Transverse momentum spectra of π ⁺ , K ⁺ , p , K S 0 , Λ, Ξ or Ξ ̄ + and Ω or Ω ̄ + or Ω + Ω ̄ in copper–copper (Cu–Cu), gold–gold (Au–Au) and lead–lead (Pb–Pb) collisions at 200 GeV, 62.4 GeV and 2.76 TeV respectively, are analyzed in different centrality bins by the blast wave model with Tsallis statistics. The model results are approximately in agreement with the experimental data measured by BRAHMS, STAR and ALICE Collaborations in special transverse momentum ranges. Kinetic freeze out temperature, transverse flow velocity and kinetic freezeout volume are extracted from the transverse momentum spectra of the particles. It is observed that Ξ ̄ + and Ω or Ω ̄ + or Ω + Ω ̄ have larger kinetic freezeout temperature followed by K ⁺ , K S 0 and Λ than π ⁺ and p due to smaller reaction cross-sections of multi-strange and strange particles than non-strange particles. The present work reveals the scenario of triple kinetic freezeout in collisions at BRAHMS, STAR and ALICE Collaborations, however the transverse flow velocity and kinetic freezeout volume are mass dependent and they decrease with the increasing rest mass of the particle. In addition, the kinetic freezeout temperature, transverse flow velocity and kinetic freezeout volume are decreasing from central to peripheral collisions while the parameter q increase from central to peripheral collisions, indicating the approach of quick equilibrium in the central collisions. Besides, the kinetic freezeout temperature and kinetic freezeout volume are observed to be larger in larger collision system which shows its dependence on the size of the interacting system, while transverse flow velocity increase with increasing energy.

By using the method of data-driven reanalysis, the midrapidity transverse momentum pT spectra of charged hadrons (π+, K+, and p) 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 using the blast-wave model with the Boltzmann-Gibbs statistics. The model results 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 T0, transverse flow velocity βT, mean transverse momentum pT, and initial temperature Ti increase with collision energy as well as with event centrality.

The measured charged particle $$p_T$$p T spectra in proton-proton collisions obtained by the CMS experiment at CERN is compared with the simulation results of EPOS–LHC and Pythia8.24 models at 7 TeV center-of-mass energy. The Pythia8.24 model describes the experimental data very well, particularly in the high $$p_T$$p T region. The model also predicts the $$p_T$$p T spectra for $$|$$| $$\eta $$η $$|$$| < 2.4 at 0 $$\le $$≤ $$p_T$$p T $$\le $$≤ 6 $$\text {GeV/}c$$GeV/ c . The EPOS–LHC model underpredicts the $$p_T$$p T spectra from 0.1 to 2 $$\text {GeV/}c$$GeV/ c in all $$\eta $$η bins for about 20% and the $$p_T$$p T spectrum from 0.1 to 4.2 $$\text {GeV/}c$$GeV/ c for $$|$$| $$\eta $$η $$|$$| < 2.4 by about 15% while reasonably predicts well for $$p_T$$p T > 4.2 $$\text {GeV/}c$$GeV/ c within the experimental errors. Furthermore, to get information about collective properties of the hadronic matter, modified Hagedorn function with embedded transverse flow velocity and thermodynamically consistent Tsallis distribution functions are used to fit the experimental data and simulated results. The values of $$\chi ^2/ndf$$χ 2 / n d f show that the functions fit the data and simulation results well. The parameter extracted by the functions: $$\beta _T$$β T , $$T_0$$T 0 , and $$T_{eff}$$T eff decreases with increasing $$\eta $$η . The decrease in $$\beta _T$$β T with increasing $$\eta $$η is due to the large energy deposition in lower rapidity bins producing rapid expansion due to large pressure gradient resulting quick expansion of the fireball. Similarly, large energy transfer in the lower pseudo-rapidity bin results in higher degree of excitation of the system which results larger values of $$T_0$$T 0 and $$T_{eff}$$T eff . The values of the fit constant $$N_0$$N 0 increase with $$\eta $$η where the values of $$N_0$$N 0 extracted from Pythia8.24 are closer to the data than the EPOS–LHC model. The Pythia8.24 model has better prediction than the EPOS–LHC model which might be connected to its flow-like features and color re-connections resulting from different Parton interactions in the initial and final state.