Saturation of $E_T/N_{ch}$ and Freeze-Out Criteria in Heavy-Ion Collisions
J. Cleymans, R. Sahoo, D. P. Mahapatra, D K Srivastava, S. Wheaton
备注：
7 pages, 3 figures, ORAL presentation in 20th International Conference on Ultrarelativistic Nucleus-Nucleus Collisions: Quark Matter 2008 (QM 2008), Jaipur, India, 4-10 Feb. 2008. To appear in Journal of Phys. G: Nucl. Part. Phys
The pseudorapidity densities of transverse energy, the charged particle multiplicity and their ratios, $E_T/N_{ch}$, are estimated at mid-rapidity, in a statistical-thermal model based on chemical freeze-out criteria, for a wide range of energies from GSI-AGS-SPS to RHIC. It has been observed that in nucleus-nucleus collisions, $E_T/N_{ch}$ increases rapidly with beam energy and remains approximately constant at about a value of 800 MeV for beam energies from SPS to RHIC. $E_T/N_{ch}$ has been observed to be almost independent of centrality at all measured energies. The statistical-thermal model describes the energy dependence as well as the centrality independence, qualitatively well. The values of $E_T/N_{ch}$ are related to the chemical freeze-out criterium, $E/N \approx 1 GeV$ valid for primordial hadrons. We have studied the variation of the average mass $(<MASS>), N_{decays}/N_{primordial}, N_{ch}/N_{decays}$ and $E_T/N_{ch}$ with $\sqrt{s_{NN}}$ for all freeze-out criteria discussed in literature. These observables show saturation around SPS and higher $\sqrt{s_{NN}}$, like the chemical freeze-out temperature ($T_{ch}$).
For beam energies from SPS to RHIC, the transverse energy per charged particle, $E_T/N_{\textrm{ch}}$, saturates at a value of approximately 0.8 GeV. A direct connection between this value and the freeze-out criterium $E/N \approx 1$ GeV for the primordial energy and particle number in the hadronic resonance gas model is established.
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…
In relativistic nucleus-nucleus collisions the transverse energy per charged particle, E_T/N_ch, increases rapidly with beam energy and remains approximately constant at about 800 MeV for beam energies from SPS to RHIC. It is shown that the hadron resonance gas model describes the energy dependence, as well as the lack of centrality dependence, qualitatively. The values of E_T/N_ch are related to the chemical freeze-out criterium E/N about 1 GeV valid for primordial hadrons.
In hydrodynamical modelling of ultrarelativistic heavy-ion collisions the freeze-out is typically assumed to take place on a surface of constant temperature or energy density. In this work we apply a dynamical freeze-out criterion, which compares the hydrodynamical expansion rate with the pion scattering rate, to an event-by-event ideal hydrodynamics at the full RHIC collision energy. We present hadron spectra and elliptic flow calculated using (2+1)-dimensional ideal hydrodynamics, and show the differences between constant temperature and dynamical freeze-out criteria. We find that when the f…
Intensive investigations of freeze-out criteria in a hot and dense fireball provide important information regarding particle emission from the fireball. A systematic comparison of these proposals is presented here in the framework of a thermodynamically consistent excluded volume model which has been found to describe the properties of hadron gas (HG) quite well. We find that the impact of excluded volume correction is considerably large and the average energy per hadron is 0.9 GeV, $n_b+n_{\bar b}$ stays nearly constant at 0.12/fm$^3$ and the normalized entropy density $s/T^3\approx 6$ in thi…
Particle production in central S-A collisions at 200 GeV/A energy is analysed within a thermal model. Present data imply that the strange particles freeze out at a higher temperature than the non-strange particles and that the strangeness saturation is incomplete.
One of the most remarkable results to emerge from heavy-ion collisions over the past two decades is the striking regularity shown by particle yields at all energies. This has led to several very successful proposals describing particle yields over a very wide range of beam energies, reaching from 1 A GeV up to 200 A GeV, using only one or two parameters. A systematic comparison of these proposals is presented here. The conditions of fixed energy per particle, baryon+anti-baryon density, normalized entropy density as well as percolation model are investigated. The results are compared with the …
The transverse momentum (mass) spectra of the multi-strange and non-multi-strange (i.e. other identified) particles in central gold-gold (Au-Au), lead-lead (Pb-Pb), argon-muriate (Ar-KCl) and nickel-nickel (Ni-Ni) collisions over a wide energy range have been studied in this work. The experimental data measured by various collaborations have been analyzed. The blast-wave fit with Tsallis statistics is used to extract the kinetic freeze-out temperature and transverse flow velocity from the experimental data of transverse momentum (mass) spectra. The extracted parameters increase with the increa…
In hydrodynamical modeling of the ultrarelativistic heavy-ion collisions the freeze-out is typically performed at a constant temperature or density. In this work we apply a dynamical freeze-out criterion, which compares the hydrodynamical expansion rate with the pion scattering rate. Recently many calculations have been done using event-by-event hydrodynamics where the initial density profile fluctuates from event to event. In these event-by-event calculations the expansion rate fluctuates strongly as well, and thus it is interesting to check how the dynamical freeze-out changes hadron distrib…
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…
We analyse the centrality dependence of thermal parameters deduced from hadron m ultiplicities in Au + Au collisions at $\sqrt{s_{NN}} = 130 GeV$. While the chemical freeze-out temperature and chemical potentials are found to be roughly centrality-independent, the strangeness saturation factor $γ_S$ increases with participant number towards unity, supporting the assumption of equilibrium freeze-out conditions in central collisions.
The collision system and multiplicity dependence of chemical freeze-out temperature ($T_{\rm ch}$) and strangeness saturation factor ($γ_{s}$) are obtained by studying the particle ratios at the Large Hadron Collider (LHC) energies. Here, we consider the new results in pp at 13 TeV, p+Pb at $\sqrt{s_{\rm NN}}$ = 5.02 TeV, Xe+Xe at $\sqrt{s_{\rm NN}}$ = 5.44 TeV and Pb+Pb at $\sqrt{s_{\rm NN}}$ = 5.02 TeV along with the earlier results in pp at $\sqrt{s}$ = 7 TeV and Pb+Pb at $\sqrt{s_{\rm NN}}$ = 2.76 TeV. A statistical thermal model is used to extract the chemical freeze-out parameters in dif…
The event-shape and multiplicity dependence of the chemical freeze-out temperature ($T_{\text{ch}}$), freeze-out radius ($R$), and strangeness saturation factor ($γ_{s}$) are obtained by studying the particle yields from the PYTHIA8 Monte Carlo event generator in proton-proton (pp) collisions at the centre-of-mass $\sqrt{s}$ = 13 TeV. Spherocity is one of the transverse event-shape techniques to distinguish jetty and isotropic events in high-energy collisions and helps in looking into various observables in a more differential manner. In this study, spherocity~classes are divided into three ca…
We have estimated centrality variation of chemical freeze-out parameters from yield data at mid-rapidity of $π^\pm$, $K^\pm$ and $p$, $\bar{p}$ for collision energies of RHIC (Relativistic Heavy Ion Collider), Beam Energy Scan (RHIC-BES) program, and LHC (Large Hadron Collider). We have considered a simple hadron resonance gas model and employed a formalism involving conserved charges ($B, Q, S$) of QCD for parameterization. Along with temperature and three chemical potentials ($T,μ_B,μ_Q,μ_S$), a strangeness under-saturation factor ($γ_S$) has been used to incorporate the partial equilibratio…
Oliinychenko, Bugaev and Sorin [arXiv:1204.0103 [hep-ph]] considered the role of conservation laws in discussing possible weaknesses of thermal models which are utilized in describing the hadron multiplicities measured in central nucleus-nucleus collisions. They argued to analyse the criteria for chemical freeze-out and to conclude that none of them were robust. Based on this, they suggested a new chemical freeze-out criterion. They assigned to the entropy per hadron the ad hoc value 7.18 and supposed to remain unchanged over the whole range of the baryo-chemical potentials. Due to unawareness…
Driven by the Beam Energy Scan (BES) program at the RHIC, researches and discussions on the QCD phase diagram have flourished recently. In order to provide a reference from microscopic transport models, we performed a systematic analysis, using a multiphase transport (AMPT) model for the particle yields and a statistical model (THERMUS) for the thermal fit, for Au+Au collisions at $\sqrt{s_{\text{NN}}}$=7.7-200 GeV. It is found that at a fixed collision centrality the chemical freeze-out parameter, temperature $T_{\text{ch}}$, increases with collision energy and somehow saturates at certain va…
Hadronic freezeout during the evolution of the medium created in heavy-ion collisions is an important phenomena. It is quite useful to find a universal freezeout condition for each and every nuclear collisions. In this article, we have constructed a hybrid model to calculate the ratio of transverse energy to total mean multiplicity $E_{T} /N_{ch}$, since this ratio can possibly act as a freezeout condition in heavy-ion collision experiments. Present hybrid model blends two approaches : Tsallis statistics and wounded quark approach. Recently, Tsallis statistics has been reliably used to obtain …
The freeze-out process in heavy ion collisions is driven by the competition between the scattering rate and the expansion rate of the matter. We analyse the expansion rate $Θ$ (often called Hubble flow) in relativistic heavy ion collisions in the FAIR and RHIC-BES energy regimes and compare it to the scattering rate $Γ$ using the UrQMD transport model. We observe that the time evolution of the system is clearly separated into a compression phase and an expansion phase with time dependent $Θ_\parallel$ and $Θ_\perp$. The calculated values of the Hubble expansion at kinetic decoupling are in lin…
We argue that the observed antiproton production in heavy-ion collisions at CERN-SpS energies can be understood if (contrary to most sequential scattering approaches) the backward direction in the process $p\bar p \leftrightarrow \bar{n}π$ (with $\bar{n}$=5-6) is consistently accounted for within a thermal framework. Employing the standard picture of subsequent chemical and thermal freezeout, which induces an over-saturation of pion number with associated chemical potentials of $μ_π\simeq$~60-80 MeV, enhances the backward reaction substantially. The resulting rates and corresponding cross sect…
Transverse momentum (mass) spectra of positively and negatively charged pions, positively and negatively charged kaons, protons and antiprotons produced at mid-(pseudo)rapidity in various collisions at high energies are analyzed in this work. The experimental data measured in central gold-gold, central lead-lead, and inelastic proton-proton collisions by several international collaborations are studied. The (two-component) standard distribution is used to fit the data and extract the excitation function of effective temperature. Then, the excitation functions of kinetic freeze-out temperature,…
We explain how fluctuations of ratios can constrain and falsify the statistical model of particle production in heavy ion collisions, using $K/π$ fluctuations as an example. We define an observable capable of determining which statistical model, if any, governs freeze-out in ultrarelativistic heavy ion collisions. We calculate this observable for $K/π$ fluctuations, and show that it should be the same for RHIC and LHC energies, as well as independent of centrality, if the Grand-Canonical statistical model is an appropriate description and chemical equilibrium applies. We describe variations of…
It is shown that hadron abundances in high energy e+e-, pp and p{\bar p} collisions, calculated by assuming that particles originate in hadron gas fireballs at thermal and partial chemical equilibrium, are in very good agreement with the data. The freeze-out temperature of the hadron gas fireballs turns out to be nearly constant over a large center of mass energy range and not dependent on the initial colliding system. The only deviation from chemical equilibrium resides in the incomplete strangeness phase space saturation. Preliminary results of an analysis of hadron abundances in S+S and S+A…
The data on average hadron multiplicities in central A+A collisions measured at CERN SPS are analysed with the ideal hadron gas model. It is shown that the full chemical equilibrium version of the model fails to describe the experimental results. The agreement of the data with the off-equilibrium version allowing for partial strangeness saturation is significantly better. The freeze-out temperature of about 180 MeV seems to be independent of the system size (from S+S to Pb+Pb) and in agreement with that extracted in e+e-, pp and p{\bar p} collisions. The strangeness suppression is discussed at…
The statistical model with exact conservation of baryon number, electric charge, and strangeness - the Canonical Statistical Model (CSM) - is used to analyze the dependence of yields of light nuclei at midrapidity on charged pion multiplicity at the LHC. The CSM calculations are performed assuming baryon-symmetric matter, using the recently developed Thermal-FIST package. The light nuclei-to-proton yield ratios show a monotonic increase with charged pion multiplicity, with a saturation at the corresponding grand-canonical values in the high-multiplicity limit, in good qualitative agreement wit…
Hydrodynamics merged with single-freeze-out statistical hadronization is used to describe the midrapidity hadron production in relativistic heavy-ion collisions at the highest RHIC energies and to make predictions for the LHC. Thermodynamic properties of the quark-gluon plasma are taken from lattice simulations, at low temperatures the hadron-gas equation of state is used, while in the cross-over region an interpolation between the two equations of state is constructed. The initial condition for hydrodynamics is obtained from a Glauber profile for the entropy, with the initial central temperat…
The assumption that the production of quark-antiquark pairs and their sequential string-breaking taking place through the event horizon of the color confinement determines freezeout temperature and gives a plausible interpretation of the thermal pattern of pp and AA collisions. When relating the black-hole electric charges to the baryon-chemical potentials it was found that the phenomenologically-deduced parameters from various particle ratios in the statistical thermal models agree well with the ones determined from the thermal radiation from charged black-hole. Accordingly, the resulting fre…
Kinetic freeze-out and diffusion dynamics in small-system asymmetric collisions at sqrt(sNN)=200 GeV in light of a generalized Fokker-Planck distribution
Hubei University of Automotive Technology（湖北汽车工业学院）；Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Physical-Technical Institute of Uzbekistan Academy of Sciences（乌兹别克斯坦科学院物理技术研究所）；Abdul Wali Khan University Mardan（马尔丹阿卜杜勒瓦利汗大学）；University of Tabuk（塔布克大学）；Princess Nourah bint Abdulrahman University（公主努拉·宾特·阿卜杜勒拉赫曼大学）；Ajman University（阿治曼大学）
% An analysis is made of the particle composition (hadrochemistry) of the final state in proton-proton (p-p), proton-lead (p-Pb) and lead-lead (Pb-Pb) collisions as a function of the charged particle multiplicity ($\dNchdeta$). The thermal model is used to determine the chemical freeze-out temperature as well as the radius and strangeness saturation factor $γ_s$. Three different ensembles are used in the analysis namely, the grand canonical ensemble, the canonical ensemble with exact strangeness conservation and the canonical ensemble with exact baryon number, strangeness and electric charge c…
Neural network enhanced Bayesian global analysis of relativistic heavy ion collisions
Incubator of Scientific Excellence - Centre for Simulations of Superdense Fluids, University of Wrocław（弗罗茨瓦夫大学超密流体模拟中心卓越科学孵化器）；University of Jyväskylä（于韦斯屈莱大学）；Helsinki Institute of Physics（赫尔辛基物理研究所）；Vanderbilt University（范德堡大学）
We present a detailed study of chemical freeze-out in nucleus-nucleus collisions at beam energies of 11.6, 30, 40, 80 and 158A GeV. By analyzing hadronic multiplicities within the statistical hadronization approach, we have studied the strangeness production as a function of centre of mass energy and of the parameters of the source. We have tested and compared different versions of the statistical model, with special emphasis on possible explanations of the observed strangeness hadronic phase space under-saturation. We show that, in this energy range, the use of hadron yields at midrapidity in…
The ratio of (pseudo)rapidity density of transverse energy and the (pseudo)rapidity density of charged particles, which is a measure of the mean transverse energy per particle, is an important observable in high energy heavy-ion collisions, which reveals about the mechanism of particle production and the freeze-out criteria. Its collision energy and centrality dependence is exactly like the chemical freeze-out temperature till top RHIC energy. The LHC measurement at $\sqrt{s_{NN}}$ = 2.76 TeV brings up new challenges to rule out the mechanisms of gluon saturation or non-equilibrium phenomena b…
We review the charged particle and photon multiplicity, and transverse energy production in heavy-ion collisions starting from few GeV to TeV energies. The experimental results of pseudorapidity distribution of charged particles and photons at different collision energies and centralities are discussed. We also discuss the hypothesis of limiting fragmentation and expansion dynamics using the Landau hydrodynamics and the underlying physics. Meanwhile, we present the estimation of initial energy density multiplied with formation time as a function of different collision energies and centralities…
Here we thoroughly discuss some weak points of the thermal model which is traditionally used to describe the hadron multiplicities measured in the central nucleus-nucleus collisions. In particularly, the role of conservation laws, the values of hard-core radii along with the effects of the Lorentz contraction of hadron eigen volumes and the hadronic surface tension are systematically studied. It is shown that for the adequate description of hadron multiplicities the conservation laws should be modified, whereas for the description of hadron yield ratios the conservation laws are not necessary …
We consider two theoretical scenarios, each including a $\mathbb{Z}_{2}$-odd sector and leading to an elementary dark matter candidate. The first one is a variant of the Type-III seesaw model where one lepton triplet is $\mathbb{Z}_{2}$-odd, together with a heavy sterile neutrino. It leads to a fermionic dark matter, together with the charged component of the triplet being a quasi-stable particle which decays only via a higher-dimensional operator suppressed by a high scale. The second model consists of an inert scalar doublet together with a $\mathbb{Z}_{2}$-odd right-handed Majorana neutrino…
The kaon number density in nucleus+nucleus and p+p reactions is investigated for the first time as a function of the initial energy density $ε$ and is found to exhibit a discontinuity around $ε$=1.3 GeV/fm$^3$. This suggests a higher degree of chemical equilibrium for $ε>$ 1.3 GeV/fm$^3$. It can also be interpreted as reflection of the same discontinuity, appearing in the chemical freeze out temperature (T) as a function of $ε$. The $N^{α\sim 1}$ dependence of (u,d,s) hadrons, with N the number of participating nucleons, also indicates a high degree of chemical equilibrium and T saturation, re…
The kaon number density in nucleus+nucleus and p+p reactions is investigated for the first time as a function of the initial energy density $ε$ and is found to exhibit a discontinuity around $ε$=1.3 GeV/fm$^3$. This suggests a higher degree of chemical equilibrium for $ε>$ 1.3 GeV/fm$^3$. It can also be interpreted as reflection of the same discontinuity, appearing in the chemical freeze out temperature (T) as a function of $ε$. The $N^{α\sim 1}$ dependence of (u,d,s) hadrons, whith N the number of participating nucleons, also indicates a high degree of chemical equilibrium and T saturation, r…
