High energy heavy-ion collisions in laboratory produce a form of matter that can test Quantum Chromodynamics (QCD), the theory of strong interactions, at high temperatures. One of the exciting possibilities is the existence of thermodynamically distinct states of QCD, particularly a phase of de-confined quarks and gluons. An important step in establishing this new state of QCD is to demonstrate that the system has attained thermal equilibrium. We present a test of thermal equilibrium by checking that the mean hadron yields produced in the small impact parameter collisions as well as grand canonical fluctuations of conserved quantities give consistent temperature and baryon chemical potential for the last scattering surface. This consistency for moments up to third order of the net-baryon number, charge, and strangeness is a key step in the proof that the QCD matter produced in heavy-ion collision attains thermal equilibrium. It is a clear indication for the first time, using fluctuation observables, that a femto-scale system attains thermalization. The study also indicates that the relaxation time scales for the system are comparable to or smaller than the life time of the fireball.
If the interaction rates between the visible and the dark sectors were never strong enough, the observed dark matter relic abundance could have been produced in the early Universe by non-thermal processes. This is what occurs in the so-called freeze-in mechanism. In the simplest version of the freeze-in paradigm, after dark matter is produced from the standard model thermal bath, its abundance is frozen and remains constant. However, thermalization and number-changing processes in the dark sector can have strong impacts, in particular enhancing the dark matter relic abundance by several orders…
The deconfinement transition and the hadronization mechanism at high energy are related to the quark-antiquark string breaking and the corresponding temperature depends on the string tension $σ$. In the Unruh scheme of hadron production it turns out $T = \sqrt{σ/2π}$, with $σ\simeq \E$, the vacuum energy density. In heavy ion collisions at lower energy, i.e. large baryonchemical potential, $μ_B$, the dynamics is dominated by Fermi statistics and baryon repulsion. However one can still consider $\E$ as the relevant physical scale and its evaluation as a function of the baryon density, in a nucl…
Thermal models are commonly used to interpret heavy-ion data on particle yields and spectra and to extract the conditions of chemical and thermal freeze-out in heavy-ion collisions. I discuss the usefulness and limitations of such thermal model analyses and review the experimental and theoretical evidence for thermalization in nuclear collisions. The crucial role of correlating strangeness production data with single particle spectra and two-particle correlation measurements is pointed out. A consistent dynamical picture for the heavy-ion data from the CERN SPS involves an initial prehadronic …
We investigate the form of the viscous correction to the equilibrium distribution function in the context of a Cooper-Frye freeze out prescription for viscous hydrodynamic simulations of relativistic heavy ion collisions. The standard quadratic ansatz used by all groups for the case of shear viscosity is found to be disfavored by experimental data for v4/(v2)^2 at the Relativistic Heavy Ion Collider, and is unlikely to be correct for the hadron resonance gas present at freeze out. Instead, data for v2(pt) along with v4/(v2)^2 favor a momentum dependence between linear and quadratic.
WIMP-like Dark Matter Without Thermalization At Freeze-Out
University of Wisconsin, Madison（威斯康星大学麦迪逊分校）；Wisconsin IceCube Particle Astrophysics Center (WIPAC), University of Wisconsin, Madison（威斯康星冰立方粒子天体物理中心，威斯康星大学麦迪逊分校）；Fermi National Accelerator Laboratory（费米国家加速器实验室）；Kavli Institute for Cosmological Physics, University of Chicago（芝加哥大学卡弗里宇宙物理学研究所）；Department of Astronomy and Astrophysics, University of Chicago（芝加哥大学天文与天体物理系）；Texas Center for Cosmology and Astroparticle Physics, Weinberg Institute for Theoretical Physics, Department of Physics, The University of Texas at Austin（德克萨斯大学奥斯汀分校物理系温伯格理论物理研究所宇宙线与高能天体物理中心）
The directed flow of particles emitted from the fireball created in a heavy-ion collision is shown to be a very sensitive measure of the pressure equilibration in the first 1 fm/c of the evolution. Performing a 3+1 dimensional relativistic hydrodynamic calculation with nonequilibrated longitudinal and transverse pressures, we show that the directed flow is strongly reduced if the pressure imbalance survives for even a short time. Transverse momentum spectra, elliptic flow and interferometry correlation radii are not very sensitive to this early pressure anisotropy. Comparison with the data poi…
We introduce a novel approach based on elastic and inelastic scattering rates to extract the hyper-surface of the chemical freeze-out from a hadronic transport model in the energy range from E$_\mathrm{lab}=1.23$ AGeV to $\sqrt{s_\mathrm{NN}}=62.4$ GeV. For this study, the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model combined with a coarse-graining method is employed. The chemical freeze-out distribution is reconstructed from the pions through several decay and re-formation chains involving resonances and taking into account inelastic, pseudo-elastic and string excitation reacti…
We estimate the ratio of the thermalization time over the freeze-out time using a holographic AdS-Vaidya model for quark-gluon plasma formed in the heavy ion collisions. In the model the process of thermalization is described as formation of the black hole in AdS space while dethermalization process, related with the freeze-out, as the black hole evaporation due to the Hawking radiation that is modeled by the Vaidya metric with a negative mass. In this model the thermalization takes place only at small scales and absent in the infrared region. At small scales the system tends towards a state o…
We investigate the effect of early chemical freeze-out on radial flow, elliptic flow and HBT radii by using a fully three dimensional hydrodynamic model. When we take account of the early chemical freeze-out, the space-time evolution of temperature in the hadron phase is considerably different from the conventional model in which chemical equilibrium is always assumed. As a result, we find that radial and elliptic flows are suppressed and that the lifetime and the spatial size of the fluid are reduced. We analyze the p_t spectrum, the differential elliptic flow, and the HBT radii at the RHIC e…
The space-time structure of the multipion system created in central relativistic heavy-ion collisions is investigated. Using the microscopic transport model UrQMD we determine the freeze-out hypersurface from equation on pion density n(t,r)=n_c. It turns out that for proper value of the critical energy density ε_c equation ε(t,r)=ε_c gives the same freeze-out hypersurface. It is shown that for big enough collision energies E_kin > 40A GeV/c (sqrt(s) > 8A GeV/c) the multipion system at a time moment τ ceases to be one connected unit but splits up into two separate spatial parts (drops), which m…
A finite unbound system which is equilibrium in one reference frame is in general nonequilibrium in another frame. This is a consequence of the relative character of the time synchronization in the relativistic physics. This puzzle was a prime motivation of the Cooper--Frye approach to the freeze-out in relativistic hydrodynamics. Solution of the puzzle reveals that the Cooper--Frye recipe is far not a unique phenomenological method that meets requirements of energy-momentum conservation. Alternative freeze-out recipes are considered and discussed.
We present calculations of the chemical freeze-out temperature (T_ch) based on particle yields from STAR and ALICE measured at collision energies ranging from sqrt{s_{NN}} = 11.5 GeV to 5.02 TeV. Employing the Grand Canonical Ensemble approach using the Thermal-FIST Hadron Resonance Gas model package, we show evidence for a flavour-dependent chemical freeze-out in the crossover region of the QCD phase diagram. At a vanishing baryochemical potential, we calculate light and strange flavour freeze-out temperatures T_L = 150.2 +- 2.6 MeV and T_S = 165.1 +- 2.7 MeV, respectively.
We confront the hypothesis of chemical freeze-out in ultra-relativistic heavy-ion collisions with the hypothesis of large modifications of hadron masses in nuclear medium. We find that the thermal-model predictions for the ratios of particle multiplicities are sensitive to the values of in-medium hadronic masses. In particular, the $π^+/p$ ratio decreases by 35% when the masses of all hadrons (except for pseudo-Goldstone bosons) are scaled down by 30%.
We address the issue of the degree of equilibrium achieved in a high energy heavy-ion collision. Specifically, we explore the consequences of incomplete strangeness chemical equilibrium. This is achieved over a volume V of the order of the strangeness correlation length and is assumed to be smaller than the freeze-out volume. Probability distributions of strange hadrons emanating from the system are computed for varying sizes of V and simple experimental observables based on these are proposed. Measurements of such observables may be used to estimate V and as a result the degree of strangeness…
Using the UrQMD/coarse graining approach we explore the kinetic freeze-out stage in central Au + Au collisions at various energies. These studies allow us to obtain detailed information on the thermodynamic properties (e.g. temperature and chemical potential) of the system during the kinetic decoupling stage. We explore five relevant collision energies in detail, ranging from $\sqrt{s_{NN}}=2.4\,\mathrm{GeV}$ (GSI-SIS) to $\sqrt{s_{NN}}=200\,\mathrm{GeV}$ (RHIC). By adopting a standard Hadron Resonance Gas equation of state, we determine the average temperature $\langle T \rangle$ and the aver…
We compute by numerical integration of the Dirac equation the number of quark-antiquark pairs initially produced in the classical color fields of colliding ultrarelativistic nuclei. While the number of qqbar pairs is parametrically suppressed in the coupling constant, we find that in this classical field model their production rate is comparable to the thermal ratio of gluons/pairs = 9 N_f/32. After isotropization one thus would have quark-gluon plasma in chemical equilibrium.
We analyze hadrochemical freeze-out in central Pb+Pb collisions at CERN SPS energies, employing the hybrid version of the Ultrarelativistic Quantum Molecular Dynamics model, which describes the transition from a hydrodynamic stage to hadrons by the Cooper-Frye mechanism, and matches to a final hadron-resonance cascade. We fit the results both before and after the cascade stage using the Statistical Model, to assess the effect of the cascade phase. We observe a strong effect on antibaryon yields except anti-Omega, resulting in a shift in T and mu_B of the freeze-out curve. We discuss indication…
A system size scan program was recently proposed for the STAR experiments at the Relativistic Heavy Ion Collider(RHIC). In this study, we employ a multiphase transport (AMPT) model for considering the bulk properties at the freeze-out stage for $\mathrm{^{10}B+^{10}B}$, $\mathrm{^{12}C+^{12}C}$, $\mathrm{^{16}O+^{16}O}$, $\mathrm{^{20}Ne+^{20}Ne}$, $\mathrm{^{40}Ca+^{40}Ca}$, $\mathrm{^{96}Zr+^{96}Zr}$, and $\mathrm{^{197}Au+^{197}Au}$ collisions at RHIC energies $\sqrt{s_{NN}}$ of 200, 20, and 7.7 GeV. The results for $\mathrm{^{197}Au+^{197}Au}$ collisions are comparable with those of previo…
Global evolution of the matter in relativistic collisions of heavy nuclei and the resulting global freeze-out parameters are analyzed in a wide range of incident energies 2.7 GeV $\le \sqrt{s_{NN}}\le$ 39 GeV. The analysis is performed within the three-fluid model employing three different equations of state (EoS): a purely hadronic EoS, an EoS with the first-order phase transition and that with a smooth crossover transition. Global freeze-out parameters deduced from experimental data within the statistical model are well reproduced within the crossover scenario. The 1st-order-transition scena…
We introduce a combined macroscopic/microscopic transport approach employing relativistic hydrodynamics for the early, dense, deconfined stage of the reaction and a microscopic non-equilibrium model for the later hadronic stage where the equilibrium assumptions are not valid anymore. Within this approach we study the dynamics of hot, bulk QCD matter, which is expected to be created in ultra-relativistic heavy ion collisions at the SPS, the RHIC and the LHC. Our approach is capable of self-consistently calculating the freeze-out of the hadronic system, while accounting for the collective flow o…
We study production of scalar dark matter via the freeze--in mechanism in the relativistic regime, focussing on the simplest Higgs portal model. We derive the corresponding relativistic reaction rates based on the Bose--Einstein statistics taking into account the thermal mass effects as well as the change in the Higgs degrees of freedom at the electroweak phase transition. The consequent constraints on the Higgs portal coupling are obtained.
We use the framework of relativistic and non-relativistic conformal field theories (CFT) to derive general results relevant for the production of weakly coupled and strongly coupled dark sectors through thermal interactions. Our result reproduce trivially known formulas for $2\to n $ processes and extend to general $m\to n$ processes as well as interacting dark sectors. As concrete examples we consider freeze-in of a relativistic CFT coupled to the SM with contact interactions and derive Sommerfeld enhancement of non-relativistic cross-sections from the theory of fermions at unitarity.
We investigate an effective relativistic equation of state at finite values of temperature and baryon chemical potential with the inclusion of the full octet of baryons, the Delta-isobars and the lightest pseudoscalar and vector meson degrees of freedom. These last particles have been introduced within a phenomenological approach by taking into account of an effective chemical potential and mass depending on the self-consistent interaction between baryons. In this framework, we study of the hadron yield ratios measured in central heavy ion collisions over a broad energy range and present the b…
We introduce a new scenario for heavy ion collisions that could solve the lingering problems associated with the so-called HBT puzzle. We postulate that the system starts expansion as the perfect quark-gluon fluid but close to freeze-out it splits into clusters, due to a sharp rise of bulk viscosity in the vicinity of the hadronization transition. We then argue that the characteristic cluster size is determined by the viscosity coefficient and the expansion rate. Typically it is much smaller and independent of the total system volume. These clusters maintain the pre-existing outward-going flow…
The production and the observability of $Λ(1520)$, $K^0(892)$ $Φ$ and $Δ(1232)$ hadron resonances in central Pb+Pb collisions at 160 AGeV is addressed. The rescattering probabilities of the resonance decay products in the systems evolution are studied. Strong changes in the reconstructable particle yields and spectra between chemical and thermal freeze-out are estimated. Abundances and spectra of reconstructable resonances are predicted.
Rapid thermalization in ultra-relativistic heavy-ion collisions leads to fast changing potential between a heavy quark and antiquark from zero temperature potential to the finite temperature one. Time dependent perturbation theory can then be used to calculate the survival probability of the initial quarkonium state. In view of very short time scales of thermalization at RHIC and LHC energies, we calculate the survival probability of $J/ψ$ and $Υ$ using sudden approximation. Our results show that quarkonium decay may be significant even when temperature of QGP remains low enough so that the co…
The LHC data on event-by-event harmonic flow coefficients measured in PbPb collisions at center-of-mass energy 2.76 TeV per nucleon pair are analyzed and interpreted within the HYDJET++ model. To compare the model results with the experimental data the unfolding procedure is employed. The essentially dynamical origin of the flow fluctuations in hydro-inspired freeze-out approach has been established. It is shown that the simple modification of the model via introducing the distribution over spatial anisotropy parameters permits HYDJET++ to reproduce both elliptic and triangular flow fluctuatio…
The strong longitudinal expansion of the reaction zone formed in relativistic heavy-ion collisions is found to significantly reduce the spatially averaged pion phase-space density, compared to naive estimates based on thermal distributions. This has important implications for data interpretation and leads to larger values for the extracted pion chemical potential at kinetic freeze-out.
The freeze-out conditions in the light (S+S) and heavy (Pb+Pb) colliding systems of heavy nuclei at 160 AGeV/$c$ are analyzed within the microscopic Quark Gluon String Model (QGSM). We found that even for the most heavy systems particle emission takes place from the whole space-time domain available for the system evolution, but not from the thin ''freeze-out hypersurface", adopted in fluid dynamical models. Pions are continuously emitted from the whole volume of the reaction and reflect the main trends of the system evolution. Nucleons in Pb+Pb collisions initially come from the surface regio…
We report the excitation energy dependence of specific heat (\cv) of hadronic matter at freeze-out in Au+Au and Cu+Cu collisions at the Relativistic Heavy Ion Collider energies by analyzing the published data on event-by-event mean transverse momentum (\meanpt) distributions. The \meanpt~distributions in finite \pt~ranges are converted to distributions of effective temperatures, and dynamical fluctuations in temperature are extracted by subtracting widths of the corresponding mixed event distributions. The heat capacity per particle at the kinetic freeze-out surface is presented as a function …
A brief review is presented of the status of the thermal model and chemical freeze-out in relativistic heavy-ion collisions. Some interewsting aspects at lower energies are emphasized.
The non-uniform longitudinal flow model (NUFM) propsed recently is extended to include also transverse flow. The resulting longitudinally non-uniform collective expansion model (NUCEM) is applied to the calculation of rapidity distribution of kaons, lambdas and protons in relativistic heavy ion collisions at CERN-SPS energies. The model results are compared with the 200 A GeV/$c$ S-S and 158 A GeV/$c$ Pb-Pb collision data. The central dips observed in experiments are reproduced in a natural way.
The early thermalization and HBT puzzles in relativistic heavy-ion collisions studied at RHIC are shortly reviewed. The results of recent hydrodynamic calculations that shed light on these two intriguing issues are presented. In particular, the role of the elliptic flow as a signature of early thermalization is critically examined.
We analyze the transverse momentum distribution of $J/ψ$ mesons produced in Au + Au collisions at the top RHIC energy within a blast-wave model that accounts for a possible inhomogeneity of the charmonium distribution and/or flow fluctuations. The results imply that the transverse momentum spectra of$J/ψ$, $ϕ$ and $Ω$ hadrons measured at the RHIC can be described well if kinetic freeze-out takes place just after chemical freeze-out for these particles.
We investigate chemical and thermal freeze-out time dependencies for strange particle production for CERN SPS heavy ion collisions in the framework of a dynamical hadronic transport code. We show that the Lambda yield changes considerably after hadronization in the case of Pb+Pb collisions, whereas for smaller system sizes (e.g. S+S) the direct particle production dominates over production from inelastic rescattering. Chemical freeze-out times for strange baryons in Pb+Pb are smaller than for non-strange baryons, but they are still sufficiently long for hadronic rescattering to contribute sign…
Hydrodynamic description requires a local thermodynamic equilibrium of the system under study but an approximate hydrodynamic behaviour is already manifested when a momentum distribution of liquid components is not of equilibrium form but merely isotropic. While the process of equilibration is relatively slow, the parton system becomes isotropic rather fast due to the plasma instabilities. Azimuthal fluctuations observed in relativistic heavy-ion collisions are argued to distinguish between a fully equilibrated and only isotropic parton system produced in the collision early stage.
The freeze-out of hot and dense hadronic matter formed in relativistic nuclear collisions is probed by HBT interferometry of identical pions, kaons, etc. Coulomb repulsion/attraction of positive/negative particles show up at small particle momenta and is also very sensitive to the freeze-out conditions. The source sizes and times freeze-out are extracted from $π^-/π^+$ spectra and HBT radii and compared.
We show that the measured yield ratio $^3_Λ$H/$^3$He ($^3_{\overlineΛ}\overline{\text{H}}$/$^3\overline{\text{He}}$) in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV can be understood within a covariant coalescence model if (anti-)$Λ$ particles freeze out earlier than (anti-)nucleons but their relative freezeout time is closer at $\sqrt{s_{NN}}=2.76$ TeV than at $\sqrt{s_{NN}}=200$ GeV. The earlier (anti-)$Λ$ freezeout can significantly enhance the yield of (anti)hypernucleus $^4_Λ$H ($^4_{\overlineΛ}\overline{\text{H}}$), leading to that $^4_{…
Comment on "Evaluation of kinetic freeze-out properties in different relativistic heavy-ion collision systems at \sqrtsNN = 200 GeV'' (Eur. Phys. J. Plus (2025) 140:179) https://doi.org/10.1140/epjp/s13360-025-06119-0
We carry out hydrodynamical simulation of the evolution of fluid in relativistic heavy-ion collisions with random initial fluctuations. The time evolution of power spectrum of momentum anisotropies shows very strong correspondence with the physics of cosmic microwave anisotropies as was earlier predicted by some of us. In particular our results demonstrate suppression of superhorizon fluctuations and the correspondence between the location of the first peak in the power spectrum of momentum anisotropies and the length scale of fluctuations and expected freezeout time scale (more precisely, the…
Elastic scattering of charm (c) and bottom (b) quarks via D- and B-meson resonance states in an expanding, strongly interacting quark-gluon plasma is investigated. Drag and diffusion coefficients are calculated from an effective model based on chiral symmetry and heavy-quark effective theory, and utilized in a relativistic Langevin simulation to obtain transverse-momentum spectra and elliptic flow (v_2) of c- and b-quarks. The hadronization to D- and B-mesons is described by coalescence and fragmentation, and the resulting decay-electron spectra are compared to recent RHIC data.
Transverse-mass spectra, their inverse slopes and mean transverse masses in relativistic collisions of heavy nuclei are analyzed in a wide range of incident energies 2.7 GeV $\le \sqrt{s_{NN}}\le$ 39 GeV. The analysis is performed within the three-fluid model employing three different equations of state (EoS's): a purely hadronic EoS, an EoS with the first-order phase transition and that with a smooth crossover transition into deconfined state. Calculations show that inverse slopes and mean transverse masses of all the species (with the exception of antibaryons within the hadronic scenario) ex…
We explore relativistic freeze-in production of scalar dark matter in gauged $B-L$ model, where we focus on the production of dark matter from the decay and annihilation of Standard Model (SM) and $B-L$ Higgs bosons. We consider the Bose-Einstein (BE) and Fermi-Dirac (FD) statistics, along with the thermal mass correction of the SM Higgs boson in our analysis. We show that in addition to the SM Higgs boson, the annihilation and decay of the $B-L$ scalar can also contribute substantially to the dark matter relic density. Potential effects of electroweak symmetry breaking (EWSB) and thermal mass…
We have developed a fast Monte Carlo procedure of hadron generation allowing one to study and analyze various observables for stable hadrons and hadron resonances produced in ultra-relativistic heavy ion collisions. Particle multiplicities are determined based on the concept of chemical freeze-out. Particles can be generated on the chemical or thermal freeze-out hypersurface represented by a parameterization or a numerical solution of relativistic hydrodynamics with given initial conditions and equation of state. Besides standard space-like sectors associated with the volume decay, the hypersu…
Despite the fact that a system created in relativistic heavy ion collisions is an isolated quantum system, which cannot increase its entropy in the course of unitary quantum evolution, hydrodynamical analysis of experimental data seems to indicate that the matter formed in the collisions is thermalized very quickly. Based on common consideration of hydrodynamics as an effective theory in the domain of slow- and long-length modes, we discuss the physical mechanisms responsible for the decoherence and emergence of the hydrodynamic behavior in such collisions, and demonstrate how such physical me…
Kinetic equations are used to study thermalization of the anisotropic quark-gluon plasma produced by decays of color flux tubes possibly created at the very early stages of relativistic heavy-ion collisions. The decay rates of the initial color tubes are given by the Schwinger formula, while the collision terms are taken in the relaxation-time approximation. By connecting the relaxation time with viscosity we analyze production and thermalization processes in the plasma characterized by different values of the ratio of the shear viscosity to entropy density.
We present a detailed study of chemical freeze-out in p-p, C-C, Si-Si and Pb-Pb collisions at beam momenta of 158A GeV as well as Pb-Pb collisions at beam momenta of 20A, 30A, 40A and 80A GeV. By analyzing hadronic multiplicities within the statistical hadronization model, we have studied the parameters of the source as a function of the number of the participating nucleons and the beam energy. We observe a nice smooth behaviour of temperature, baryon chemical potential and strangeness under-saturation parameter as a function of energy and nucleus size. Interpolating formulas are provided whic…
A new thermalization scenario for heavy ion collisions is discussed. It is based on the Hawking--Unruh effect: an observer moving with an acceleration $a$ experiences the influence of a thermal bath with an effective temperature $T = a / 2π$, similar to the one present in the vicinity of a black hole horizon. In the case of heavy ion collisions, the acceleration is caused by a pulse of chromo--electric field $E \sim Q_s^2/g$ ($Q_s$ is the saturation scale, and $g$ is the strong coupling), the typical acceleration is $a \sim Q_s$, and the heat bath temperature is $T \simeq Q_s / 2π\sim 200$ MeV…
Bose-Einstein correlations in relativistic heavy ion collisions are examined in a general model containing the essential features of hydrodynamical, cascade as well as other models commonly employed for describing the particle freeze-out. In particular the effects of longitudinal and transverse expansion, emission from surfaces moving in time, the thickness of the emitting layer varying from surface to volume emission and other effects are studied. Model dependences of freeze-out sizes and times are discussed and compared to recent $Pb+Pb$ data at 160A$\cdot$GeV.
We analyze the transverse momentum spectra of charged pions measured in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV using the Tsallis distribution modified to include transverse flow. All the spectra are well described by the modified Tsallis distribution in an extended transverse momentum range upto 6 GeV/$c$. The kinetic freeze-out temperature ($T$), average transverse flow ($β$) and degree of non thermalization ($q$) are obtained as a function of system size for both the energies. With increasing system size $β$ shows increasing trend …
