Thermal-model-based characterization of heavy-ion-collision systems at chemical freeze-out
Jamie M. Karthein, Paolo Alba, Valentina Mantovani-Sarti, Jacquelyn Noronha-Hostler, Paolo Parotto, Israel Portillo-Vazquez, Volodymyr Vovchenko, Volker Koch, Claudia Ratti
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5 pages, 2 figures, 1 table, Proceedings of SQM 2021 - Strangeness in Quark Matter
We investigate the chemical freeze-out in heavy-ion collisions (HICs) and the impact of the hadronic spectrum on thermal model analyses. Detailed knowledge of the hadronic spectrum is still an open question, which has phenomenological consequences on the study of HICs. By varying the number of resonances included in Hadron Resonance Gas (HRG) Model calculations, we can shed light on which particles may be produced. Furthermore, we study the influence of the number of states on the so-called two flavor freeze-out scenario, in which strange and light particles can freeze-out separately. We consider results for the chemical freeze-out parameters obtained from thermal model fits and from calculating net-particle fluctuations. We will show the effect of using one global temperature to fit all particles and alternatively, allowing particles with and without strange quarks to freeze-out separately.
The status of the energy dependence of the chemical freeze-out temperature and chemical potential obtained in heavy ion collisions is presented. Recent proposals for chemical freeze-out conditions are compared.
We propose the entropy density as the thermodynamic condition driving best the chemical freeze-out in heavy-ion collisions. Taking its value from lattice calculations at zero chemical potential, we find that it is excellent in reproducing the experimentally estimated freeze-out parameters. The two characteristic endpoints in the freeze-out diagram are reproduced as well.
The evolution of a hadronic system after its chemical decomposition is described through a model that conserves the hadronic multiplicities to their values at chemical freeze-out. The state of the system is found as function of temperature and the corresponding baryon density is evaluated. The baryon density at thermal decoupling is also computed.
We use a kinetic condition to predict the chemical freeze-out parameters for hadronic species produced in heavy ion collisions. The resulting freeze-out lines for different hadrons lie close to one another in the temperature and baryochemical potential plane, defining a universal, narrow region. The chemical freeze-out is driven by the localization of hadrons due to the chiral symmetry breaking and confining aspects of the QCD transition.
The evolution of a hadronic system after its chemical decomposition is described through a model that conserves the hadronic multiplicities to their values at chemical freeze-out. In the partition function describing the model all known hadronic resonances with masses up to 2400 MeV have been included. The state of the system is found as function of temperature and the corresponding baryon density is evaluated. The baryon density at thermal decoupling is also computed.
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.
We propose an elaborate version of the hadron resonance gas model with the combined treatment of separate chemical freeze-outs for strange and non-strange hadrons and with an additional γ_{s} factor which accounts for the remaining strange particle non-equilibration. Two sets of chemical freeze-outs parameters are connected by the conservation laws of entropy, baryonic charge, isospin projection and strangeness. The developed approach enables us to perform a high-quality fit of the hadron multiplicity ratios for AGS, SPS and RHIC energies with total χ^2/dof \simeq 1.05. A special attention is …
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.
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…
The lattice QCD data of pressure and the energy density have been used to extract the hadronic radius parameter of the excluded volume hadron resonance gas (EVHRG) model. The equation of state can be described well with the extracted radius parameter $R_h= 0.15$ fm. Specific heat is also calculated in the EVHRG model. Further, two new universal descriptions of chemical freeze-out parameters have been introduced based on pressure and specific heat respectively. It is shown that the chemical freeze-out parameters obtained at various $\sqrt{s_{NN}}$ in ideal HRG model approximately correspond to …
We discuss details of our thermal model applied to extract chemical freeze-out conditions from fluctuations in the net-electric charge and net-proton number measured at RHIC. A parametrization for these conditions as a function of the beam energy is given.
We introduce a new prescription for obtaining the chemical freeze-out parameters in the heavy-ion collision experiments using the Hadron Resonance Gas model. The scheme is found to reliably estimate the freeze-out parameters and predict the hadron yield ratios, which themselves were never used in the parametrization procedure.
We present a summary of the recent results obtained with the novel hadron resonance gas model with the multicomponent hard-core repulsion which is extended to describe the mixtures of hadrons and light (anti-, hyper-)nuclei. A very accurate description is obtained for the hadronic and the light nuclei data measured by STAR at the collision energy $\sqrt{s_{NN}} =200$ GeV and by ALICE at $\sqrt{s_{NN}} =2.76$ TeV. The most striking result discussed here is that for the most probable chemical freeze-out scenario for the STAR energy the found parameters allow us to reproduce the values of the exp…
We present an overview of a proposal in relativistic proton-proton ($pp$) collisions emphasizing the thermal or kinetic freeze-out stage in the framework of the Tsallis distribution. In this paper we take into account the chemical potential present in the Tsallis distribution by following a two step procedure. In the first step we used the redundancy present in the variables such as the system temperature, $T$, volume, $V$, Tsallis exponent, $q$, chemical potential, $μ$, and performed all fits by effectively setting to zero the chemical potential. In the second step the value $q$ is kept fixed…
The Hadron Resonance Gas Model with two chemical freeze-outs, connected by conservation laws is considered. We are arguing that the chemical freeze-out of strange hadrons should occur earlier than the chemical freeze-out of non-strange hadrons. The hadron multiplicities measured in the heavy ion collisions for the center of mass energy range 2.7 - 200 GeV are described well by such a model. Based on a success of such an approach, a radical way to improve the Hadron Resonance Gas Model performance is suggested. Thus, we suggest to identify the hadronic reactions that freeze-out noticeably earli…
We explore net charge probability distributions in heavy ion collisions within the hadron resonance gas model. The distributions for strangeness, electric charge and baryon number are derived. We show that, within this model, net charge probability distributions and the resulting fluctuations can be computed directly from the measured yields of charged and multi-charged hadrons. The influence of multi-charged particles and quantum statistics on the shape of the distribution is examined. We discuss the properties of the net proton distribution along the chemical freeze-out line. The model resul…
We confront the lattice results on QCD phase diagram for two and three flavors with the hadron resonance gas model. Taking into account the truncations in the Taylor-expansion of energy density $ε$ done on the lattice at finite chemical potential $μ$, we find that the hadron resonance gas model under the condition of constant $ε$ describes very well the lattice phase diagram. We also calculate the chemical freeze-out curve according to the entropy density $s$. The $s$-values are taken from lattice QCD simulations with two and three flavors. We find that this condition is excellent in reproduci…
It is demonstrated that there exists a direct correlation between chemical freeze-out point and the softest point of the equation of state where the pressure divided by the energy density, $p(ε)/ε$, has a minimum. A dynamical model is given as an example where the passage of the softest point coincides with the condition for chemical freeze-out, namely an average energy per hadron $\approx$ 1 GeV. The sensitivity of the result to the equation of state used is discussed.
We study the production and the observability of Lambda*(1520), K*0(892), and Sigma*(1385), strange hadron resonances as function of the freeze-out conditions within the statistical model of hadron production. We obtain an estimate of how many decay products are rescattered in evolution towards thermal freeze-out following chemical freeze-out, and find that the resonance decay signal is strong enough to be detected. We show how a combined analysis of at least two resonances can be used to understand the chemical freeze-out temperature, and the time between chemical and thermal freeze-outs.
We calculate the first six non-normalized moments of particle multiplicity within the framework of the hadron resonance gas model. In terms of the lower order moments and corresponding correlation functions, general expressions of higher order moments are derived. Thermal evolution of the first four normalized moments and their products (ratios) are studied at different chemical potentials μ, so that it is possible to evaluate them at chemical freeze out curve. It is found that a non-monotonic behavior, reflecting the dynamical fluctuation and strong correlation of particles starts to appear f…
At thermal equilibrium, different chemical freezeout conditions have been proposed so far. They have an ultimate aim of proposing a universal description for the chemical freezeout parameters ($T_{ch}$ and $μ_b$), which are to be extracted from the statistical fitting of different particle ratios measured at various collision energies with calculations from thermal models. A systematic comparison between these conditions is presented. The physical meaning of each of them and their sensitivity to the hadron mass cuts are discussed. Based on availability, some of them are compared with recent la…
The present knowledge about hadrons produced in relativistic heavy ion collisions is compatible with chemical freeze-out happening when the energy density divided by the particle density reaches the value of 1 GeV. This observation is used to determine the energy dependence of the chemical freeze-out parameters T_{ch} and mu_B^{ch} for beam energies varying between 1 and 200 A.GeV. The consequences of this energy dependence are studied for various particle ratios. Predictions for particle ratios at beam energy 40 A.GeV are presented. The conditions for thermal freeze-out are also determined. T…
We suggest other decays which can more effectively identify the effect of rotational motion and presence of the magnetic field, compared to $Λ,\barΛ$ hyperon decayse used so far.
We compare the statistical thermodynamics of hadron resonance gas with recent LGT results at finite chemical potential. We argue that for $T\leq T_c$ the equation of state derived from Monte--Carlo simulations of two quark--flavor QCD at finite chemical potential is consistent with that of a hadron resonance gas when applying the same set of approximations as used in LGT calculations. We indicate the relation of chemical freezeout conditions obtained from a detailed analysis of particle production in heavy ion collisions with the critical conditions required for deconfinement. We argue that th…
The proposed analogy between hadron production in high-energy collisions and Hawking-Unruh radiation process in the black holes shall be extended. This mechanism provides a theoretical basis for the freeze-out parameters, the temperature ($T$) and the baryon chemical potential ($μ$), characterizing the final state of particle production. The results from charged black holes, in which the electric charge is related to $μ$, are found comparable with the phenomenologically deduced parameters from the ratios of various particle species and the higher-order moments of net-proton multiplicity in the…
We investigate the effect of early chemical freeze-out on radial and elliptic flow by using a fully three dimensional hydrodynamic model. We find that the time evolution of temperature and the thermal freeze-out temperature dependence of average radial flow are different from the results by using a conventional hydrodynamic model in which chemical equilibrium is always assumed. We also analyse the p_t spectrum and v_2(p_t) at the RHIC energy and consistently reproduce experimental data by choosing the thermal freeze-out temperature T_th = 140 MeV.
Based on simple scale arguments we argue that any thermalized fireball evolution scenario which is in agreement with the observed Hanbury-Brown Twiss (HBT) correlation radii at RHIC and reproduces the measured total multiplicity cannot reflect the distribution of matter at or close to a phase transition temperature of ~170 MeV and any scenario which assumes that HBT reflects these properties cannot be reached by a sensible choice of evolution parameters while agreeing with all correlation radii. We investigate this question in more detail using a parametrized version of the fireball evolution …
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 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 argue that the chemical freeze-out in heavy ion collisions at high baryon density is not associated to a phase transition or rapid crossover. We employ the linear nucleon-meson model with parameters fixed by the zero-temperature properties of nuclear matter close to the liquid-gas quantum phase transition. For the parameter region of interest this yields a reliable picture of the thermodynamic and chiral properties at non-zero temperature. The chemical freeze-out observed in low-energy experiments occurs when baryon densities fall below a critical value of about 15 percent of nuclear densit…
We provide a framework to estimate the systematic uncertainties in chemical freeze-out parameters extracted from $χ^2$ analysis of thermal model, using hadron multiplicity ratios in relativistic heavy-ion collision experiments. Using a well known technique of graph theory, we construct all possible sets of independent ratios from available hadron yields and perform $χ^2$ minimization on each set. We show that even for ten hadron yields, one obtains a large number ($10^8$) of independent sets which results in a distribution of extracted freeze-out parameters. We analyze these distributions and …
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…
We compare chemical and thermal analysis of the SPS Pb--Pb results at $158A$ GeV, and present a first chemical analysis of RHIC results. We show how a combined analysis of several strange hadron resonances can be used in a study of freeze-out dynamics.
Systematics of the chemical freeze-out line in the high baryon density regime explored at SIS100
GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI亥姆霍兹重离子研究中心）；Liebfrauenschule Bensheim（本斯海姆圣母学校）；Department of Physics, Duke University（杜克大学物理系）；Department of Physics, University of Houston（休斯顿大学物理系）；Frankfurt Institute for Advanced Studies（法兰克福高等研究所）；Institut für Theoretische Physik, Goethe-Universität Frankfurt（歌德大学法兰克福理论物理研究所）；Helmholtz Research Academy Hesse for FAIR (HFHF)（黑森亥姆霍兹FAIR研究学院）
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 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…
It is shown that the freezeout parameters estimated in the heavy-ion collisions all are well described by a constant value of the entropy density $s$ divided by $T^3$. The value of $s/T^3$ has been taken from the lattice QCD simulations at zero baryo-chemical potential $μ_B$ and assumed to remain constant for finite $μ_B$. This implies that the hadronic matter in rest frame of produced system can be determined by constant degrees of freedom. Furthermore, this condition has been used to predict the freezeout parameters at low temperatures.
By analyzing the calculated baryon number susceptibility ratios ${χ_{1}^{B}}/{χ_{2}^{B}}$ and ${χ_{3}^{B}}/{χ_{1}^{B}}$ in two-flavor system via the Dyson-Schwinger equation approach of QCD, we determine the chemical freeze-out temperature and baryon chemical potential in cases of both thermodynamic limit and finite size. We calculate the center-of-mass energy dependence of the ${χ_{4}^{B}}/{χ_{2}^{B}}\, (κσ^{2})$ at the freeze-out line and find an excellent agreement with experimental data in $\sqrt{S_{NN}^{}} \geq 19.6\,$GeV region when taking into account the finite size effect. Our calcula…
We discuss universal properties of higher order cumulants of net baryon number fluctuations and point out their relevance for the analysis of freeze-out and critical conditions in heavy ion collisions at LHC and RHIC.
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 calculate the non-normalized moments of the particle multiplicity within the framework of the hadron resonance gas (HRG) model. At finite chemical potential $μ$, a non-monotonic behavior is observed in the thermal evolution of third order moment (skewness $S$) and the higher order ones as well. Among others, this observation likely reflects dynamical fluctuations and strong correlations. The signatures of non-monotonicity in the normalized fourth order moment (kurtosis $κ$) and its products get very clear. Based on these findings, we introduce a novel condition characterizing the universal …
Finding out universal conditions describing the freeze-out parameters was a subject of various phenomenological studies. In the present work, we introduce a new condition based on constant trace anomaly (or interaction measure) calculated in the hadron resonance gas (HRG) model. Various extensions to the {\it ideal} HRG which are conjectured to take into consideration different types of interactions have been analysed. When comparing HRG thermodynamics to that of lattice quantum chromodynamics, we conclude that the hard-core radii are practically irrelevant, especially when HRG includes all re…
The fast Monte Carlo procedure of hadron generation developed in our previous work is extended to describe noncentral collisions of nuclei. We consider different possibilities to introduce appropriate asymmetry of the freeze-out hyper-surface and flow velocity profile. For comparison with other models and experimental data we demonstrate the results based on the standard parametrizations of the hadron freeze-out hyper-surface and flow velocity profile assuming either a common chemical and thermal freeze-out or the chemically frozen evolution from chemical to thermal freeze-out. The C++ generat…
We study chemical freeze-out parameters for heavy-ion collisions by performing two different thermal analyses. We analyze results from thermal fits for particle yields, as well as, net-charge fluctuations in order to characterize the chemical freeze-out. The Hadron Resonance Gas (HRG) model is employed for both methods. By separating the light hadrons from the strange hadrons in thermal fits, we study the proposed flavor hierarchy. For the net-charge fluctuations, we calculate the mean-over-variance ratio of the net-kaon fluctuations in the HRG model at the five highest energies of the RHIC Be…
We calculate the mean-over-variance ratio of the net-kaon fluctuations in the Hadron Resonance Gas (HRG) Model for the five highest energies of the RHIC Beam Energy Scan (BES) for different particle data lists. We compare these results with the latest experimental data from the STAR collaboration in order to extract sets of chemical freeze-out parameters for each list. We focused on the PDG2012 and PDG2016+ particle lists, which differ largely in the number of resonant states. Our analysis determines the effect of the amount of resonances included in the HRG on the freeze-out conditions.
A detailed discussion of recent results obtained within the hadron resonance gas model with the multi-component hard core repulsion is presented. Among them there are the adiabatic chemical freeze-out criterion, the concept of separate chemical freeze-out of strange particles and the effects of enhancement and sharpening of wide resonances and quark gluon bags occurring in a thermal medium. These findings are discussed in order to strengthen the planned heavy-ion collision experimental programs at low collision energies. We argue, that due to found effects, at the center of mass collision ener…
The prediction for $p_T$ spectra of various resonances produced in Pb+Pb collisions at 2.76 TeV at the LHC in equilibrium and non-equilibrium models is made. It includes the $η$, $ρ$(770), $Σ$(1385), $Λ$(1520), and $Ξ$(1530). The apparent differences may allow to distinguish between the models.
Because of relativistic off-center motion of the charged spectators and the local momentum-imbalance experienced by the participants, a huge magnetic field is likely generated in high-energy collisions. The influence of such short-lived magnetic field on the QCD phase-transition(s) shall be analysed. From Polyakov linear-sigma model, we study the chiral phase-transition and the magnetic response and susceptibility in dependence on temperature, density and magnetic field strength. The systematic measurements of the phase-transition characterizing signals, such as the fluctuations, the dynamical…
Two approaches to treat the chemical freeze-out of strange particles in hadron resonance gas model are analyzed. The first one employs their non-equillibration via the usual γ_s factor and such a model describes the hadron multiplicities measured in nucleus-nucleus collisions at AGS, SPS and RHIC energies with χ^2/dof = 1.15. Surprisingly, at low energies we find not the strangeness suppression, but its enhancement. Also we suggest an alternative approach to treat the strange particle freeze-out separately, but with the full chemical equilibration. This approach is based on the conservation la…
The transverse momentum distributions measured in $p-p$ collisions at the LHC determine the kinetic freeze-out stage of the collision. The parameters deduced from these distributions differ from those determined at chemical freeze-out. The present investigation focuses on the chemical potentials at kinetic freeze-out, these are not necessarily zero as they are at chemical freeze-out, the only constraint is that they should be equal for particles and antiparticles at LHC energies. The thermodynamic variables are determined in the framework of the Tsallis distribution. The chemical potentials in…
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…
A new way to overcome the $Λ$ hyperon selective suppression, which is known as the $Λ$-anomaly, has been suggested. In particular, the additional radius of a $Λ$ hyperon is introduced into the model of hadron resonance gas with the multicomponent hard-core repulsion. The proposed approach allows one to describe the hadron multiplicity ratios measured at the AGS, SPS and RHIC energies with the accuracy $χ^{2}/dof=$52/55$\simeq $0.95.
We argue that hadron multiplicities in central high energy nucleus-nucleus collisions are established very close to the phase boundary between hadronic and quark matter. In the hadronic picture this can be described by multi-particle collisions whose importance is strongly enhanced due to the high particle density in the phase transition region. As a consequence of the rapid fall-off of the multi-particle scattering rates the experimentally determined chemical freeze-out temperature is a good measure of the phase transition temperature.
