Some recent developments in exact results in relativistic hydrodynamics is reviewed. We discuss phenomenological applications in high-energy collisions and theoretical features of the solutions. We compare the method of numerical modelling to the strategy based on exact solutions. We argue that the efforts made and progress achieved in this seemingly purely theoretical topic is of interest for phenomenology.
Finding the existence and the location of the QCD critical point is one of the main goals of the RHIC beam energy scan program. To make theoretical predictions and corroborate with the experimental data requires modeling the space-time evolution of the matter created in heavy-ion collisions by dynamical models such as the relativistic hydrodynamics with an appropriate Equation of State (EoS). In the present exploratory study, we use a viscous 2+1 dimensional event-by-event (e-by-e) hydrodynamic code at finite baryon densities with two different EoSs (i) Lattice QCD + HRG with a crossover trans…
We discuss the Hard Dense Loop resummation at finite quark mass and evaluate the equation of state (EoS) of cold and dense QCD matter in $β$ equilibrium. The resummation in the quark sector has an effect of lowering the baryon number density and the EoS turns out to have much smaller uncertainty than the perturbative QCD estimate. Our numerical results favor smooth matching between the EoS from the resummed QCD calculation at high density and the extrapolated EoS from the nuclear matter density region. We also point out that the speed of sound in our EoS slightly exceeds the conformal limit.
We present a recent development towards a unified description of quark-hadron matter in the QCD phase diagram that is based on a cluster decomposition of the generalized Beth-Uhlenbeck approach to quark matter, selfconsistently coupled to Polyakov-loop and mesonic background fields. The Mott dissociation of hadrons under extreme conditions of temperature and density is triggered by chiral symmetry restoration and confining aspects are modeled by the coupling to the background mean fields. First results for the QCD phase diagram with the capability to describe critical endpoints as well as cros…
Equation of state (EOS) of pure neutron matter (PNM) is studied in QCD sum rules (QCDSR). It is found that the QCDSR results on EOS of PNM are in good agreement with predictions by current advanced microscopic many-body theories. Moreover, the higher-order density terms in quark condensates are shown to be important to describe the empirical EOS of PNM in the density region around and above nuclear saturation density although they play minor role at subsaturation densities. The chiral condensates in PNM are also studied, and our results indicate that the higher-order density terms in quark con…
We present a strangeness-neutral equation of state for QCD that exhibits critical behavior and matches lattice QCD results for the Taylor-expanded thermodynamic variables up to fourth-order in $μ_B/T$. It is compatible with the SMASH hadronic transport approach and has a range of temperatures and baryonic chemical potentials relevant for phase II of the Beam Energy Scan at RHIC. We provide an updated version of the software BES-EoS, which produces an equation of state for QCD that includes a critical point in the 3D Ising model universality class. This new version also includes isentropic trej…
We investigate the fundamental mode of non-radial oscillations of non-rotating compact stars in general relativity using a set of equations of state (EOS) connecting state-of-the-art calculations at low and high densities. Specifically, a low density model based on the chiral effective field theory (EFT) and high density results based on perturbative Quantum Chromodynamics (QCD) are matched through different interpolating polytropes fulfilling thermodynamic stability and subluminality of the speed of sound, together with the additional requirement that the equations of state support a two sola…
The cold and dense QCD equation of state (EoS) at high baryon chemical potential $μ_B$ involves at order $α^2_S$ an all-loop summation of the soft mode $m_E\sim α_S^{1/2} μ_B$ contributions. Recently, the complete soft contributions at order $α^3_S$ were calculated, using the hard thermal loop (HTL) formalism. By identifying {\em massive} renormalization group (RG) properties within HTL, we resum to all orders $α_S^p, p\ge 3$ the leading and next-to-leading logarithmic soft contributions. We obtain compact analytical expressions, that show visible deviations from the state-of-the art results, …
We investigate the equation of state(EoS) and the effect of the hadron-quark phase transition of strong interaction matter in compact stars. The hadron matter is described with the relativistic mean field theory,and the quark matter is described with the Dyson-Schwinger equation approach of QCD. The complete EoS of the hybrid star matter is constructed with not only the Gibbs construction but also the 3-window interpolation. The mass-radius relation of hybrid stars is also investigated. We find that, although the EoSs of both the hadron matter with hyperon and $Δ$-baryon and the quark matter a…
Currently at the Beam Energy Scan at RHIC experimental efforts are being made to find the QCD critical point. On the theoretical side, the behavior of higher-order susceptibilities of the net-baryon charge from Lattice QCD at $μ_{_B}\!=\!0$ may allow us to estimate the position of the critical point in the QCD phase diagram. However, even if the series expansion continues to higher-orders, there is always the possibility to miss the critical point behavior due to truncation errors. An alternative approach is to use a black hole engineered holographic model, which displays a critical point at l…
We study light (u, d) quark matter with charm impurities. These impurities are added to the Lagrangian density. We derive the equation of state (EOS) of this kind of quark matter, which contains a Kondo phase. We explore this EOS and study the structure of stars, identifying the effects of the Kondo phase. Solving the TOV equations and computing the mass-radius diagram, we find that the presence of a Kondo phase leads to smaller and lighter stars.
Quark flavors in hot and dense holographic QCD: setup and comparison to data
Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Department of Physics, Pohang University of Science and Technology（浦项科技大学物理系）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Institute for Theoretical Physics, University of Heidelberg（海德堡大学理论物理研究所）
Frankfurt Institute for Advanced Studies（法兰克福高等研究院）；Department of Physics, University of California, Berkeley（加州大学伯克利分校物理系）；Nuclear Science Division, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室核科学部）；Institut für Theoretische Physik, Goethe Universität（歌德大学理论物理研究所）；GSI Helmholtzzentrum für Schwerionenforschung（亥姆霍兹重离子研究中心）；Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University（华中师范大学夸克与轻子物理教育部重点实验室及粒子物理研究所）
Supervised learning with a deep convolutional neural network is used to identify the QCD equation of state (EoS) employed in relativistic hydrodynamic simulations of heavy-ion collisions from the simulated final-state particle spectra $ρ(p_T,Φ)$. High-level correlations of $ρ(p_T,Φ)$ learned by the neural network act as an effective "EoS-meter" in detecting the nature of the QCD transition. The EoS-meter is model independent and insensitive to other simulation inputs, especially the initial conditions. Thus it provides a powerful direct-connection of heavy-ion collision observables with the bu…
A state-of-the-art 3+1 dimensional cascade + viscous hydro + cascade model vHLLE+UrQMD has been applied to heavy ion collisions in RHIC Beam Energy Scan range $\sqrt{s_{\rm NN}}=7.7\dots 200$ GeV. Based on comparison to available experimental data it was estimated that an effective value of shear viscosity over entropy density ratio $η/s$ in hydrodynamic stage has to decrease from $η/s=0.2$ to $0.08$ as collision energy increases from $\sqrt{s_{\rm NN}} = 7.7$ to $39$ GeV, and to stay at $η/s=0.08$ for $39\le\sqrt{s_{\rm NN}}\le200$ GeV. In this work we show how an equation of state with first…
Abstract (abridged edition): Properties of the relativistic nucleon self-energy decomposition of the symmetry energy as well as the equation of state (EOS) of pure neutron matter (PNM) are explored systematically within the QCD sum rules (QCDSR). Our results in the present work have demonstrated that the QCDSR approach can be used to explore the properties of asymmetric nuclear matter (ANM) in a quantitative manner, at least in lower density region. The QCDSR approach establishes a bridge connecting the EOS of ANM and the non-perturbative QCD vacuum, and thus provides a useful way to understan…
Taking into account the recently developed van der Waals (VDW) like equation of state (EoS) for grand canonical ensemble of fermions, the temperature dependent profiles of normalized entropy density ($s /T^3$) and the ratio of shear viscosity and entropy density ($η/ s$) for hadron resonance gas have been evaluated. The VDW parameters, corresponding to interactions between (anti)baryons, have been obtained by contrasting lattice EoS for QCD matter at finite chemical potentials ($μ_{B}$) and for $T \le$ 160 MeV. The temperature and chemical potential dependent study of $s /T^3$ and $η/s$ for ha…
The equation of state (EoS) of quantum chromodynamics (QCD) at zero temperature can be calculated in two different perturbative regimes: for small values of the baryon chemical potential $μ$, one may use chiral perturbation theory (ChEFT); and for large values of $μ$, one may use perturbative QCD (pQCD). There is, however, a gap for $μ\in (0.97\text{ GeV},\, 2.6\text{ GeV})$, where these theories becomes non-perturbative, and where there is currently no known microscopic description of QCD matter. Unfortunately, this interval obscures the values of $μ$ found within the cores of neutron stars (…
Neutron star observations, including direct mass and radius measurements as well as the analysis of gravitational wave signals emitted by stellar mergers, provide valuable and unique insights into the properties of strongly interacting matter at high densities. In this proceedings contribution, I review recent efforts to systematically constrain the equation of state (EoS) of dense nuclear and quark matter using a combination of ab initio particle and nuclear physics calculations and astrophysical data. In particular, I discuss the constraints that the gravitational wave observation GW170817 h…
We demonstrate in a general and analytic way how high-density information about the equation of state (EoS) of strongly interacting matter obtained using perturbative Quantum Chromodynamics (pQCD) constrains the same EoS at densities reachable in physical neutron stars. Our approach is based on utilizing the full information of the thermodynamic potentials at the high-density limit together with thermodynamic stability and causality. This requires considering the pressure as a function of chemical potential $p(μ)$ instead of the commonly used pressure as a function of energy density $p(ε)$. Th…
The Equation of State and Quark Number Susceptibility in Hard-Dense-Loop Approximation
基于[ H. S. Zong，W. M. Sun，Phys. Rev. \textbf{D 78}，054001（2008）]，我们在硬稠密圈（HDL）近似下计算了零温有限夸克化学势下QCD的物态方程。本文将HDL近似下的状态方程与Fraga、Pisarski和Schaffner-Bielich提出的QCD冷微扰状态方程作了比较。结果表明，HDL近似下的压强一般比微扰结果小。此外，我们还计算了有限温度和有限化学势下的夸克数磁化率（QNS），并将所得结果与文献中的相应结果进行了比较.
Determining the phase structure of Quantum Chromodynamics (QCD) and its Equation of State (EOS) at densities and temperatures realized inside neutron stars and their mergers is a long-standing open problem. The holographic V-QCD framework provides a model for the EOS of dense and hot QCD, which describes the deconfinement phase transition between a dense baryonic and a quark matter phase. We use this model in fully general relativistic hydrodynamic (GRHD) simulations to study the formation of quark matter and the emitted gravitational wave signal of binary systems that are similar to the first…
Compact Stars, Heavy Ion Collisions, and Possible Lessons For QCD at Finite Densities
最近测量到的PSR J1614-2230的$1.97\pm0.04$ M $_\odot$的大中子星质量为致密物质、核物质和夸克物质的状态方程的刚度提供了一个有价值的下限。作为补充，对重离子碰撞中椭圆流的分析表明，EoS刚度存在一个上限。我们说明了这种二分法如何允许约束有效的EoS模型，否则不能明确地从第一原则的参数。
