Freeze-out Temperature Research Articles

Analysis of transverse momentum spectra of protons, deuterons, and tritons in symmetric heavy-ion collisions at √(s_NN ) = 200 GeV at the RHIC

Abstract The blast wave model with Tsallis statistics is used to analyze the transverse momentum spectra of the protons (p), deuteron (d), and triton (t) in √(s_NN ) = 200 GeV gold-gold (Au-Au) collisions at RHIC in various centrality bins. In particular transverse momentum ranges, model results closely match experimental data from the PHENIX (p) and STAR (d and t) Collaborations. The data is compared with protons obtained in Cu+Cu collisions and deuteron and triton in Ru+Ru collisions at 200 GeV, center of mass energy from STAR collaboration. Particle spectra are used to derive the kinetic freeze-out temperatures, transverse flow velocities, and freeze-out volumes. According to the findings, the kinetic freeze-out temperature rises as one goes from the central to peripheral collisions. In this transition, the transverse flow velocity and the freeze-out volume both drop. In the collisions of both Collaborations, this work reveals mass-dependent kinetic freeze-out temperature and differential volume possibilities. On the whole, the non-extensivity parameter q decreases with increasing centrality of the studied heavy-ion collisions, and heavier mass particles have smaller values of q, which implies higher degrees of thermalization and equilibrium in more central collisions and for heavier particles.

Analytical insights into the interplay of momentum, multiplicity, and the speed of sound in heavy-ion collisions

We introduce a minimal model of ultracentral heavy-ion collisions to study the relation between the speed of sound of the produced plasma and the final particles' energy and multiplicity. We discuss how the particles' multiplicity Ntot and average energy Etot/Ntot is related to the speed of sound cs by cs2=dln(Etot/Ntot)/dlnNtot if the fluid is inviscid, its speed of sound is constant and all final particles can be measured. We show that finite rapidity cuts on the particles' multiplicity N and energy E introduce corrections between cs2 and dln(E/N)/dlnN that depend on the system's lifetime. We study analytically these deviations with the Gubser hydrodynamic solution, finding that, for ultrarelativistic bosons, they scale as the ratio of the freeze-out temperature TFO over the maximum initial temperature of the fluid T0; the nonthermodynamic aspect of these corrections is highlighted through their dependence on the system's initial conditions. Published by the American Physical Society 2024

Bulk properties of the system in Au–Au collisions at 3 GeV and their dependence on collision centrality and particle rapidity

We analyze the transverse momentum spectra of proton (p), deuteron (d), triton (t), and helium (3He and 4He) in different centrality intervals in various rapidity slices in gold–gold (Au–Au) collisions at sNN=3 GeV. We apply the blast-wave model with Tsallis statistics (TBW) to transverse momentum spectra of the particles, which fits well the data of STAR Collaboration. The freezeout parameters such as kinetic freezeout temperature, transverse flow velocity, and kinetic freezeout volume are extracted. Our findings reveal that central collisions exhibit higher values for the kinetic freezeout temperature, transverse flow velocity, and kinetic freezeout volume (which means that the central collisions are more hot and expansive), and observed that they decrease from central to peripheral collisions, and the former two parameters decrease from backward rapidity regions to mid-rapidity. This indicates a rapid expansion of the system in central collisions and in backward rapidities. The above parameters are mass-dependent, and the former increases, while the latter two decrease for heavier particles, reflecting the multiple kinetic freezeout and volume differential freezeout scenarios. Besides, the entropy parameter (q) is extracted, and it increases from peripheral to central and from backward to mid-rapidity regions.

Dependence of thermodynamic quantities at freeze-out on pseudorapidity and collision energy in p-p collisions at LHC energies* *Supported by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R106), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. In addition, the authors extend their appreciation to the Deanship of Scientific Research at Northern Border University, Arar, KSA for funding this research

The transverse momentum distributions of charged hadrons produced in proton-proton collisions at center-of-mass energies ( ) of 0.9 TeV and 2.36 TeV, as measured by the CMS detector at the Large Hadron Collider (LHC), have been analyzed within various pseudorapidity classes utilizing the thermodynamically consistent Tsallis distribution. The fitting procedure resulted in the key parameters, namely, effective temperature (T), non-extensivity parameter (q), and kinetic freezeout volume (V). Additionally, the mean transverse momentum ( ) and initial temperature (Ti ) of the particle source are determined through the fit function and string percolation method, respectively. An alternative method is employed to calculate the kinetic freezeout temperature ( ) and transverse flow velocity ( ) from T. Furthermore, thermodynamic quantities at the freezeout, including energy density (ε), particle density (n), entropy density (s), pressure (P), and squared speed of sound ( ), are computed using the extracted T and q. It is also observed that, with a decrease in pseudorapidity, all thermodynamic quantities except V and q increase. This trend is attributed to greater energy transfer along the mid pseudorapidity. q increases towards higher values of pseudorapidity, indicating that particles close to the beam axis are far from equilibrium. Meanwhile, V remains nearly independent of pseudorapidity. The excitation function of these parameters (q) shows a direct (inverse) correlation with collision energy. The ε, n, s, and P show a strong dependence on collision energies at low pseudorapidities. Explicit verification of the thermodynamic inequality suggests the formation of a highly dense droplet-like Quark-Gluon Plasma (QGP). Additionally, the inequality is explicitly confirmed, aligning with the evolution of the produced fireball.

Centrality dependency of proton, deuteron, and triton’s temperatures in Au+Au collisions at 200 GeV

The transverse momentum (pT) spectra of protons (p), deuterons (d), and tritons (t) in 200 GeV gold–gold (Au + Au) collisions at RHIC are examined across a range of centrality bins using the Levy Tsallis (TS) statistical model. The model's predictions closely match the experimental results from PHENIX (p) and STAR (d and t) Collaborations. Kinetic freeze-out temperatures of hadrons are obtained from particle spectra. The results showed that the kinetic freeze-out temperature decreases as collisions move from center to the periphery. This work found mass-dependent kinetic freeze-out temperatures, heavier particles arrive to the freeze-out phase before lighter ones. Comparison with same data fitted by blast wave function with Tsallis statistics (BWTS) showed that T0 values are increasing from central to peripheral collisions, while in case of TS function (current analysis) it decreases. This behavior puts a question mark on the reliability of using such functions for temperature extraction.

K*(892)± resonance production in Pb-Pb collisions at sNN=5.02 TeV

The production of K*(892)± meson resonance is measured at midrapidity (|y|<0.5) in Pb−Pb collisions at sNN=5.02 TeV using the ALICE detector at the CERN Large Hadron Collider. The resonance is reconstructed via its hadronic decay channel K*(892)±→KS0π±. The transverse momentum distributions are obtained for various centrality intervals in the pT range of 0.4−16 GeV/c. Measurements of integrated yields, mean transverse momenta, and particle yield ratios are reported and found to be consistent with previous ALICE measurements for K*(892)0 within uncertainties. The pT-integrated yield ratio 2K*(892)±/(K++K−) in central Pb−Pb collisions shows a significant suppression at a level of 9.3σ relative to pp collisions. Thermal model calculations result in an overprediction of the particle yield ratio. Although both hadron resonance gas in partial chemical equilibrium (HRG-PCE) and + simulations consider the hadronic phase, only HRG-PCE accurately represents the measurements, whereas + simulations tend to overpredict the particle yield ratio. These observations, along with the kinetic freeze-out temperatures extracted from the yields measured for light-flavored hadrons using the HRG-PCE model, indicate a finite hadronic phase lifetime, which decreases with increasing collision centrality percentile. The pT-differential yield ratios 2K*(892)±/(K++K−) and 2K*(892)±/(π++π−) are presented and compared with measurements in pp collisions at s=5.02 TeV. Both particle ratios are found to be suppressed by up to a factor of five at pT<2.0 GeV/c in central Pb−Pb collisions and are qualitatively consistent with expectations for rescattering effects in the hadronic phase. The nuclear modification factor (RAA) shows a smooth evolution with centrality and is found to be below unity at pT>8 GeV/c, consistent with measurements for other light-flavored hadrons. The smallest values are observed in most central collisions, indicating larger energy loss of partons traversing the dense medium. ©2024 CERN, for the ALICE Collaboration 2024 CERN

Extracting Kinetic Freeze-Out Properties in High-Energy Collisions Using a Multisource Thermal Model

We study the transverse momentum (pT) spectra of neutral pions and identified charged hadrons produced in proton–proton (pp), deuteron–gold (d–Au), and gold–gold (Au–Au) collisions at the center of mass energy sNN=200 GeV. The study is made in the framework of a multisource thermal model used in the partonic level. It is assumed that the contribution to the pT-value of any hadron comes from two or three partons with an isotropic distribution of the azimuthal angle. The contribution of each parton to the pT-value of a given hadron is assumed to obey any one of the standard (Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein) distributions with the kinetic freeze-out temperature and average transverse flow velocity. The pT spectra of the final-state hadrons can be fitted by the superposition of two or three components. The results obtained from our Monte Carlo method are used to fit the experimental results of the PHENIX and STAR Collaborations. The results of the present work serve as a suitable reference baseline for other experiments and simulation studies.

Spontaneous baryogenesis and generation of gravitational waves in a new model of quintessential [formula omitted]-attractor

We study the role of α-parameter of the newly proposed model of quintessential α-attractor inflation (arXiv: 2305.00230 [gr-qc]) to the case of quintessential spontaneous baryogenesis and generation of relic gravitational waves in presence of a rolling scalar field during kination. An effective 4-Fermi construct technique has been employed to compute the freeze-out temperature and the baryon-to-entropy ratio, of which the obtained results conform to the experimental requirements for 0.28≤α≤0.30. This range of α is found to originate from the functional behavior of the end-value expression of the potential concerned. We also find a blue-tilted gravitational wave spectrum during a transition from inflation to kination. The amplitudes of the gravitational waves during radiation domination satisfy the constraint for nucleosynthesis and the characteristic strain of the ongoing gravitational wave detectors. Thus, the most important observation emerged from the present study is that, increasingly small fractional values of α are favorable for unification of inflation, baryogenesis, quintessence and gravitational waves within a single model. This could have an interesting connection with the fundamental origin of α-attractor.

System-size dependence of collective transverse flow in relativistic nuclear collisions

The transverse momentum distributions of identified hadrons (π±, K±, p, p, K0S, Λ, Λ, Ξ−, Ξ+, φ, Ω−, and Ω+) produced in Au+Au collisions at RHIC-BES energies are analyzed with Blast-Wave model and with Boltzmann-Gibbs statistics. The kinetic freeze-out temperature, the average transverse flow velocity and the flow profile exponent are extracted from the transverse momentum spectra of the particles. The study of system-size dependence of the kinetic freeze-out parameters showed that kinetic freeze-out temperature increases, while average transverse flow ve- locity decreases from central to peripheral collisions. The larger freeze-out temperature for peripheral collisions may indicate an earlier decoupling of the expanding system. For the same centrality class, it is observed that the transverse flow velocity and flow profile exponent have an increasing trend with increasing collision energy.

Varying entropy degrees of freedom effects in low-scale leptogenesis

We analyze in detail the effect of varying entropy degrees of freedom on low-scale leptogenesis models. As an archetypal model, we consider the triresonant leptogensis (TRL) scenario introduced recently by the authors, where the neutrino-Yukawa coupling matrix is dictated by an approximate Zn discrete symmetry (with n=3, 6). TRL models exhibit no preferred direction in the leptonic flavor space and have the remarkable feature that leptogenesis can successfully take place even if all light neutrinos are strictly massless up to one-loop order. Most interestingly, for TRL scenarios with heavy Majorana neutrinos lighter than 100 GeV, temperature varying degrees of freedom associated with the entropy of the plasma have a dramatic impact on the predictions of the baryon asymmetry in the Universe (BAU), and may depend on the freeze-out sphaleron temperature Tsph. We find that this is a generic feature of most freeze-out low-scale leptogenesis models discussed in the literature. In the same context, we consider heavy-neutrino scenarios realizing dynamics related to critical unstable qudits in the thermal plasma and assess their significance in generating the BAU. The phenomenological implications of TRL scenarios at the intensity and high-energy frontiers are analyzed. Published by the American Physical Society 2024

Chemical freeze-out parameters via a functional renormalization group approach

We study the freeze-out parameters in a QCD-assisted effective theory that accurately captures the quantum and in-medium effects of QCD at low energies. The functional renormalization group approach is implemented in our work to incorporate the nonperturbative quantum, thermal, and density fluctuations. By analyzing the calculated baryon number susceptibility ratios χ2B/χ1B and χ3B/χ2B, we determine the chemical freeze-out temperatures and baryon chemical potentials in cases of hard thermal or dense loop improved μ-dependent gluon potential and μ-independent gluon potential. We calculate the χ4B/χ2B(κσ2) and χ6B/χ2B along the freeze-out line for both cases. It is found that κσ2 exhibits a nonmonotonic behavior in a low collision energy region and approaches one for lower collision energy. χ6B/χ2B shows a similar complicated behavior in our calculation. Published by the American Physical Society 2024

Multiplicity dependence of the freezeout parameters in high energy hadron-hadron collisions* *Supported by Princess Nourah bint Abdulrahman University, Researchers Supporting Project Number PNURSP2024R106, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. We would like to express our gratitude for the support received from Abdul Wali Khan University Mardan, Pakistan; Hubei University of Automotive Technology, Doctoral Research Fund number BK202313; University

We examined the transverse momentum ( ) spectra of various identified particles, encompassing both light-flavored and strange hadrons ( , , , ϕ, , , , and ), across different multiplicity classes in proton-proton collisions (p-p) at a center-of-mass energy of TeV. Utilizing the Tsallis and Hagedorn models, parameters relevant to the bulk properties of nuclear matter were extracted. Both models exhibit good agreement with experimental data. In our analyses, we observed a consistent decrease in the effective temperature (T) for the Tsallis model and the kinetic or thermal freeze-out temperature ( ) for the Hagedorn model, as we transitioned from higher multiplicity (class-I) to lower multiplicity (class-X). This trend is attributed to the diminished energy transfer in higher multiplicity classes. Additionally, we observed that the transverse flow velocity ( ) experiences a decline from class-I to class-X. The normalization constant, which represents the multiplicity of produced particles, was observed to decrease as we moved toward higher multiplicity classes. While the effective and kinetic freeze-out temperatures, as well as the transverse flow velocity, show a mild dependency on multiplicity for lighter particles, this dependency becomes more pronounced for heavier particles. The multiplicity parameter for heavier particles was observed to be smaller than that of lighter particles, indicating a greater abundance of lighter hadrons compared to heavier ones. Various particle species were observed to undergo decoupling from the fireball at distinct temperatures: lighter particles exhibit lower temperatures, while heavier ones show higher temperatures, thereby supporting the concept of multiple freeze-out scenarios. Moreover, we identified a positive correlation between the kinetic freeze-out temperature and transverse flow velocity, a scenario where particles experience stronger collective motion at a higher freeze-out temperature. The reason for this positive correlation is that, as the multiplicity increases, more energy is transferred into the system. This increased energy causes greater excitation and pressure within the system, leading to a quick expansion.

Comparative analysis of charged particle distributions in [formula omitted] collisions at [formula omitted] using Monte Carlo models and fitting functions

We conducted a detailed analysis of charged particle transverse momentum distributions using multiple Monte Carlo models – Pythia, HIJING, and QGSJET – compared against experimental data from the ATLAS detector in pp collisions at s=0.9TeV. Pythia emerged as the best among the models under study in representing most of the distributions due to its comprehensive modeling of parton showers, multiparton interactions, and underlying event dynamics, while QGSJET showed good results with the data in some of the distributions only. HIJING, however, was only able to replicate reduced phase-space distributions only.To further explore the collision medium and to extract important information about collective properties, we used the Tsallis-Pareto (TP) type function and the modified Hagedorn (MH) function. The Tsallis function enabled determination of the effective temperature (Teff) and the non-extensivity parameter (n1) while the MH function provided the kinetic freeze-out temperature (T0), transverse flow velocity (<βT>), and a secondary non-extensivity parameter (n2). Our investigation revealed changes in the effective freeze-out parameters based on event conditions. The Teff and <βT> derived from the TP and MH functions respectively exhibited higher values with a tighter pT cut of >500MeV compared to a more inclusive pT cut of >100MeV. Interestingly, the values of the non-extensivity parameters—n1 for the Tsallis function and n2 for the MH function were almost identical across both the experimental data and all three Monte Carlo models. These findings offer invaluable perspectives on the dynamics of charged particles in pp collisions at s=0.9TeV.

Constraining primordial black hole masses through f(R) gravity scalarons in Big Bang Nucleosynthesis

Big Bang Nucleosynthesis (BBN) is a strong probe for constraining new physics including gravitation. f(R) gravity theory is an interesting alternative to general relativity which introduces additional degrees of freedom known as scalarons. In this work we demonstrate the existence of black hole solutions in f(R) gravity and develop a relation between scalaron mass and black hole mass. We have used observed bound on the freezeout temperature to constrain scalaron mass range by modifying the cosmic expansion rate at the BBN epoch. The mass range of primordial black holes (PBHs) which are astrophysical dark matter candidates is deduced. The range of scalaron mass which does not spoil the BBN era is found to be 10-16–104 eV for both relativistic and non-relativistic scalarons. The window 10-16–10-14 eV of scalaron mass obtained from solar system constraint on PPN parameter is compatible with the BBN bound derived in this work. The PBH mass range is obtained as 106–10-14 M ⊙. Scalarons constrained by BBN are also eligible to accommodate axion like dark matter particles. The problem of ultra-light PBHs (M ≤ 10-24 M ⊙) not constrained by the present study of BBN is still open. Estimation of deuterium (D) fraction and relative D+3He abundance in the f(R) gravity scenario shows that the BBN history mimics that of general relativity. While the PBH mass range is eligible for non-baryonic dark matter, the BBN bounded scalarons provide with an independent strong field test of f(R) gravity. The PBH mass range obtained in the study is discussed in relation to future astronomical measurements.

Exploring anisotropic flow via the Boltzmann transport equation employing the Tsallis blast wave description at LHC energies

Anisotropic flows i.e. azimuthal anisotropies in the particle production are one of the important probes in characterizing the properties of the strongly interacting matter created in the relativistic heavy-ion collisions. These observables are sensitive to both the transport properties as well as the equation of state of the quantum chromodynamics matter. We have adopted the Boltzmann transport equation (BTE) in the relaxation time approximation to describe the experimental data for harmonic flows such as elliptic flow (v 2), triangular flow (v 3), quadrangular flow (v 4) obtained in heavy-ion collisions at large hadron collider (LHC) energies. In this analysis, we have used Tsallis statistics as an initial distribution and the Tsallis blast wave description is used as the equilibrium distribution function while describing the evolution of the particle production in BTE. We have fitted the transverse momentum spectra, v 2, v 3, and v 4 of identified hadrons such as pion, kaon, and proton for Pb–Pb and Xe–Xe collisions at the LHC energies of sNN = 5.02 TeV and sNN = 5.44 TeV, respectively for various centralities. Our study offers the comparative analysis between the two distinct collision systems operating at comparable collision energies. The present formulation successfully fits the experimental data for p T - spectra upto p T = 8 GeV and effectively explains the anisotropic flows data upto p T = 10 GeV with a very favourable χ 2/ndf. We observe that the average transverse flow velocity (〈β〉) and the kinetic freeze-out temperature (T) extracted in our analysis decrease as we go towards the peripheral collisions. Non-extensive parameters (q AA and q pp ) exhibit an ascending trend from central to peripheral collisions, signifying an almost thermalized system in the most central collisions and a non-equilibrium state in peripheral ones. The azimuthal modulation amplitudes (ρ a ) for v 2, v 3, and v 4 exhibit an increasing pattern as one moves from the most central to peripheral collisions in both the Pb–Pb and Xe–Xe nuclei interactions.

System-size dependence of the hadronic rescattering effect at energies available at the CERN Large Hadron Collider

The first measurements of K*(892)0 resonance production as a function of charged-particle multiplicity in Xe-Xe collisions at sNN=5.44 TeV and pp collisions ats=5.02 TeV using the ALICE detector are presented. The resonance is reconstructed at midrapidity (|y| &lt; 0.5) using the hadronic decay channel K*0 →K±π∓. Measurements of transverse-momentum integrated yield, mean transverse-momentum, nuclear modification factor of K*0, and yield ratios of resonance to stable hadron (K*0/K) are compared across different collision systems (pp, p-Pb, Xe-Xe, and Pb-Pb) at similar collision energies to investigate how the production of K*0 resonances depends on the size of the system formed in these collisions. The hadronic rescattering effect is found to be independent of the size of colliding systems and mainly driven by the produced charged-particle multiplicity, which is a proxy of the volume of produced matter at the chemical freeze-out. In addition, the production yields of K*0 in Xe-Xe collisions are utilized to constrain the dependence of the kinetic freeze-out temperature on the system size using the hadron resonance gas–partial chemical equilibrium model. ©2024 CERN, for the ALICE Collaboration 2024 CERN

Exploring the hadron gas phase of relativistic heavy-ion collisions at the LHC

The lifetimes of hadronic resonances are comparable to the one of the hadron gas phase created in the late stages of high-energy nuclear collisions. Therefore, a significant fraction of resonances decay inside a high-density medium and their decay daughters rescatter with nearby hadrons destroying their initial kinematic correlations. The competing effect of resonance regeneration via pseudo-elastic interactions of hadrons interplays between the rescattering effect, modifying the measured yields and transverse-momentum spectra of hadronic resonances. These effects are studied by measuring the production yield ratio of resonances to the corresponding long-lived particle as a function of the hadronic lifetime, i.e. charged-particle multiplicity. In addition, measurements of the differential yields of resonances with different masses, quark content, and quantum numbers help in understanding particle production mechanisms, strangeness production, and parton energy loss. This article reports recent ALICE measurements on resonances and the use of the experimental input in a partial chemical equilibrium-based thermal model to constrain the kinetic freezeout temperature. This is a novel procedure that is independent of assumptions on the flow velocity profile and the freeze-out hypersurface.

Thermodynamic and hydrodynamic characteristics of interacting system formed in relativistic heavy ion collisions

To study the energy-dependent characteristics of thermodynamic and hydrodynamic parameters, based on the framework of a multi-source thermal model, we analyze the soft transverse momentum ([Formula: see text]) spectra of the charged particles ([Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and p) produced in gold–gold (Au–Au) collisions at the center-of-mass energies [Formula: see text], 11.5, 14.5, 19.6, 27, 39, 62.4, and 200[Formula: see text]GeV from the STAR Collaboration and in lead–lead (Pb–Pb) collisions at [Formula: see text] and 5.02[Formula: see text]TeV from the ALICE Collaboration. In the rest framework of emission source, the probability density function obeyed by meson momenta satisfies the Bose–Einstein distribution, and that obeyed by baryon momenta satisfies the Fermi–Dirac distribution. To simulate the [Formula: see text] of the charged particles, the kinetic freeze-out temperature T and transverse expansion velocity [Formula: see text] of emission source are introduced into the relativistic ideal gas model. Our results, based on the Monte Carlo method for numerical calculation, show a good agreement with the experimental data. The excitation functions of thermodynamic parameter T and hydrodynamic parameter [Formula: see text] are then obtained from the analyses, which shows an increasing tendency from 7.7[Formula: see text]GeV to 5.02[Formula: see text]TeV in collisions with different centralities.

Excitation function of thermal freeze-out parameters and their correlations from strange hadrons spectra in Au–Au collision at 54.4 GeV

We present a systematic study of Gold–Gold (Au–Au) collision system at 54.4 GeV conducted by the STAR Collaboration at RHIC. The transverse momentum spectra of the strange hadrons, namely KS0, Λ, Λ̄, Ξ̄+ and Ξ− are studied at mid-rapidity |y|<0.5 for seven centrality classes. We applied the blast wave model with Tsallis statistics (TBW) with two flow profiles (n0 = 1 and n0 = 2) in order to compare the results and to check the sensitivity of n0 to the freeze-out parameters. It is found that the TBW model with both the flow profiles can describe the particle spectra. In addition, the bulk properties in terms of kinetic freeze-out temperature (T0), transverse flow velocity (βT), the non-extensive parameter (q), the kinetic freeze-out volume (V), the mean transverse momentum (〈pT〉), and the multiplicity parameter (N0) are also extracted. All the parameters decrease with decreasing the event centrality, however, the non-extensive parameter q has the opposite behavior. There is an abrupt decrease seen in 0–5% to 30–40% centrality, while a slight decrease appears in 40–60% and 60–80% centrality in T0, βT, V, and 〈pT〉. On the other hand, the parameter q follows the same scenario with an opposite trend with centrality. T0 and 〈pT〉 are larger for massive particles while βT, q, V and N0 are larger for lighter particles. The larger T0 and 〈pT〉, and smaller βT, V, and q for the massive particles affirm that the heavy particles freeze-out early. Moreover, the multiple kinetic freeze-out and volume differential freeze-out scenarios are reported, as the former increase while the latter decrease with particle mass. In addition, T0, q, V, and N0 obtained from TBW model with n0 = 1 are compatible to that of n0 = 2. On the other hand, βT is slightly larger in n0 = 2, while 〈pT〉 is slightly larger in n0 = 1. Furthermore, we also reported some important correlations among the extracted parameters. Among these correlations, the positive correlation exist between T0 and βT, T0 and V, T0 and 〈pT〉, T0 and N0, βT and 〈pT〉, βT and V, βT and N0, V and N0, and 〈pT〉 and N0, while the negative correlation of T0 and q, and 〈pT〉 and q.

Centrality and System Size Dependence among Freezeout Parameters and the Implications for EOS and QGP in High-Energy Collisions.

Utilizing the Modified Hagedorn function with embedded flow, we analyze the transverse momenta (pT) and transverse mass (mT) spectra of π+ in Au-Au, Cu-Cu, and d-Au collisions at sNN = 200 GeV across various centrality bins. Our study reveals the centrality and system size dependence of key freezeout parameters, including kinetic freezeout temperature (T0), transverse flow velocity (βT), entropy-related parameter (n), and kinetic freezeout volume (V). Specifically, T0 and n increase from central to peripheral collisions, while βT and V show the opposite trend. These parameters also exhibit system size dependence; T0 and βT are smaller in larger collision systems, whereas V is larger. Importantly, central collisions correspond to a stiffer Equation of State (EOS), characterized by larger βT and smaller T0, while peripheral collisions indicate a softer EOS. These insights are crucial for understanding the properties of Quark-Gluon Plasma (QGP) and offer valuable constraints for Quantum Chromodynamics (QCD) models at high temperatures and densities.