the quark-gluon plasma or a hadron gas, even at the lower temperatures expected in the critical point region. The qua…
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, …
SUBATECH UMR 6457 (IMT Atlantique, Université de Nantes, IN2P3/CNRS)（苏巴泰克联合研究实验室（大西洋高等矿业学院，南特大学，法国国家科学研究中心））；Department of Physics, Niigata University（新潟大学物理系）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所跨学科理论与数学科学中心）
We introduce a theoretical framework to analyze the thermal properties of a recently proposed "excluded volume" model of quarkyonic matter. This entails proposing finite temperature distribution functions and entropy functionals constrained by internal theoretical consistency. We use the formalism developed here to analyze the effect of temperature on the quark onset as a function of baryon density. We find that the baryon density at which the quarkyonic phase emerges decreases only slightly with temperature, an effect produced by large $N_c$. We furthermore find that a finite temperature incr…
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.
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 $…
Quarkyonic matter is a new phase of QCD at finite temperature and density which is distinct from the confined and de-confined phases. Its existence is unambiguously argued in the large number of colors limit in QCD. Hints of its existence for 3 color QCD are shown in lattice Monte-Carlo data and heavy ion experiments.
We examine the phase diagram of hadronic matter when the number of colours $N_c$, as well as temperature and density, are varied. We show that in this regime a new percolation phase transition is possible, and examine the implications of this transition for extrapolations to physical QCD of the large-N_c limit.
After combined character and hopping expansions and integration over the spatial gauge links, lattice QCD reduces to a three-dimensional $SU(3)$ Polyakov loop model with complicated interactions. A simple truncation of the effective theory is valid for heavy quarks on reasonably fine lattices and can be solved by linked cluster expansion in its effective couplings. This was used ealier to demonstrate the onset transition to baryon matter in the cold and dense regime. Repeating these studies for general $N_c$, one finds that for large $N_c$ the onset transition becomes first-order, and the pres…
The phase space structure of zero temperature Quarkyonic Matter is a Fermi sphere of Quark Matter, surrounded by a shell of Nucleonic Matter. We construct a quasi particle model of Quarkyonic Matter based on the constituent quark model, where the quark and nucleon masses are related by m_Q = m_N/N_c, and N_c is the number of quark colors. The region of occupied states is for quarks k_Q < k_F/N_c, and for nucleons k_F < k_N < k_F + Δ. We first consider the general problem of Quarkyonic Matter with hard core nucleon interactions. We then specialize to a quasi-particle model where the hard core n…
I describe a novel mechanism where the variation of an $ω_0$ condensate can generate a "spike" in the speed of sound in hadronic matter. An $ω_0$ condensate naturally increases the speed of sound; the real problem is how to get the speed of sound to decrease. I suggest this can happen through the appearance of a Quantum Pion Liquid.
Based on the fact that the constituent quark model reproduces the recent lattice result on baryon-baryon repulsion at short distance and that it includes the quark dynamics with confinement, we analyze to what extent the quarkyonic modes appear in the phase space of baryons as one increases the density before only quark dynamics and hence deconfinement occurs. We find that as one increases the baryon density, the initial quark mode that appears will involve the $d(u)$-quark from a neutron (proton), which will leave the most attractive ($ud$) diquark intact.
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 examine the interplay between the percolation and the deconfinement phase transitions of Yang-Mills matter at finite temperature, quark chemical potential $μ_Q$ and number of colors $N_c$. We find that, whereas the critical $N_c$ for percolation goes down with density, the critical $N_c$ for confinement generally goes up. Because of this, Yang-Mills matter falls into two qualitatively different regimes: the "low-$N_c$ limit", where percolation does not occur because matter deconfines before it percolates, and the high-$N_c$ limit, where there are three distinct phases characterizing Yang-Mi…
The single-flavor excluded-volume model based on the effective size of baryons reproduces the hard-soft density evolution of the equation of state (EoS) required by the recent studies of GW170817. This phenomenological model basically realizes the concept of quarkyonic matter which is introduced from large-$N_{c}$ gauge theory for dense matter. Enhanced nucleon interactions and dynamically generated quark degrees of freedom can reproduce the hard-soft evolution of the EoS. In this paper, we extend the excluded-volume model to a three-flavor system by considering electromagnetic charge and poss…
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 …
During the last years it has become possible to address the cold and dense regime of QCD directly for sufficiently heavy quarks, where combined strong coupling and hopping expansions are convergent and a 3d effective theory can be derived, which allows to control the sign problem either in simulations or by fully analytic calculations. In this contribution we review the effective theory and study the $N_c$-dependence of the nuclear liquid gas transition, as well as the equation of state of baryonic matter in the strong coupling limit. We find the transition to become more strongly first order …
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 argue that features of hadron production in relativistic nuclear collisions, mainly at CERN-SPS energies, may be explained by the existence of three forms of matter: Hadronic Matter, Quarkyonic Matter, and a Quark-Gluon Plasma. We suggest that these meet at a triple point in the QCD phase diagram. Some of the features explained, both qualitatively and semi-quantitatively, include the curve for the decoupling of chemical equilibrium, along with the non-monotonic behavior of strange particle multiplicity ratios at center of mass energies near 10 GeV. If the transition(s) between the three pha…
We suggest an extension to isospin asymmetric matter of the quarkyonic model from McLerran and Reddy. This extension allows us to construct the $β$-equilibrium between quarks, nucleons and leptons. The concept of the quarkyonic matter originates from the large number of color limit for which nucleons are the correct degrees of freedom near the Fermi surface -- reflecting the confining forces -- while deep inside the Fermi sea quarks naturally appear. In isospin asymmetric matter, we suggest that this new concept can be implemented within a global isoscalar relation between the shell gaps diffe…
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, …
We extend the excluded-volume model of isospin symmetric two-flavor dense quarkyonic matter [Phys. Rev. C 101, 035201 (2020)] including strange particles and address its implications for neutron stars. The effective sizes of baryons are defined from the diverging hard-core potentials in the short interdistance regime. Around the hard-core density, the repulsive core between baryons at short distances leads to a saturation in the number density of baryons and generates perturbative quarks from the lower phase space, which leads to the shell-like distribution of baryons by the Pauli exclusion pr…
Quarkyonic matter and hadron-quark crossover from an ultracold atom perspective
The University of Tokyo（东京大学）；RIKEN Nishina Center（理化学研究所仁科中心）；Quark Nuclear Science Institute, The University of Tokyo（东京大学夸克核科学研究所）；The Open University of Japan（日本开放大学）；High Energy Accelerator Research Organization (KEK)（高能加速器研究机构（KEK））；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences（理化学研究所交叉理论与数学科学中心）
We study the color-spin interaction energy of a quark, a diquark and a baryon with their surrounding baryons and/or quark matter. This is accomplished by classifying all possible flavor and spin states of the resulting multiquark configuration in both the flavor SU(2) and SU(3) symmetric cases. We find that while the baryon has the lowest interaction energy when there is only a single surrounding baryon, the quark has the lowest interaction energy when the surrounding has more than three baryons or becomes a quark gas. As the short range nucleon-nucleon interactions are dominated by the color-…
Quarkyonic matter with strangeness in an extended relativistic mean-field model
School of Physics, Zhengzhou University（郑州大学物理学院）；Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University（扬州大学物理科学与技术学院引力与宇宙学中心）
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…
Evolution of strangeness and hyperons in quarkyonic matter
Institute for Nuclear Theory, University of Washington（华盛顿大学核理论研究所）；Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN（理化学研究所跨学科理论与数学科学项目（iTHEMS））；Department of Physics, University of California, Berkeley（加州大学伯克利分校物理系）；Theory Center, IPNS, High Energy Accelerator Research Organization (KEK)（高能加速器研究机构（KEK）IPNS理论中心）；Department of Physics, Tohoku University（东北大学物理系）
Lattice QCD with heavy quarks reduces to a three-dimensional effective theory of Polyakov loops, which is amenable to series expansion methods. We analyse the effective theory in the cold and dense regime for a general number of colours, $N_c$. In particular, we investigate the transition from a hadron gas to baryon condensation. For any finite lattice spacing, we find the transition to become stronger, i.e. ultimately first-order, as $N_c$ is made large. Moreover, in the baryon condensed regime, we find the pressure to scale as $p\sim N_c$ through three orders in the hopping expansion. Such a…
Theory Center, IPNS, High Energy Accelerator Research Organization (KEK)（高能加速器研究机构（KEK））；Graduate Institute for Advanced Studies, SOKENDAI（SOKENDAI高级研究研究生院）
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…
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 discuss theoretical scenarios on crossover between nuclear matter (NM) and quark matter (QM). We classify various possibilities into three major scenarios according to the onset of diquark degrees of freedom that characterizes color-superconducting (CSC) states. In the conventional scenario NM occurs at the liquid-gas (or liquid-vacuum at zero temperature) phase transition and QM occurs next, after which CSC eventually appears. With the effect of strong correlation, the BEC-BCS scenario implies that CSC occurs next to NM and QM comes last in the BCS regime. We adopt the quarkyonic scenario …
I discuss the phase diagram for QCD in the baryon chemical potential and temperature plane. I argue that there is a new phase of matter different from the deconfined Quark Gluon Plasma: Quarkyonic Matter. Quarkyonic Matter is confined and exists at densities parametrically large compared to the QCD scale, when the number of quark colors, $N_c$ is large. I motivate the possibility that Quarkyonic Matter is in an inhomogeneous phase, and is surrounded by lines of phase transitions, making a Happy Island in the $μ_B$-T plane. I conjecture about the geography of Happy Island.
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 examine the nuclear liquid-gas phase transition at large number of colors ($N_c$) within the framework of the Van Der Waals (VdW) model. We argue that the VdW equation is appropriate at describing inter-nucleon forces, and discuss how each parameter scales with $N_c$. We demonstrate that $N_c=3$ (our world) is not large with respect to the other dimensionless scale relevant to baryonic matter, the number of neighbors in a dense system $N_N$. Consequently, we show that the liquid-gas phase transition looks dramatically different at $N_c \to \infty$ with respect of our world: The critical poi…
