Larry McLerran
At high baryon number density, it has been proposed that a new phase of QCD matter controls the physics. This matter is confining but can have densities much larger than $Λ^3_{QCD}$ QCD. Its existence is argued from large Nc approximations, and model computations. It is approximately chirally symmetric.
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We study the phase diagram of quark matter at finite temperature and density in the strong coupling lattice QCD with one species of unrooted staggered fermions including finite coupling ($1/g^2$) effects for color SU($N_c$). We find that we may have partially chiral restored medium density matter at $N_c=3$, which would correspond to the quarkyonic matter suggested at large $N_c$.
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 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 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…
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…
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…
Quarkyonic picture of isospin QCD
本文提出同位旋QCD物质在夸克子框架下的新图像，由π介子凝聚和自由夸克构成，其起始密度可低于两倍核饱和密度，并与格点QCD及微扰结果一致。
Momentum Shell in Quarkyonic Matter from Explicit Duality: A Dual Model for Cold, Dense QCD
该模型通过夸克-重子对偶关系统一描述冷致密QCD物质，解析求解发现低密度核物质区与高密度夸克物质区，后者形成动量壳层，并导致状态方程由软变硬、压力骤增。
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。
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.
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…
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 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.
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…
$f$-mode oscillations of dark matter admixed quarkyonic neutron star
本研究在Cowling近似下系统研究了含暗物质的夸克物质中子星的$f$-模振荡，发现转变密度、QCD禁闭尺度和暗物质费米动量显著影响振荡频率，但振荡性质间的普适关系依然稳健。
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。
Universality in Space Time $ω$ modes of Quarkyonic Stars
本文研究了夸克离子星的$ω$模式，发现其谱特征与EOS关系不大，且具有独特的模式签名。
Quarkyonic Model for Neutron Star Matter: A Relativistic Mean-Field Approach
本文采用相对论平均场方法构建夸克子物质状态方程，研究静态中子星性质，发现其可支持约2.8倍太阳质量的中子星，且声速与QCD共形极限一致，潮汐形变符合GW170817和GW190425观测约束。
Quarkyonic or baryquark matter? On the dynamical generation of momentum space shell structure
本研究对比了零温度下夸克与核子混合物的两种费米海-壳层结构方案，发现baryquark matter比quarkyonic matter在能量上更受青睐且声速行为更合理，指出需修改动力学机制以保留quarkyonic matter。
Dark Matter Influence on Quarkyonic Stars: A Relativistic Mean Field Analysis
本研究通过相对论平均场方法，在夸克子物质模型中引入费米子暗物质，分析其对中子星结构的影响，发现夸克子物质硬化状态方程而暗物质软化，二者结合可满足观测约束。
Microscopic Insights into the Quarkyonic Hadron--Quark Crossover: Lessons from Ultracold Fermi Gases
通过类比超冷费米气体的BEC-BCS交叉，研究强子-夸克交叉中的三重涨落机制，解释重子动量壳层和声速峰值，并联系唯象夸克物态方程。
Dark Matter Effects on the Curvature of Neutron Stars within the new Quarkyonic Model Coupled with Relativistic Mean Field Theory
本研究首次结合夸克子有效场论与相对论平均场模型，分析暗物质对中子星曲率的影响，发现暗物质软化物态方程、降低中心压力，而转变密度增强致密性，为理解奇异物质致密天体提供新视角。
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 use QCD sum rules to obtain the weak parity-violating pion-nucleon coupling constant $f_{πNN}$. We find that $f_{πNN}\approx 2\times 10^{-8}$, about an order of magnitude smaller than the ``best estimates'' based on quark models. This result follows from the cancellation between perturbative and nonperturbative QCD processes not found in quark models, but explicit in the QCD sum rule method. Our result is consistent with the experimental upper limit found from $^{18}$F parity-violating measurements.
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.
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 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.
Core or Halo? Two-Fluid Analysis of Dark Matter-Admixed Quarkyonic Stars in the Multi-Messenger Era
本文提出双流体框架研究暗物质混合夸克星，发现其可达到GW190814质量范围，并区分核心与晕形态，与多信使观测约束一致。
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 suggest baryon-baryon correlations as an experimentally accessible signature for a first-order phase transition between a baryon-rich phase, like quarkyonic, and a baryon-suppressed hadronic phase in the QCD phase diagram. We examine the consequences of baryon-rich bubble formation in an expanding medium and show how the two-particle correlations vary in the transverse and longitudinal direction depending on the strength of the radial flow, the bubble temperature, and the time when the baryons are emitted.
It is shown that to leading order the QCD collisional energy loss reads $dE/dx \sim α(m_D^2)T^2$. Compared to prevalent expressions, $dE^B/dx \sim α^2 T^2 \ln(ET/m_D^2)$, which could be considered adaptions of the (QED) Bethe-Bloch formula, the rectified result takes into account the running coupling, as dictated by renormalization. As one significant consequence, due to asymptotic freedom, the collisional energy loss becomes independent of the jet energy $E$. Some implications with regard to heavy ion collisions are pointed out.
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 heavy quarkonium spectrum of Two Color QCD (QC$_2$D) at non-zero quark chemical potential $μ$ and temperature $T$ with $μ/T\gg1$ has been calculated in both $S$- and $P$-wave channels using a lattice non-relativistic formulation of QC$_2$D. As $μ$ is varied, the quarkonium spectra reveal three separate regions, corroborating previous findings that there are three distinct physical regimes of QC$_2$D at low temperature and high baryon density: hadronic matter, quark/quarkyonic matter, and deconfined matter. The results are interpreted in terms of the formation of heavy-light $Qq$ states in …
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 $N_c=3$.
Advances in the holographic description of hot and dense QCD matter
本文基于规范-引力对偶，借助Witten-Sakai-Sugimoto模型拓展了热密QCD物质的全息描述，定位了相关相并分析其特性，还探讨了该领域未来方向。
We study the phase diagram of (large-$N_c$) QCD using a simplistic holographic hard-wall model with a dynamical scalar field and a homogeneous Ansatz representing a smeared instanton/baryon density. The resulting phase diagram is qualitatively consistent with expectations, including a mesonic, baryonic, quarkyonic, and quark-gluon plasma phase. As in other holographic models, we also find a baryonic popcorn transition, which appears at large chemical potential as a crossover. We then evaluate the nuclear matter equation of state, which turns out to be rather stiff with a large peaked sound vel…
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…
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…
Probing the nonstrange quark star equation of state with compact stars and gravitational waves
基于修正的微扰QCD模型，研究了ud夸克星的最大质量限制，并通过引力波事件验证其可行性。
Two Lectures on the Phase Diagram of QCD
本文基于QCD在有限温度和密度下的相图，利用大色数N_c解释其特征，探讨了零重子数密度下的三个相，以及高重子数密度和低温下的相变，强调了Chiral对称性恢复和Quarkyonic相的特性。
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 …
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 $…
A New State of Matter between the Hadronic Phase and the Quark-Gluon Plasma?
本文提出在强子相与夸克-胶子等离子体之间存在一个中间新相SQGB，其中夸克解约束而胶子仍约束于胶球，并通过大N_c分析和熵密度计算确认该相，给出修正相图及手征对称性恢复分析。
With the explicit breaking of scale invariance by the trace anomaly of QCD rephrased in terms of spontaneous breaking, low-energy strong interaction dynamics of dense (and also hot) matter can be effectively captured by -- in addition to the Nambu-Goldstone bosons and the vector mesons -- two dilaton fields, the "soft" ($χ_s$) field that is locked to chiral symmetry and the "hard" ($χ_h$) field which remains unaffected by chiral symmetry. The interplay of the soft and hard dilatons plays a subtle role in how chiral symmetry is manifested in hot and/or dense matter. The scale anomaly in which t…
Functional Renormalization Group analysis of the quark-condensation pattern on the Fermi surface: A simple effective-model approach
本文构建了一个简单的有效模型，利用泛函重整化群方法分析费米面上夸克凝聚模式，发现静态平均场近似下存在非平凡凝聚，但动态玻色子模式的扩散性质会破坏该凝聚。
The hadronic matter described as a skyrmion matter embedded in an FCC crystal is found to turn into a half-skyrmion matter with vanishing (in the chiral limit) quark condensate and {\em non-vanishing} pion decay constant at a density $n_{1/2S}$ lower than or at the critical density $n_c^{χSR}$ at which hadronic matter changes over to a chiral symmetry restored phase with deconfined quarks. When hidden local gauge fields and dilaton scalars -- one "soft" and one "hard" -- are incorporated, this phase is characterized by $a=1$, $f_π\neq 0$ with the hidden gauge coupling $g\neq 0$ but $\ll 1$. Wh…
Holographic QCD at finite baryon number density and zero temperature is studied within the five-dimensional Sakai-Sugimoto model. We introduce a new approximation that models a smeared crystal of solitonic baryons by assuming spatial homogeneity to obtain an effective kink theory in the holographic direction. The kink theory correctly reproduces a first order phase transition to lightly bound nuclear matter. As the density is further increased the kink splits into a pair of half-kink constituents, providing a concrete realization of the previously suggested dyonic salt phase, where the bulk so…
Thermodynamics and phase diagrams of the Polyakov quark-meson model with on-shell versus curvature mass parameter fixing
本文通过引入在壳重整化方案修正PQM模型真空项的不自洽性，构建RPQM模型，系统比较不同Polyakov圈势下各模型的相图与热力学，揭示夸克背反应和化学势依赖参数对夸克子相区域的抑制作用。
The hadronic matter described as a skyrmion matter embedded in an FCC crystal is found to turn into a half-skyrmion matter with vanishing (in the chiral limit) quark condensate and {\it non-vanishing} pion decay constant {$f_π$} at a density $n_{1/2}$ lower than or near the critical density $n_c$ at which hadronic matter changes over to a chiral symmetry restored phase with possibly deconfined quarks. When hidden local gauge fields and a dilaton scalar of spontaneously broken scale symmetry with decay constant $f_χ$ are incorporated, this half-skyrmion phase is characterized by $f_χ\approx f_π…
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