Chemical Freeze-out Parameters Research Articles

Cumulants of net-strangeness multiplicity distributions at energies available at the BNL Relativistic Heavy Ion Collider

The higher-order cumulants of net-proton number, net-charge, and net-strangeness multiplicity distributions are widely studied to search for the quantum-chromodynamics critical point and extract the chemical freeze-out parameters in heavy-ion collisions. In this context, the event-by-event fluctuations of the net-strangeness multiplicity distributions play important roles in extracting the chemical freeze-out parameter in the strangeness sector. Due to having difficulties in detecting all strange hadrons event by event, the kaon ($K$) and lambda ($\Lambda$) particles serve as a proxy for the strangeness-related observables in heavy-ion collisions. We have studied the net-$K$, net-$\Lambda$, and net-($K$ + $\Lambda$) multiplicity distributions and calculated their different order of cumulants using the ultrarelativistic quantum molecular dynamics model and hadron resonance gas calculation. To adequately account for the net-strangeness cumulants, it has been found that the inclusion of resonance decay contributions in $K$ and $\Lambda$ is necessary.

Thermal-model-based characterization of heavy-ion-collision systems at chemical freeze-out

We investigate the chemical freeze-out in heavy-ion collisions (HICs) and the impact of the hadronic spectrum on thermal model analyses [1, 2]. 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 freezeout 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.

Multiplicity dependence of freezeout scenarios in pp collisions at s=7 TeV

The data on transverse momentum integrated hadron yields in different multiplicity classes of $p+p$ collisions at $\sqrt{s}=7$ TeV have been analyzed to extract the chemical freeze-out parameters using a thermal model. The chemical freeze-out parameters have been extracted for three different freeze-out schemes: (i) unified freeze-out for all hadrons in complete thermal equilibrium (1CFO), (ii) unified freeze-out for all hadrons with an additional parameter ${\ensuremath{\gamma}}_{S}$ which accounts for possible out-of-equilibrium production of strange hadrons ($1\mathrm{CFO}+{\ensuremath{\gamma}}_{S}$), and (iii) separate freeze-out for hadrons with and without strangeness content (2CFO). It has been observed that the $1\mathrm{CFO}+{\ensuremath{\gamma}}_{S}$ scheme gives the best description of the hadronic yields at midrapidity when multiplicity ($\ensuremath{\langle}d{N}_{ch}/d\ensuremath{\eta}\ensuremath{\rangle}$) of the collision is less than 10. This indicates that the strangeness is out of equilibrium in most of the multiplicity classes of $p+p$ collisions. All three parameters of this CFO scheme, temperature $T$, radius $R$ of the fireball, and strangeness suppression factor ${\ensuremath{\gamma}}_{S}$ increase with the increase of $\ensuremath{\langle}d{N}_{ch}/d\ensuremath{\eta}\ensuremath{\rangle}$. Furthermore, we have compared applicability of different CFO schemes considering two more colliding systems $p+\text{Pb}$ at $\sqrt{{s}_{\mathrm{NN}}}=5.02$ and $\text{Pb}+\text{Pb}$ at $\sqrt{{s}_{\mathrm{NN}}}=2.76$ TeV along with $p+p$ collisions at $\sqrt{s}=7$ TeV. We observe a freeze-out volume (or multiplicity) dependence of CFO schemes regardless of colliding ions. The $1\text{CFO}+{\ensuremath{\gamma}}_{S}$, 1CFO, and 2CFO schemes provide the best description of the data when the dimensionless quantity $V{T}^{3}$ approximately satisfies the conditions $V{T}^{3}<50, 50<V{T}^{3}<100$, and $V{T}^{3}>100$, respectively, or the corresponding multiplicity satisfies the conditions $\ensuremath{\langle}d{N}_{ch}/d\ensuremath{\eta}\ensuremath{\rangle}<30, 30<d{N}_{ch}/d\ensuremath{\eta}<60$, and $\ensuremath{\langle}d{N}_{ch}/d\ensuremath{\eta}\ensuremath{\rangle}>100$, respectively.

Centrality Dependence of Chemical Freeze-Out Parameters and Strangeness Equilibration in RHIC and LHC Energies

We have estimated centrality variation of chemical freeze-out parameters from yield data at midrapidity of π ± , K ± and p , 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 undersaturation factor ( γ S ) has been used to incorporate the partial equilibration in the strange sector. Our obtained freeze-out temperature does not vary much with centrality, whereas chemical potentials and γ S seem to have a significant dependence. The strange hadrons are found to deviate from a complete chemical equilibrium at freeze-out at the peripheral collisions. This deviation appears to be more prominent as the collision energy decreases at lower RHIC-BES energies. We have also shown that this departure from equilibrium reduces towards central collisions, and strange particle equilibration may happen after a threshold number of participants in A - A collision.

Chemical freeze-out systematics of thermal model analysis using hadron yield ratios

We provide a framework to estimate the systematic uncertainties in chemical freeze-out parameters extracted from $\chi^2$ 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 $\chi^2$ 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 compare our results for chemical freeze-out parameters and associated systematic uncertainties with previous results available in the literature.

A Baseline Study of the Event-Shape and Multiplicity Dependence of Chemical Freeze-Out Parameters in Proton-Proton Collisions at \( {\sqrt{s}} \) = 13 TeV Using PYTHIA8

The event-shape and multiplicity dependence of the chemical freeze-out temperature (Tch), freeze-out radius (R), and strangeness saturation factor (γs) are obtained by studying the particle yields from the PYTHIA8 Monte Carlo event generator in proton-proton (pp) collisions at the centre-of-mass 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 categories, namely (i) spherocity integrated, (ii) isotropic, and (iii) jetty. The chemical freeze-out parameters are extracted using a statistical thermal model as a function of the spherocity class and charged particle multiplicity in the canonical, strangeness canonical, and grand canonical ensembles. A clear observation of the multiplicity and spherocity class dependence of Tch, R, and γs is observed. A final state multiplicity, Nch≥ 30 in the forward multiplicity acceptance of the ALICE detector appears to be a thermodynamic limit, where the freeze-out parameters become almost independent of the ensembles. This study plays an important role in understanding the particle production mechanism in high-multiplicity pp collisions at the Large Hadron Collider (LHC) energies in view of a finite hadronic phase lifetime in small systems.

Chemical freeze-out parameters of net-kaons in heavy-ion collisions

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 Beam Energy Scan (BES) for different particle data lists. We compare these results with recent experimental data from the STAR collaboration in order to extract sets of chemical freeze-out parameters for each list. We focused on particle lists which differ largely in the number of resonant states. By doing so, our analysis determines the effect of the amount of resonances included in the HRG model on the freeze-out conditions. Our findings have potential impact on various other models in the field of relativistic heavy ion collisions.

Second virial coefficients of light nuclear clusters and their chemical freeze-out in nuclear collisions

Here we develop a new strategy to analyze the chemical freeze-out of light (anti)nuclei produced in high energy collisions of heavy atomic nuclei within an advanced version of the hadron resonance gas model. It is based on two different, but complementary approaches to model the hard-core repulsion between the light nuclei and hadrons. The first approach is based on an approximate treatment of the equivalent hard-core radius of a roomy nuclear cluster and pions, while the second approach is rigorously derived here using a self-consistent treatment of classical excluded volumes of light (anti)nuclei and hadrons. By construction, in a hadronic medium dominated by pions, both approaches should give the same results. Employing this strategy to the analysis of hadronic and light (anti)nuclei multiplicities measured by ALICE at $\sqrt{s_{NN}} =2.76$ TeV and by STAR at $\sqrt{s_{NN}} =200$ GeV, we got rid of the existing ambiguity in the description of light (anti)nuclei data and determined the chemical freeze-out parameters of nuclei with high accuracy and confidence. At ALICE energy the nuclei are frozen prior to the hadrons at the temperature $T = 175.1^{+2.3}_{-3.9}$ MeV, while at STAR energy there is a single freeze-out of hadrons and nuclei at the temperature $T = 167.2 \pm 3.9$ MeV. We argue that the found chemical freeze-out volumes of nuclei can be considered as the volumes of quark-gluon bags that produce the nuclei at the moment of hadronization.

Chemical freeze-out conditions from net-kaon fluctuations at RHIC

We compare the mean-over-variance ratio of the net-kaon distribution calculated within a state-of-the-art hadron resonance gas model to the latest experimental data from the Beam Energy Scan at RHIC by the STAR collaboration. Our analysis indicates that it is not possible to reproduce the experimental results using the freeze-out parameters from the existing combined fit of net-proton and net-electric charge mean-over-variance. The strange mesons need about 10-15 MeV higher temperatures than the light hadrons at the highest collision energies. In view of the ongoing lambda fluctuation measurements, we predict the net-lambda variance-over-mean at the light and strange chemical freeze-out parameters. We observe that the lambda fluctuations are sensitive to the difference in the freeze-out temperatures established in this analysis. Our results have implications for other phenomenological models in the field of relativistic heavy-ion collisions.

Systematics of chemical freeze-out parameters in heavy-ion collision experiments

We discuss systematic uncertainties in the chemical freeze-out parameters from the $\chi^2$ analysis of hadron multiplicity ratios in the heavy-ion collision experiments. The systematics due to the choice of specific hadron ratios are found to lie within the experimental uncertainties. The variations obtained by removing the usual constraints on the conserved charges show similar behavior. The net charge to net baryon ratios in such unconstrained systems are commensurate with the expected value obtained from the protons and neutrons of the colliding nuclei up to the center of mass energies $\sim 40$ GeV. Beyond that the uncertainties in this ratio gradually increases, possibly indicating the reduction in baryon stopping.

Freeze-out scenarios in small systems at RHIC and LHC energies

We study the hadronic yields produced in two small collision systems [Formula: see text] at [Formula: see text][Formula: see text]TeV and [Formula: see text] at [Formula: see text][Formula: see text]TeV, and extracted the chemical freeze-out (CFO) parameters. The CFO parameters are obtained using a hadron resonance gas (HRG) model and in this study present the system size dependence of the parameters. We observe that with the strangeness suppression factor [Formula: see text] included in the model, a single freeze-out scenario can describe hadronic yields for all the centralities of [Formula: see text] collision at [Formula: see text][Formula: see text]TeV, indicating that the strange hadrons have not reached full equilibrium. On the other hand, for small average charged particle multiplicity ([Formula: see text]) bins of [Formula: see text] collision at [Formula: see text][Formula: see text]TeV strangeness is not fully equilibrated whereas strangeness equilibration seems to be reached in large [Formula: see text]. For both the collision systems, no significant system volume dependence of the temperature has been observed. However, in comparable [Formula: see text] values, temperatures are 10–20[Formula: see text]MeV larger for [Formula: see text] collision compared to [Formula: see text] collision. We observe that the volume of the system at the CFO increases with increase of charge multiplicity for both the collisions. The increase is much steeper in [Formula: see text] collision at [Formula: see text][Formula: see text]TeV than [Formula: see text] collision at [Formula: see text][Formula: see text]TeV. Further, we analyze the transverse momentum ([Formula: see text]) spectra of different hadrons produced in [Formula: see text] collision at [Formula: see text][Formula: see text]TeV in a combined freeze-out scenario. We show the [Formula: see text] dependence of freeze-out parameters. It is observed that with [Formula: see text] included in the model, a single freeze-out scheme can describe the [Formula: see text] spectra. For similar [Formula: see text] values, [Formula: see text] in both the collision systems are close to each other and overall values of [Formula: see text] increase with increase of [Formula: see text]. Unlike CFO scenario using the produced hadron yields only, freeze-out temperature in combined scenario of chemical and kinetic freeze-out, obtained from [Formula: see text] spectra, increases with increase of [Formula: see text]. For smaller [Formula: see text] values, the temperature in [Formula: see text] collision at [Formula: see text][Formula: see text]TeV is similar to that of [Formula: see text] collision at [Formula: see text][Formula: see text]TeV. However, temperatures are larger in [Formula: see text] collision than [Formula: see text] collision at larger [Formula: see text] values.

Chemical freeze-out conditions and fluctuations of conserved charges in heavy-ion collisions within a quantum van der Waals model

The chemical freeze-out parameters in central nucleus-nucleus collisions are extracted consistently from hadron yield data within the quantum van der Waals (QvdW) hadron resonance gas model. The beam energy dependences for skewness and kurtosis of net baryon, net electric, and net strangeness charges are predicted. The QvdW interactions in asymmetric matter, $Q/B \neq 0.5$, between (anti)baryons yield a non-congruent liquid-gas phase transition, together with a nuclear critical point (CP) with critical temperature of $T_c=19.5$ MeV. The nuclear CP yields the collision energy dependence of the skewness and the kurtosis to both deviate significantly from the ideal hadron resonance gas baseline predictions even far away, in $(T,\mu_B)$-plane, from the CP. These predictions can readily be tested by STAR and NA61/SHINE Collaborations at the RHIC BNL and the SPS CERN, respectively, and by HADES at GSI. The results presented here offer a broad opportunity for the search for signals of phase transition in dense hadronic matter at the future NICA and FAIR high intensity facilities.

Novel scheme for parametrizing the chemical freeze-out surface in heavy ion collision experiments

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.

Freeze-out temperature from net-kaon fluctuations at energies available at the BNL Relativistic Heavy Ion Collider

We compare the mean-over-variance ratio of the net-kaon distribution calculated within a state-of-the-art hadron resonance gas model to the latest experimental data from the Beam Energy Scan at RHIC by the STAR collaboration. Our analysis indicates that it is not possible to reproduce the experimental results using the freeze-out parameters from the existing combined fit of net-proton and net-electric charge mean-over-variance. The strange mesons need about 10-15 MeV higher temperatures than the light hadrons at the highest collision energies. In view of the future $\Lambda$ fluctuation measurements, we predict the $\Lambda$ variance-over-mean and skewness-times-variance at the light and strange chemical freeze-out parameters. We observe that the $\Lambda$ fluctuations are sensitive to the difference in the freeze-out temperatures established in this analysis. Our results have implications for other phenomenological models in the field of relativistic heavy ion collisions.

Testing the system size dependence of hydrodynamical expansion and thermal particle production with π, K, p, and ϕ in Xe–Xe and Pb–Pb collisions with ALICE

We present new results on transverse momentum spectra, integrated yields, and mean transverse momenta of pions, kaons, and protons, as well as of ϕ-mesons for various centrality classes measured in Pb–Pb and Xe–Xe collisions at the LHC. This unique set of data allows us to investigate bulk particle production for very different systems at similar multiplicities. The chemical and kinetic freeze-out parameters are extracted via statistical-thermal and combined blast-wave fits to the data in heavy-ion collisions and are compared to results obtained in pp and p–Pb collisions at similar multiplicities. The evolution of collective-like effects from pp and p–Pb collisions to Xe–Xe and Pb–Pb collisions is further investigated by detailed comparisons to predictions from models.

Higher moment fluctuations of identified particle distributions from ALICE

Cumulants of conserved charges fluctuations are regarded as a potential tool to study the criticality in the QCD phase diagram and to determine the freeze-out parameters in a model-independent way. At LHC energies, the measurements of the ratio of the net-baryon (net-proton) cumulants can be used to test the lattice QCD predictions. In this work, we present the first measurements of cumulants of the net-proton number distributions up to 4th order in Pb–Pb collisions at sNN=2.76and5.02TeV as a function of collision centrality. We compare our cumulant ratios results with the STAR experiment net-proton results measured in the first phase of the Beam Energy Scan program at RHIC. The results can be used to obtain the chemical freeze-out parameters at LHC.

Statistical hadron-gas treatment of systems created in proton-proton interactions at energies available at the CERN Super Proton Synchrotron

We analyze the newest data from the NA61/SHINE collaboration which, in addition to previous results on pions and kaons, include mean multiplicities of $p$, $\Lambda$, and $\phi$-mesons produced in inelastic proton-proton (p+p) interactions at $\sqrt{s_{NN}}=6.3-17.3$~GeV. The canonical ensemble formulation of the ideal hadron resonance gas (HRG) model is used with exact conservation of net baryon number $B=2$, electric charge $Q=2$, and strangeness $S=0$. The chemical freeze-out parameters in p+p interactions are obtained and compared to those in central nucleus-nucleus collisions. Several features of p+p interactions at the CERN SPS within a statistical model are studied: 1) the inclusion of the $\phi$-meson yields in thermal fits worsens significantly the fit quality; 2) the data show large event-by-event multiplicity fluctuations in inelastic p+p interactions which can not be explained by a single fireball described by a statistical model; 3) the fits within the canonical ensemble formulation of HRG do not give any improvement over the fits within the grand canonical ensemble formulation, i.e., there are no indications for existence of a single statistical system in p+p inelastic interactions in the considered energy range.

Role of new resonance states on fluctuations and correlations of conserved charges in hadron resonance gas model

We investigate the role of suspected resonance states, that are yet to be confirmed experimentally, on different thermodynamic quantities as well as the higher-order fluctuations and the correlation between conserved charges using ideal hadron resonance gas (HRG) model. We have discussed the temperature dependence of the various thermodynamic quantities and compared them with the lattice QCD result. We observe that the values of the bulk thermodynamic variables such as pressure, energy density, entropy density and second-order susceptibilities are increased by the inclusion of the additional resonances. Further, we find that the hadronic phase of lattice QCD result of [Formula: see text] and [Formula: see text] can be described well in ideal HRG model with the additional resonances. We have also studied the [Formula: see text] dependence of the fluctuation observables of net-proton, net-kaon and net-charge. Proper experimental acceptance cuts have been used in the model to compare with the data from experimental measurements. It has been observed that the experimental data of lower-order fluctuation observable can be described well by the ideal HRG model. However, higher-order fluctuation observables cannot be described by ideal HRG model for all [Formula: see text] studied here, which indicates the possibility of presence of critical or nonequilibrium physics for those energies. The effect of additional resonances on fluctuation observables of net-charge at different [Formula: see text] has also been studied. Finally, the chemical freeze-out parameters have been extracted from the experimental data of [Formula: see text] of net-proton and net-charge using two different sets of hadronic spectra. We find that for both the sets, the extracted temperature is slightly lower than those obtained from the hadronic yields. Moreover, it is observed that the extracted temperature of the system gets further reduced with addition of more resonances.

Freeze-out properties from net-Kaon fluctuations at RHIC

We calculate the net-kaon mean-over-variance in the hadron resonance gas model and compare it to the experimental data by the STAR collaboration. We show that it is not possible to match the experimental values using the freeze-out parameters obtained from a combined fit of net-proton and net-electric charge mean-over-variance. At the highest collision energies, kaons need about 10-15 MeV higher freeze-out temperatures than the light hadrons. We also predict the variance-over-mean and skewness-times-variance for net-Λ particles at the light and strange chemical freeze-out parameters. It turns out that these Λ fluctuations are sensitive to the difference in the freeze-out temperatures observed in our analysis.

Universal descriptions of chemical freeze-out based on pressure and specific heat

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 [Formula: see text] 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 [Formula: see text] in ideal hadron resonance gas (HRG) model approximately correspond to [Formula: see text] and [Formula: see text], respectively. These two quantities are important to describe the thermodynamic properties of the hadronic matter created in heavy-ion collision experiment. The sensitivity of universal chemical freeze-out lines on repulsive interaction is also studied. It has been observed that the behaviors of chemical freeze-out lines for [Formula: see text] and [Formula: see text] in EVHRG model remain similar to ideal HRG model for the best fit value of hadronic radii.