Strongly Interacting High Baryon Density Matter
Strongly Interacting High Baryon Density Matter
McLerran, Larry↗
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Quark Matter at High Baryon Density, Conformality and Quarkyonic Matter
This paper discusses high-baryon-density quarkyonic matter in the context of recent observations concerning neutron stars and the qualitative reasons why quarkyonic matter explains certain features of the equation of state that arises from these observations. The paper then provides a qualitative discussion of the quarkyonic hypotheses, and the essential features of quarkyonic matter that explain the outstanding features of the equation of state.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Correlations of conserved quantities at finite baryon density
Correlations involving the seven conserved quantities, namely energy, baryon number, electric charge, strangeness, and the three components of momentum, give rise to correlations in heavy-ion collisions. Through the utilization of a simple one-dimensional hydrodynamic model, we calculate the evolution of the entire 7×7 matrix of correlations as a function of relative spatial rapidity. This comprehensive analysis accounts for finite baryon density, which results in off-diagonal correlations between the charge-related quantities and the energy-momentum quantities. These correlations in coordinate space are subsequently transformed into correlations in momentum space using statistical weighting. As a result, the entire matrix of correlations is revealed to be highly sensitive to the equation of state, viscosity, and diffusivity.
Equations of state of nuclear matter↗
Measurement of kaon directed flow in Au+Au collisions in the high baryon density region
Rapidity-odd directed flow v 1 measurements are presented for $K^±$ and $K^0_S$ in Au + Au collisions for $\sqrt{s_{NN}}$ from 3.0 to 3.9 GeV with the STAR experiment. For comparison, v 1 of π ± , protons, and Λ from the same collisions are also discussed. The mid-rapidity v 1 slope dv 1 /dy| y=0 for protons and Λ is positive in these collisions. On the other hand, v 1 slope of kaons exhibits a strong dependence: negative at p T < 0.6 GeV/c and positive at higher p T . A similar p T dependence is also evident for the v 1 slope of charged pions. Compared to the spectator-removed calculations in Au+Au collisions at $\sqrt{s_{NN}}$ = 3.0–3.9 GeV, the JAM model demonstrates a pronounced shift of the v 1 slopes of mesons towards the negative direction. It suggests that the shadowing effect of the spectators plays an important role in the observed kaon anti-flow at low p T in the high baryon density region of non-central collisions.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Systematics of the chemical freeze-out line in the high baryon density regime explored at SIS100
The systematic uncertainties of chemical freeze-out fits at SIS100 energies (Au+Au reactions at $\sqrt{s_{NN}}$ = 3 – 5 GeV) are studied using UrQMD simulations. Although hadron production in UrQMD does not occur on a sharp chemical freeze-out hyper-surface, the extracted fit quality is shown to be very good. The extracted chemical parameters depend on the selected hadron species as well as the underlying equation of state (EoS) of the matter. Including light nuclei and anti-protons in the fit increases the expected freeze-out temperature, while a stiffer EoS increases the obtained chemical potential. Similarly, the baryon densities extracted by the thermal fits depend on the choice of hadrons as well as the underlying equation of state. These results are important for the upcoming CBM@FAIR physics program and highlight that a degree of caution is advised when one relates the chemical freeze-out curve to features on the QCD phase diagram like the critical endpoint or a possible phase transition.
Hofmann, Emma Lilith [GSI Helmholtzzentrum für Sch↗
Chiral condensate and the equation of state at nonzero baryon density from the hadron resonance gas model with a repulsive mean field
We study the QCD equation of state and the chiral condensate using the hadron resonance gas model with repulsive mean-field interactions. We find that the repulsive interactions improve the agreement with the lattice results on the derivatives of the pressure with respect to the baryon chemical potential up to eighth order. From the temperature dependence of the chiral condensate we estimate the crossover temperature as a function of baryon chemical potential, T p c ( μ B ) . We find that the chiral crossover line starts to deviate significantly from the chemical freeze-out line already for μ B > 400 MeV . Furthermore, we find that the chiral pseudocritical line can be parametrized as T p c ( μ B ) / T p c ( 0 ) = 1 − κ 2 [ μ B / T p c ( 0 ) ] 2 − κ 4 [ μ B / T p c ( 0 ) ] 4 with κ 2 = 0.0150 ( 2 ) and κ 4 = 3.1 ( 6 ) × 10 − 5 , which are in agreement with lattice QCD results for small values of μ B . For the first time we find a tiny but nonzero value of κ 4 in our study. Published by the American Physical Society 2024
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Probing late-stage hadronic interactions at high baryon density via $K^{⁎0}$ production in the RHIC beam energy scan program
A precision measurement of the $K^{⁎0}$ meson yield is reported in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7, 11.5, 14.6, 19.6, and 27 GeV using the high-statistics data sample collected by the STAR experiment during the Beam Energy Scan II (BES-II) program at RHIC. The transeverse momentum (p T )-integrated yield ratios $\large{(}K^{⁎0} + \overline{K^{⁎0}}\large{)}/(K^+ + K^{-})$ in central collisions show a suppression relative to peripheral collisions at the (1.7–3.6) σ level, while a thermal model without final-stage rescattering overpredicts this ratio with a deviation of (6.9–8.2) σ. These results indicate a loss of the measured $K^{⁎0}$ signal in central collisions due to re-scattering of its hadronic decay products in the hadronic phase. The p T -integrated yield of charged kaons exhibits an approximate scaling with charged-particle multiplicity, independent of collision energy and system size. A similar trend is observed for the short-lived $K^{⁎0}$ resonance, although significant deviations emerge at lower energies. At BES energies, the $K^{⁎0}/K$ ratio shows stronger suppression than at the highest RHIC and LHC energies within a given multiplicity bin, particularly in central and mid-central collisions. This behavior is consistent with changes in the effective hadronic interaction cross section and is supported by transport model calculations, which indicate dominant meson–baryon interactions at lower energies and meson–meson interactions at higher energies.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Finite density QCD equation of state: Critical point and lattice-based 𝑇′ expansion
Here, we present a novel construction of the QCD equation of state (EoS) at finite baryon density. Our work combines a recently proposed resummation scheme for lattice QCD results with the universal critical behavior at the QCD critical point. This allows us to obtain a family of equations of state in the range 0 ≤ 𝜇 𝐵 ≤ 700 MeV and 25 MeV ≤ 𝑇 ≤ 800 MeV, which match lattice QCD results near 𝜇 𝐵 =0 while featuring a critical point in the 3D Ising model universality class. The position of the critical point can be chosen within the range accessible to beam-energy scan heavy-ion collision experiments. The strength of the singularity and the shape of the critical region are parametrized using a standard parameter set. We impose stability and causality constraints and discuss the available ranges of critical point parameter choices, finding that they extend beyond earlier parametric QCD EoS proposals. We present thermodynamic observables, including baryon density, pressure, entropy density, energy density, baryon susceptibility and speed of sound, that cover a wide range in the QCD phase diagram relevant for experimental exploration.
Astronomy & Astrophysics↗
Dynamical Aspects of the Quark Gluon Plasma
Shortly after the Big Bang the entire universe was filled with a nearly perfect fluid known as the Quark Gluon Plasma. Relativistic heavy ion collisions can now reproduce this fluid in the laboratory where the Quark Gluon Plasma exhibits a rapid but smooth cross-over phase transition into hadrons at vanishing net-baryon densities. Recent experiments plan to explore finite baryon densities where a critical point is expected. If found, this would mark the first discovery of a critical point in a relativistic system described by a fundamental theory of nature, which would have far-reaching consequences for high-energy nuclear physics and nuclear astrophysics (such as in neutron star mergers). Characteristic temperatures of equilibrium (e.g. the inflection point of the entropy density) and transport coefficients (e.g. minimum of the shear viscosity over entropy density) vary widely at a cross-over phase transition but converge at a critical point, and extracting the behavior of these characteristic temperatures is a major focal point of this research. Specifically, the interplay between strange and light hadrons is exploited to study the flavor hierarchy in the cross-over region. To investigate this, a viscous relativistic hydrodynamics framework with two conserved charges is being developed into a new open-source code along with initial conditions that contain baryon number and strangeness. Flow observables sensitive to the equation of state and transport coefficients are calculated across beam energies. New techniques are being developed to study this flavor hierarchy from first principles and to extract the characteristic temperatures from experimental data. Through this new dynamical framework, this project provides essential guidance to the Beam Energy Scan II runs at Relativistic Heavy-Ion Collider and the future Facility for Antiproton and Ion Research facility in the search for the Quantum Chromodynamic critical point and subsequent investigation of the baryon-rich Quark Gluon Plasma.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Hot QCD phase diagram from holographic Einstein–Maxwell–Dilaton models
In this review, we provide an up-to-date account of quantitative holographic descriptions of the strongly coupled quark-gluon plasma (QGP) produced in heavy-ion collisions, based on the class of gauge-gravity Einstein-Maxwell-Dilaton (EMD) models. Holography is employed to tentatively map the QCD phase diagram at finite temperature onto a dual theory of charged, asymptotically AdS black holes in 5D. With a quantitative focus on the hot QCD phase diagram, the EMD models reviewed are adjusted to describe lattice results for the finite-temperature QCD equation of state, with 2+1 flavors and physical quark masses, at zero chemical potential and vanishing electromagnetic fields. The predictive power of EMD models is tested by quantitatively comparing their predictions for the hot QCD equation of state at nonzero baryon density and the corresponding state-of-the-art lattice QCD results. The shear and bulk viscosities predicted by these EMD models are also compared to the corresponding profiles favored by the latest phenomenological multistage models describing different heavy-ion data. We report preliminary results from a Bayesian analysis which provide systematic evidence that lattice results at finite temperature and zero baryon density strongly constrains the free parameters of EMD models. Remarkably, the set of parameters constrained by lattice results at zero chemical potential produces EMD models in quantitative agreement with lattice QCD results also at finite baryon density. We also review results for equilibrium and transport properties from magnetic EMD models, describing the QGP at finite temperatures and magnetic fields. Lastly, we provide a critical assessment of the main limitations and drawbacks of the holographic models reviewed in the present work, and point out some perspectives we believe are of fundamental importance for future developments.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Microscopic constraints for the equation of state and structure of neutron stars: A Bayesian model mixing framework
Bayesian model mixing (BMM) is a statistical technique that can combine constraints from different regions of an input space in a principled way. Here we extend our BMM framework for the equation of state (EOS) of strongly interacting matter from symmetric nuclear matter to asymmetric matter, specifically focusing on zero-temperature, charge-neutral, 𝛽-equilibrated matter. We use Gaussian processes (GPs) to infer constraints on the neutron-star matter EOS at intermediate densities from two different microscopic theories: chiral effective-field theory (𝜒EFT) at baryon densities around nuclear saturation, 𝑛 𝐵 ∼ 𝑛 0 , and perturbative QCD at asymptotically high baryon densities, 𝑛 𝐵 ⩾ 20𝑛 0 . The uncertainties of the 𝜒EFT and pQCD EOSs are obtained using the BUQEYE truncation error model. We demonstrate the flexibility of our framework through the use of two categories of GP kernels: conventional stationary kernels and a nonstationary changepoint kernel. We use the latter to explore potential constraints on the dense matter EOS by including exogenous data representing theory predictions and heavy-ion collision measurements at densities ⩾ 2𝑛 0 . We also use our EOSs to obtain neutron-star mass-radius relations and their uncertainties. Finally, our framework, whose implementation will be available through a GitHub repository, provides a prior distribution for the EOS that can be used in large-scale neutron-star inference frameworks.
Bayesian methods↗
The Challenge of Observing Patchy Reionization with CMB Optical-Depth Fluctuations
Spatial fluctuations in the Thomson optical depth encode information about the inhomogeneous nature of cosmic reionization. We compute the optical-depth angular power spectrum, $C_\ell^{ττ}$, using past lightcones constructed from five Cosmic Reionization on Computers (CROC) radiation-hydrodynamical simulations. By decomposing the electron-density field into patchy and density components, we quantify the separate contributions of ionization-fraction and baryon-density fluctuations to the optical-depth anisotropy. Because the simulations end at $z\approx5$, we supplement the reionization-era signal with an analytic estimate of the fully ionized low-redshift contribution. We find that baryon-density fluctuations dominate the high-redshift signal over most angular scales, while the accumulated low-redshift contribution exceeds the high-redshift signal across the full multipole range considered. Our results demonstrate that a significant fraction of the optical-depth power is not uniquely associated with reionization morphology, implying that future interpretations of $C_\ell^{ττ}$ must account for the density contribution in addition to patchy ionization.
Takoudes, Nick [Chicago U., Astron. Astrophys. Ctr↗
Lattice quantum chromodynamics at large isospin density
We present an algorithm to compute correlation functions for systems with the quantum numbers of many identical mesons from lattice quantum chromodynamics (QCD). The algorithm is numerically stable and allows for the computation of n-pion correlation functions for n ϵ {1, … , N} using a single N × N matrix decomposition, improving on previous algorithms. We apply the algorithm to calculations of correlation functions with up to 6144 charged pions using two ensembles of gauge field configurations generated with quark masses corresponding to a pion mass m π = 170 MeV and spacetime volumes of (4.4 3 × 8.8) fm 4 and (5.8 3 × 11.6) fm 4 . We also discuss statistical techniques for the analysis of such systems, in which the correlation functions vary over many orders of magnitude. In particular, we observe that the many-pion correlation functions are well-approximated by log-normal distributions, allowing the extraction of the energies of these systems. Using these energies, the large-isospin-density, zero-baryon-density region of the QCD phase diagram is explored. A peak is observed in the energy density at an isospin chemical potential μ I ~ 1.5m π , signaling the transition into a Bose-Einstein condensed phase. The isentropic speed of sound, c s , in the medium is seen to exceed the ideal-gas (conformal) limit ($c^{2}_{s} ≤ 1/3)$ over a wide range of chemical potential before falling towards the asymptotic expectation at μ I ~ 15m π . These, and other thermodynamic observables, indicate that the isospin chemical potential must be large for the system to be well described by an ideal gas or perturbative QCD.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Sensitivity of Au + Au collisions to the symmetric nuclear matter equation of state at 2–5 nuclear saturation densities
We demonstrate that proton and pion flow measurements in heavy-ion collisions at incident energies ranging from 1 to 20 GeV per nucleon in the fixed target frame can be used for an accurate determination of the symmetric nuclear matter equation of state at baryon densities equal 2–4 times nuclear saturation density n 0 . We simulate Au + Au collisions at these energies using a hadronic transport model with an adjustable vector mean-field potential dependent on baryon density n B . Here, we show that the mean field can be parametrized to reproduce a given density dependence of the speed of sound at zero temperature $c$$^{2}_{s}$ (n B , T = 0), which we vary independently in multiple density intervals to probe the differential sensitivity of heavy-ion observables to the equation of state at these specific densities. Recent flow data from the STAR experiment at the center-of-mass energies √ s NN = {3.0, 4.5} GeV can be described by our model, and a Bayesian analysis of these data indicates a hard equation of state at n B ϵ (2, 3)n 0 and a possible phase transition at n B ϵ (3, 4)n 0 . More data at √ s NN = 2–5 GeV, as well as a more thorough analysis of the model systematic uncertainties will be necessary for a more precise conclusion.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Fundamental physics with ESPRESSO: a new determination of the D/H ratio towards PKS1937-101
ABSTRACT Primordial abundances of light elements are sensitive to the physics of the early Universe and can directly constrain cosmological quantities, such as the baryon-to-photon ratio $\eta _{10}$, the baryon density, and the number of neutrino families. Deuterium is especially suited for these studies: its primordial abundance is sensitive and monotonically dependent on $\eta _{10}$, allowing an independent measurement of the cosmic baryon density that can be compared, for instance, against the Planck satellite data. The primordial deuterium abundance can be measured in high H i column density absorption systems towards distant quasars. We report here a new measurement, based on high-resolution ESPRESSO data, of the primordial D i abundance of a system at redshift $z \sim 3.572$, towards PKS1937-101. Using only ESPRESSO data, we find a D /H ratio of $2.638\pm 10^{-5}$, while including the available UVES data improves the precision, leading to a ratio of $2.608 \pm 10^{-5}$. The results of this analysis agree with those of the most precise existing measurements. We find that the relatively low column density of this system ($\log {N_{\rm H_I}/ {\rm cm}^{-2}}\sim 18$) introduces modelling uncertainties, which become the main contributor to the error budget.
Guarneri, Francesco (ORCID:0000000347409762)↗
Illuminating early-stage dynamics of heavy-ion collisions through photons at RHIC BES energies
Heavy-ion collisions at $\sqrt {^SNN}$~10 GeV probe the QCD phase diagram at large baryon densities. Because the longitudinal Lorentz contraction is small at these collision energies, understanding the dynamics during the early phase of the collision is essential for the subsequent modeling of the system evolution and for constraining the QGP transport properties at finite baryon densities. Direct photons provide undistorted information on early-stage dynamics. We model relativistic heavy-ion collisions at RHIC Beam Energy Scan energies with a hybrid dynamical approach consisting of a 3D-Glauber initial state followed by viscous hydrodynamics and hadronic transport (MUSIC + UrQMD). The implemented thermal photon emission takes into account the enhancement from finite baryon chemical potentials. We show that direct photon spectra and their anisotropic flow coefficients have a strong sensitivity to the early stage of heavy-ion collisions. Thus, they provide constraints on QGP dynamics complementary to those obtained from hadronic observables.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Composite octet baryons in a relativistic mean field description of nuclear and neutron star matter
Here, we examine the properties of composite octet baryons in the nuclear medium and neutron-star matter. The internal quark-diquark structure of the octet baryons and the equations of state of nuclear matter and neutron-star matter in the mean field approximation are described by using the three-flavor Nambu-Jona-Lasinio (NJL) model as an effective quark theory of quantum chromodynamics. After introducing our model, we first discuss the properties of single baryons and their effective meson exchange interactions in symmetric nuclear matter by using concepts of Fermi-liquid theory. Several model-independent implications of this description are derived and illustrated by numerical results obtained in our model. Second, we extend the model description to high baryon densities and investigate the equation of state of neutron-star matter and the resulting star masses. We find that the so-called hyperon puzzle persists also for the case of composite hadrons. To get more information on this point, we also investigate the role of 6-Fermi and 8-Fermi interactions, in addition to the standard 4-Fermi interactions. The strengths of those higher-order Fermi interactions is determined so as not to spoil the saturation properties of nuclear matter. Among them, an interaction characterized by a product of four-quark current operators plays a special role to stabilize the stars over a large region of central baryon densities, although it has little effect on the maximum star masses.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗