The kinetic Freeze Out process of a pion gas through a finite layer with time-like normal is considered. The pion gas is described by a Boltzmann gas with elastic collisions among the pions. Within this model, the impact of the in-medium pion mass modification on the Freeze Out process is studied. A marginal change of the Freeze Out variables temperature and flow velocity and an insignificant modification of the frozen out particle distribution function has been found.
Results on the pion freeze-out phase-space density in sulphur-nucleus, Pb-Pb and pion-proton collisions at CERN-SPS are presented. All heavy-ion reactions are consistent with the thermal Bose-Einstein distrtibution f=1/(exp(E/T)-1) at T~120 MeV, modified for expansion. Pion-proton data are also consistent with f, but at T~180 MeV.
Transverse momentum spectra of pion, proton, lambda, cascade, Omega and deuteron (d) in different centrality intervals in nucleus nucleus collisions at the center of mass energy are analyzed by the blast wave model with Boltzmann Gibbs statistics. We extracted the kinetic freezeout temperature, transverse flow velocity and kinetic freezeout volume from the transverse momentum spectra of the particles. It is observed that the non-strange and strange (multi strange) particles freezeout separately due to different reaction cross-sections. While the freezeout volume and transverse flow velocity ar…
We used the blast wave model with Boltzmann Gibbs statistics and analyzed the experimental data measured by NA61/SHINE Collaboration in inelastic (INEL) proton-proton collisions at different rapidity slices at different center-of-mass energies. The particles used in this study are pion, kaon, proton and anti-proton. We extracted kinetic freeze-out temperature, transverse flow velocity and kinetic freeze-out volume from the transverse momentum spectra of the particles. We observed that the kinetic freeze-out temperature is rapidity and energy dependent, while transverse flow velocity does not d…
A thermodynamically consistent excluded volume model is proposed to account for the particle multiplicities obtained from lowest SIS energies to the highest RHIC energies. The chemical freeze-out volumes lying in a slice of one unit of rapidity for pions and kaons are separately inferred from this analysis and the results are compared with the corresponding thermal freeze-out volumes obtained from the Hanbury-Brown Twiss (HBT) pion interferometry. Furthermore, we extract the variations of freeze-out number densities for pions and nucleons with the center-of-mass energy in our model and compare…
Results on the pion phase-space density at freeze-out in sulphur-nucleus, Pb-Pb and pi-p collisions at the CERN SPS are presented. All heavy-ion reactions are consistent with the thermal Bose-Einstein distribution f=1/[exp(E/T)-1] at T ~ 120 MeV, modified for radial expansion. pi-p data are also consistent with f, but at T ~ 180 MeV and without radial flow.
Transverse momentum spectra of different types of identified charged particles in central Gold-Gold (Au-Au) collisions, and inelastic (INEL) or non-single-diffrative (NSD) proton-proton (pp) collisions at the Relativistic Heavy Ion Collider (RHIC), as well as in central and peripheral Lead-Lead (Pb-Pb) collisions, and INEL or NSD pp collisions at the Large Hadron Collider (LHC) are analyzed by the blast wave model with Tsallis statistics. The model results are approximately in agreement with the experimental data measured by STAR, PHENIX and ALICE Collaborations in special transverse momentum …
The influence of the nuclear Coulomb field on transverse spectra of $π^+$ and $π^-$ measured in $Pb+Pb$ reactions at 158 A GeV has been investigated. Pion trajectories are calculated in the field of an expanding fireball. The observed enhancement of the $π^-/π^+$ ratio at small momenta depends on the temperature and transverse expansion velocity of the source, the rapidity distribution of the net positive charge, and mainly the time of the freeze-out.
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 …
Kinetic Freeze-Out Properties from Transverse Momentum Spectra of kaon, Pion, and (anti-)proton production in U+U collisions at $\sqrt{s_{NN}}$ = 193 GeV
We used the modified Hagedron function and analyzed the experimental data measured by the BRAHMS, STAR, PHENIX and ALICE Collaborations in Copper-Copper, Gold-Gold, deuteron-Gold, Lead-Lead, proton-Lead and proton-proton collisions, and extracted the related parameters (kinetic freeze-out temperature, transverse flow velocity, kinetic freeze-out volume, mean transverse momentum and initial temperature) from the transverse momentum spectra of the particles (non-strange and strange particles). We observed that all the above parameters decrease from central to peripheral collisions, except transv…
We study the HBT interferometry of ultra-relativistic nuclear collisions using a freezeout model in which free pions emerge in the course of the last binary collisions in the hadron gas. We show that the HBT correlators of both identical and non-identical pions change with respect to the case of independent pion production. Practical consequences for the design of the event generator with the built in Bose-Einstein correlations are discussed. We argue that the scheme of inclusive measurement of the HBT correlation function does not require the symmetrization of the multi-pion transition amplit…
We analyze the transverse momentum spectra of charged pions measured in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV using the Tsallis distribution modified to include transverse flow. All the spectra are well described by the modified Tsallis distribution in an extended transverse momentum range upto 6 GeV/$c$. The kinetic freeze-out temperature ($T$), average transverse flow ($β$) and degree of non thermalization ($q$) are obtained as a function of system size for both the energies. With increasing system size $β$ shows increasing trend …
In this paper we develop all the ingredients that come into play in the freeze-out of the heavy ion fireball for Au-Au collisions at $\sqrt{s_{NN}}$=200 GeV into dipions. The resonance production of particles that decay into dipions plus minijets that also decay into dipions are explored. The final state re-scattering of the pions from minijets play an important role in the mass spectrum of the cocktail. Mass shifts due to minijet interference which depend on the volume of the re-scattering pions is presented. The effective mass balance function is explained. The dipion mass spectrum within a …
Hanburry-Brown-Twiss (HBT) correlation functions and radii of negatively charged pions from C+C, Si+Si, Cu+Cu, and In+In at lower RHIC/SPS energies are calculated with the UrQMD transport model and the CRAB analyzing program. We find a minimum in the excitation function of the pion freeze-out volume at low transverse momenta and around $E_{lab}\sim 20-30A$GeV which can be related to the transition from hadronic to string matter (which might be interpreted as a pre-cursor of the QGP). The existence of the minimum is explained by the competition of two mechanisms of the particle production, reso…
We analyze the transverse momentum ($p_T$) spectra, $1/N_{ev}$[(1/2$π$$p_T$) $d^2$$N$/$dyd$$p_T$], of kaon, proton, deuteron and triton in different centrality events in gold-gold (Au-Au) collisions at Relativistic Heavy Ion Collisions (RHIC) by Hagedorn thermal model and extracted the excitation function of effective temperature, kinetic freeze-out volume, initial temperature and kinetic freeze-out temperature. We perceived that the effective temperature, initial temperature and kinetic freeze-out temperature sharply increases from 7.7 GeV to 14.5 GeV and then remain static from 14.5-39 GeV, …
We determine the decoupling surfaces for the hydrodynamic description of heavy ion collisions at RHIC and LHC by comparing the local hydrodynamic expansion rate with the microscopic pion-pion scattering rate. The pion $p_T$ spectra for nuclear collisions at RHIC and LHC are computed by applying the Cooper-Frye procedure on the dynamical-decoupling surfaces, and compared with those obtained from the constant-temperature freeze-out surfaces. Comparison with RHIC data shows that the system indeed decouples when the expansion rate becomes comparable with the pion scattering rate. The dynamical dec…
We investigate the effect of early chemical freeze-out on radial flow, elliptic flow and HBT radii by using a fully three dimensional hydrodynamic model. When we take account of the early chemical freeze-out, the space-time evolution of temperature in the hadron phase is considerably different from the conventional model in which chemical equilibrium is always assumed. As a result, we find that radial and elliptic flows are suppressed and that the lifetime and the spatial size of the fluid are reduced. We analyze the p_t spectrum, the differential elliptic flow, and the HBT radii at the RHIC e…
The transverse momentum spectra of different types of particles produced in central and peripheral gold-gold (Au-Au) and (inelastic) proton-proton ($pp$) collisions at the Relativistic Heavy Ion Collider (RHIC), as well as in central and peripheral lead-lead (Pb-Pb) and $pp$ collisions at the Large Hadron Collider (LHC) are analyzed by the standard distribution in terms of multi-component. The obtained results from the standard distribution give an approximate agreement with the measured experimental data by the STAR, PHENIX and ALICE Collaborations. The methodical behavior of the effective (k…
The space-time structure of the multipion system created in central relativistic heavy-ion collisions is investigated. Using the microscopic transport model UrQMD we determine the freeze-out hypersurface from equation on pion density n(t,r)=n_c. It turns out that for proper value of the critical energy density ε_c equation ε(t,r)=ε_c gives the same freeze-out hypersurface. It is shown that for big enough collision energies E_kin > 40A GeV/c (sqrt(s) > 8A GeV/c) the multipion system at a time moment τ ceases to be one connected unit but splits up into two separate spatial parts (drops), which m…
We have shown that recent experimental data on radial flow, both from AGS and SPS energies, are in agreement with the Equation of State (EOS) including the QCD phase transition. New hydro-kinetic model (HKM) is developed, which incorporates hydrodynamical treatment of expansion and proper kinetics of the freeze-out. We show that the freeze-out surfaces for different secondaries and different collisions are very different, and they are not at all isotherms (as was assumed in most previous hydro works). Comparison of HKM results with cascade-based event generator RQMD is also made in some detail…
We explore the possibility that dark matter is a pair of vector-like fermionic $\mathrm{SU}(2)_{\rm L}$ doublets and propose a novel mechanism of dark matter production that proceeds through the confinement of the weak sector of the Standard Model. This confinement phase causes the Standard Model doublets and dark matter to confine into pions. The dark pions freeze-out before the weak sector deconfines and generate a relic abundance of dark matter. We solve the Boltzmann equations for this scenario to determine the scale of confinement and constituent dark matter mass required to produce the o…
We used blast wave model with Tsallis statistics to analyze the experimental data measured by ALICE Collaboration in proton-proton collisions at Large Hadron Collider and extracted the related parameters (kinetic freeze-out temperature, transverse flow velocity and kinetic freeze-out volume of emission source) from transverse momentum spectra of the particles. We found that the kinetic freeze-out temperature and kinetic freeze-out volume are mass dependent. The former increase while the latter decrease with the particle mass which is the evidence of a mass as well as volume differential kineti…
Based on the data-driven analysis, the mid-rapidity transverse momentum spectra of charged hadrons produced in central and peripheral gold-gold (Au-Au) collisions from the Beam Energy Scan (BES) program at the relativistic Heavy Ion Collider (RHIC) are fitted by the blast-wave model with Boltzmann-Gibbs statistics. The model result are in agreement with the experimental data measured by the STAR Collaboration at the RHIC-BES energies. We observe that the kinetic freeze-out temperature, transverse flow velocity, mean transverse momentum, and initial temperature increase with the collision energ…
We consider a chemical freeze-out mechanism which is based on a strong medium dependence of the rates for inelastic flavor-equilibrating collisions based on the delocalization of hadronic wave functions and growing hadronic radii when approaching the chiral restoration. We investigate the role of mesonic (pion) and baryonic (nucleon) fluctuations for melting the chiral condensate in the phase diagram in the (T,mu)-plane. We apply the PNJL model beyond mean-field and present an effective generalization of the chiral perturbation theory result which accounts for the medium dependence of the pion…
Many data in the high energy physics are, in fact, sample means. It is shown that when this exact meaning of the data is taken into account and the most weakly bound states are removed from the hadron resonance gas, the acceptable fit to the whole spectra of pions, kaons and protons measured at midrapidity in central Pb-Pb collisions at $\sqrt{s_{NN}} = 2.76$ TeV [Phys.Rev.Lett.109,252301(2012)] is obtained. The invariant distributions are predicted with the help of the single-freeze-out model in the chemical equilibrium framework. Low $p_{T}$ pions and protons are reproduced simultaneously as…
A strong magnetic field influences significantly the masses of the charged light mesons. For example, the mass of charged pion increases with the magnetic field increasing. We propose this mechanism as a possible way to extract the magnitude of magnetic field at freeze-out in heavy ion collisions and thus help constrain its lifetime which is currently a major open question to resolve. Specifically we show that the ratio between the yield of charged pions and that of charged rhos is very sensitive to the magnetic field value at freeze-out. By using a viscous-hydrodynamic framework (iEBE-VISHNU)…
The effect of the continuous emission hypothesis on the two-pion Bose-Einstein correlation function is discussed and compared with the corresponding results based on the usual freeze-out. Sizeable differences in the correlation function appear in these different descriptions of the decoupling process. This means that, when extracting properties of the hot matter formed in high-energy heavy-ion collisions from the data, completely different conclusions may be reached according to the description of the particle emission process adopted.
We study the kinetic freeze out conditions of bulk hadrons in nuclear collisions. The transverse and longitudinal momentum spectra of the identified hadrons produced in central Au+Au and Pb+Pb collisions, in the beam energy range of $E_b = 2A - 158 A$ GeV are analysed for this purpose, within a generalised non boost-invariant blast wave model. The kinetic freeze out temperature is found to vary in the range of 55 - 90 MeV, whereas the average transverse velocity of collective expansion is found to be around $0.5c$ to $0.6c$. The mean longitudinal velocity of the fireball is seen to increase mo…
A new method for evaluating spectra and correlations in the hydrodynamic approach is proposed. It is based on an analysis of Boltzmann equations (BE) in terms of probabilities for constituent particles to escape from the interacting system. The conditions of applicability of Cooper-Frye freeze-out prescription are considered within the method. The results are illustrated with a non-relativistic exact solution of BE for expanding spherical fireball as well as with approximate solutions for ellipsoidally expanding ones.
The mirror twin Higgs (MTH) addresses the little hierarchy problem by relating every Standard Model (SM) particle to a twin copy, but is in tension with cosmological bounds on light degrees of freedom. Asymmetric reheating has recently been proposed as a simple way to fix MTH cosmology by diluting the twin energy density. We show that this dilution sets the stage for an interesting freeze-in scenario where both the initial absence of dark sector energy and the feeble coupling to the SM are motivated for reasons unrelated to dark matter production. We give the twin photon a Stueckelberg mass an…
We study the transverse momentum spectra of identified pions, Kaons, protons and Lambdas produced at midrapidity (0 < y < 0.5)in most central p-Pb collisions at root(sNN) = 5.02 TeV in comparison with a Unified Statistical Thermal Freeze-out Model (USTFM). The measurements of pions are reported upto pT = 3 GeV, the kaons (K- + K+) are reported upto pT = 2.5 GeV, K0s is reported upto pT = 7 GeV and the baryons (protons and Lambdas) are reported upto pT = 3.5 GeV. A good agreement is seen between the calculated results and the experimental data points taken from the ALICE experiment. The transve…
The strong longitudinal expansion of the reaction zone formed in relativistic heavy-ion collisions is found to significantly reduce the spatially averaged pion phase-space density, compared to naive estimates based on thermal distributions. This has important implications for data interpretation and leads to larger values for the extracted pion chemical potential at kinetic freeze-out.
We study the mass dependent hierarchy of kinetic freeze-out parameters of hadrons in low energy heavy-ion collisions. For this purpose, the transverse momentum and rapidity spectra of the identified hadrons produced in central Pb+Pb collisions, available at SPS energies ranging from $\rm E_{Lab}=20A-158A $ GeV, are analyzed within a generalized non boost-invariant blast wave model. We consider separate simultaneous fits for light hadrons ($π^{-}$, $K^{\pm}$) and heavy strange hadrons ($Λ$, $\barΛ$, $ϕ$, $Ξ^{\pm}$, $Ω^{\pm}$), for which the transverse momentum spectra as well as rapidity spectr…
The kinetic freeze-out for the hydrodynamical description of relativistic heavy ion collisions is discussed using a background-fluctuation splitting of the hydrodynamical fields. For a single event, the particle spectrum, or its logarithm, can be written as the sum of background part that is symmetric with respect to azimuthal rotations and longitudinal boosts and a part containing the contribution of fluctuations or deviations from the background. Using a complete orthonormal basis to characterize the initial state allows one to write the double differential harmonic flow coefficients determi…
Yields, rapidity and transverse momentum spectra of $Δ^{++}(1232)$, $Λ(1520)$, $Σ^\pm(1385)$ and the meson resonances $K^0(892)$, $Φ$, $ρ^0$ and $f_0(980)$ are predicted. Hadronic rescattering leads to a suppression of reconstructable resonances, especially at low $p_\perp$. A mass shift of the $ρ$ of 10 MeV is obtained from the microscopic simulation, due to late stage $ρ$ formation in the cooling pion gas.
We use hydrodynamics to generate freeze-out configurations for non-central heavy-ion collisions at present and future collider energies. Such collisions are known to produce strong elliptic flow. The accompanying space-time structure of the source at freeze-out is analyzed using pion interferometry. Between RHIC and LHC energies the source deformation in the transverse plane changes sign. This leaves characteristic signatures in the emission angle dependence of the HBT radii.
We investigated the strange hadrons transverse momentum ($p_T$) spectra in Au-Au collision at $\sqrt {s_{NN}}$ = 54.4 GeV in the framework of modified Hagedorn function with embedded flow. We extracted the kinetic freeze-out temperature $T_0$, transverse flow velocity $β_T$, kinetic freeze-out volume $V$, mean transverse momentum $<p_T>$, the entropy parameter $n$ and the multiplicity parameter $N_0$. We reported that all these parameters increase towards the central collisions. The larger kinetic freeze-out temperature , transverse flow velocity, kinetic freeze-out volume and the entropy para…
The thermodynamic parameters like energy density, pressure, entropy density, temperature and particle density are determined from the transverse momentum distributions of charged particles in Pb-Pb collisions at the LHC. The results show a clear increase with the centrality and the beam energy in all parameters. It is determined that in the final freeze-out stage the energy density reaches a value of about 0.039 GeV/fm$^3$ for the most central collisions at $\sqrt{s_{NN}}$ = 5.02 TeV. This is less than that at chemical freeze-out where the energy density is about 0.36 GeV/fm$^3$. This decrease…
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…
An approach, based on Tsallis non-extensive statistics, has been employed, here, to analyse, systematically, the $p_T$-spectra of various identified secondary hadrons like pions, kaons, protons and antiprotons, produced in different central $Pb+Pb$ interactions at LHC energy 2.76 TeV in terms of multiplicity and temperature fluctuations. The results, thus obtained, have been utilized to understand the various stages of different types of hadron production during evolution of the fireball produced in such collisions.
The transverse momentum spectra of identified particles at midrapidity in Pb + Pb collisions at Root(sNN) = 2.76 TeV have been studied as a function of collision centrality by using a unified statistical thermal freeze-out model. The calculated results are found to be in good agreement with the experimental data measured by the ALICE experiment at LHC. The model calculations provide the thermal freeze-out conditions in terms of the temperature and collective flow parameters for different particle species. We observe a rise in the thermal freeze-out temperature but a mild decrease in the collec…
The transverse momentum spectra of final-state light flavor particles produced in proton-proton (p-p), copper-copper (Cu-Cu), gold-gold (Au-Au), lead-lead (Pb-Pb), and proton-lead (p-Pb) collisions for different centralities at relativistic heavy ion collider (RHIC) and large hadron collider (LHC) energies are studied in the framework of a multisource thermal model. The experimental data measured by the STAR, CMS, and ALICE Collaborations are consistent with the results calculated by the multi-component Erlang distribution and Tsallis Statistics. The effective temperature and real temperature …
Transverse momentum spectra of different particles produced in mid-rapidity interval in lead-lead (Pb-Pb) collisions with different centrality intervals, measured by the ALICE Collaboration at center-of-mass energy per nucleon pair $\sqrt{s_{NN}}=2.76$ TeV, are conformably and approximately described by the Tsallis distribution. The dependences of parameters (effective temperature, entropy index, and normalization factor) on event centrality and particle rest mass are obtained. The source temperature at the kinetic freeze-out is obtained to be the intercept in the linear relation between effec…
A method to determine the kinetic freeze-out temperature in heavy-ion collisions from measured yields of short-lived resonances is presented. The resonance production is treated in the framework of thermal model with an evolution between chemical and kinetic freeze-outs. The yields of many short-lived resonances are suppressed at $T = T_{\rm kin} < T_{\rm ch}$. We determine the values of $T_{\rm kin}$ and $T_{\rm ch}$ for various centralities in Pb--Pb collisions at $\sqrt{s_{_{NN}}} = 2.76$ TeV by fitting the abundances of both the stable hadrons and the short-lived resonances such as $ρ^0$ a…
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…
Using the UrQMD/coarse graining approach we explore the kinetic freeze-out stage in central Au + Au collisions at various energies. These studies allow us to obtain detailed information on the thermodynamic properties (e.g. temperature and chemical potential) of the system during the kinetic decoupling stage. We explore five relevant collision energies in detail, ranging from $\sqrt{s_{NN}}=2.4\,\mathrm{GeV}$ (GSI-SIS) to $\sqrt{s_{NN}}=200\,\mathrm{GeV}$ (RHIC). By adopting a standard Hadron Resonance Gas equation of state, we determine the average temperature $\langle T \rangle$ and the aver…
The freeze-out of hot and dense hadronic matter formed in relativistic nuclear collisions is probed by HBT interferometry of identical pions, kaons, etc. Coulomb repulsion/attraction of positive/negative particles show up at small particle momenta and is also very sensitive to the freeze-out conditions. The source sizes and times freeze-out are extracted from $π^-/π^+$ spectra and HBT radii and compared.
A significant fraction of the changes in momentum distributions induced by dissipative phenomena in the description of the fluid fireball created in ultrarelativistic heavy-ion collisions actually take place when the fluid turns into individual particles. We study these corrections in the limit of a low freeze-out temperature of the flowing medium, and we show that they mostly affect particles with a higher velocity than the fluid. For these, we derive relations between different flow harmonics, from which the functional form of the dissipative corrections could ultimately be reconstructed fro…
We analyzed the transverse momentum spectra of proton, deuteron and triton in Boron-Boron (B-B), Oxygen-Oxygen (O-O), and Calcium-Calcium (Ca-Ca) central collisions, as well as in several centrality bins in Gold-Gold (Au-Au) collisions at 39 GeV by using the blast wave model with Tsallis statistics. The bulk properties in terms of kinetic freeze-out temperature, transverse flow velocity and kinetic freeze-out volume are extracted from the model by the least square method. We observed that with increasing the rest mass of the particle, the kinetic freeze-out temperature becomes larger, while tr…
The transverse momentum spectra at RHIC and LHC for A+A and p+p collisions are studied with Tsallis distributions in different approaches i.e. with and without radial flow. The information on the freeze-out surface in terms of freeze-out volume, temperature, chemical potential and radial flow velocities for different particle species are obtained. These parameters are found to show a systematic behavior with mass dependence. It is observed that the heavier particles freeze-out early as compared to lighter particles and freeze-out surfaces are different for different particles, which is a direc…
We discuss the $\sqrt{s}$-dependence of the $K^+/π^+$ ratio in heavy-ion collisions (the "horn" effect) within a Mott-Anderson localization model for chemical freeze-out. The different response of pion and kaon radii to the hot and dense hadronic medium results in different freeze-out conditions. We demonstrate within a simple model that this circumstance enhances the "horn" effect relative to statistical models with universal chemical freeze-out.
