Study of Kinetic Freeze-Out Parameters as a Function of Rapidity in pp Collisions at CERN SPS Energies

We used the blast wave model with the Boltzmann–Gibbs statistics and analyzed the experimental data measured by the 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 were π+, π−, K+, K− and p¯. We extracted the 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 the transverse flow velocity does not depend on them. Furthermore, we observed that the kinetic freeze-out volume is energy dependent, but it remains constant with changing the rapidity. We also observed that all three parameters are mass dependent. In addition, with the increase of mass, the kinetic freeze-out temperature increases, and the transverse flow velocity, as well as kinetic freeze-out volume decrease.

Effects of coalescence and isospin symmetry on the freezeout of light nuclei and their anti-particles

The transverse momentum spectra of light nuclei (deuteron, triton and helion) produced in various centrality intervals in Gold–Gold (Au–Au), Lead–Lead (Pb–Pb) and proton–Lead (p–Pb) collisions, as well as in inelastic (INEL) proton–proton (p–p) collisions are analyzed by the blast wave model with Boltzmann Gibbs statistics. The model results are nearly in agreement with the experimental data measured by STAR and ALICE Collaborations in special transverse momentum ranges. We extracted the bulk properties in terms of kinetic freezeout temperature, transverse flow velocity and freezeout volume. It is observed that deuteron and anti-deuteron freezeout later than triton and helion as well as their anti-particles due to its smaller mass, while helion and triton, and anti-helion and anti-triton freezeout at the same time due to isospin symmetry at higher energies. It is also observed that light nuclei freezeout earlier than their anti-nuclei due to the large coalescence of nucleons for light nuclei compared to their anti-nuclei. The kinetic freezeout temperature, transverse flow velocity and kinetic freezeout volume decrease from central to peripheral collisions. Furthermore, the transverse flow velocity depends on mass of the particle which decreases with increasing the mass of the particle.

Analysis of kinetic freeze-out temperature and transverse flow velocity in nucleus–nucleus and proton–proton collisions at same center-of-mass energy

Transverse momentum spectra of different types of identified charged particles in central Gold–Gold (Au–Au) collisions and inelastic (INEL) or nonsingle diffractive (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 ranges. Kinetic freeze-out (KFO) temperature and transverse flow velocity are extracted from the transverse momentum spectra of the particles. It is shown that KFO temperature of the emission source depends on mass of the particles, which reveals the mass-dependent KFO scenario in collisions at RHIC and LHC. Furthermore, the KFO temperature and transverse flow velocity in central nucleus–nucleus (AA) collisions are larger than in peripheral collisions, and both of them are slightly larger in peripheral nucleus–nucleus collisions or almost equivalent to that in proton–proton collisions at the same center-of-mass energy which shows their similar thermodynamic nature.

Analyzing Transverse Momentum Spectra of Pions, Kaons and Protons in p–p, p–A and A–A Collisions via the Blast-Wave Model with Fluctuations

The transverse momentum spectra of different types of particles, π±, K±, p and p¯, produced at mid-(pseudo)rapidity in different centrality lead–lead (Pb–Pb) collisions at 2.76 TeV; proton–lead (p–Pb) collisions at 5.02 TeV; xenon–xenon (Xe–Xe) collisions at 5.44 TeV; and proton–proton (p–p) collisions at 0.9, 2.76, 5.02, 7 and 13 TeV, were analyzed by the blast-wave model with fluctuations. With the experimental data measured by the ALICE and CMS Collaborations at the Large Hadron Collider (LHC), the kinetic freeze-out temperature, transverse flow velocity and proper time were extracted from fitting the transverse momentum spectra. In nucleus–nucleus (A–A) and proton–nucleus (p–A) collisions, the three parameters decrease with the decrease of event centrality from central to peripheral, indicating higher degrees of excitation, quicker expansion velocities and longer evolution times for central collisions. In p–p collisions, the kinetic freeze-out temperature is nearly invariant with the increase of energy, though the transverse flow velocity and proper time increase slightly, in the considered energy range.

Study of Dependence of Kinetic Freezeout Temperature on the Production Cross-Section of Particles in Various Centrality Intervals in Au–Au and Pb–Pb Collisions at High Energies

Transverse momentum spectra of π+, p, Λ, Ξ or Ξ¯+, Ω or Ω¯+ 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 are mass dependent, they decrease with the resting mass of the particles. The present work reveals the scenario of a double kinetic freezeout in nucleus–nucleus collisions. Furthermore, the kinetic freezeout temperature and freezeout volume are larger in central collisions than peripheral collisions. However, the transverse flow velocity remains almost unchanged from central to peripheral collisions.

Effects of Coalescence and Isospin Symmetry on the Freezeout of Light Nuclei and Their Anti-particles

The transverse momentum spectra of light nuclei (deuteron, triton and helion) produced in various centrality intervals in Gold-Gold (Au-Au), Lead-Lead (Pb-Pb) and proton-Lead (p-Pb) collisions, as well as in inelastic (INEL) proton-proton (pp) collisions are analyzed by the blast wave model with Boltzmann Gibbs statistics. The model results are nearly in agreement with the experimental data measured by STAR and ALICE Collaborations in special transverse momentum ranges. We extracted the bulk properties in terms of kinetic freeze-out temperature, transverse flow velocity and freezeout volume. It is observed that deuteron and anti-deuteron freezeout later than triton and helion as well as their anti-particles due to its smaller mass, while helion and tri-ton, and anti-helion and anti-triton freezeout at the same time due to isospin symmetry at higher energies. It is also observed that light nuclei freezeout earlier than their anti-nuclei due to the large coalescence of nucleons for light nuclei compared to their anti-nuclei. The kinetic freezeout temperature, transverse flow velocity and kinetic freezeout volume decrease from central to peripheral collisions. Furthermore, the transverse flow velocity depends on mass of the particle which decreases with increasing the mass of the particle.PACS: 12.40.Ee, 13.85.Hd, 25.75.Ag, 25.75.Dw, 24.10.Pa

Study of Dependence of Kinetic Freezeout Temperature on Production Cross-Section of the Particles in Various Centrality Intervals in Au-Au and Pb-Pb Collisions at High Energies

Transverse momentum spectra of +, p, Λ, Ξ or ¯Ξ+, Ω or ¯Ω+ and deuteron (d) in different centrality intervals in Gold-Gold (Au-Au) and Lead-Lead (Pb-Pb) collisions at 62.4 GeV and 2.76 TeV respectively, are analyzed by the blast wave model with Boltzmann Gibbs statistics. We extracted Kinetic freeze out 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 are mass dependent which decrease with the rest mass of the particles. The present work reveals the scenario of double kinetic freezeout in collisions at STAR and ALICE Collaborations. Furthermore, the kinetic freezeout temperature and freezeout volume are larger in central collisions than the peripheral collisions and they decrease from central to periphery. However the transverse flow velocity remains almost unchanged from central to peripheral collisions.

Study of Proton, Deuteron, and Triton at 54.4 GeV

Transverse momentum spectra of proton, deuteron, and triton in gold-gold (Au-Au) collisions at 54.4 GeV 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 STAR Collaboration in special transverse momentum ranges. We extracted the kinetic freeze-out temperature, transverse flow velocity, and freeze-out volume from the transverse momentum spectra of the particles. It is observed that the kinetic freeze-out temperature is increasing from the central to peripheral collisions. However, the transverse flow velocity and freeze-out volume decrease from the central to peripheral collisions. The present work reveals the mass dependent kinetic freeze-out scenario and volume differential freeze-out scenario in collisions at STAR Collaboration. In addition, parameter q characterizes the degree of nonequilibrium of the produced system, and it increases from the central to peripheral collisions and increases with mass .