Rapidity and Energy Dependencies of Temperatures and Volume Extracted from Identified Charged Hadron Spectra in Proton-Proton Collisions at a Super Proton Synchrotron (SPS).

The standard (Bose-Einstein/Fermi-Dirac, or Maxwell-Boltzmann) distribution from the relativistic ideal gas model is used to study the transverse momentum (pT) spectra of identified charged hadrons (π-, π+, K-, K+, p¯, and p) with different rapidities produced in inelastic proton-proton (pp) collisions at a Super Proton Synchrotron (SPS). The experimental data measured using the NA61/SHINE Collaboration at the center-of-mass (c.m.) energies s=6.3, 7.7, 8.8, 12.3, and 17.3 GeV are fitted well with the distribution. It is shown that the effective temperature (Teff or T), kinetic freeze-out temperature (T0), and initial temperature (Ti) decrease with the increase in rapidity and increase with the increase in c.m. energy. The kinetic freeze-out volume (V) extracted from the π-, π+, K-, K+, and p¯ spectra decreases with the rapidity and increase with the c.m. energy. The opposite tendency of V, extracted from the p spectra, is observed to be increasing with the rapidity and decreasing with the c.m. energy due to the effect of leading protons.

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.

Excitation Functions of Tsallis-Like Parameters in High-Energy Nucleus-Nucleus Collisions.

The transverse momentum spectra of charged pions, kaons, and protons produced at mid-rapidity in central nucleus-nucleus (AA) collisions at high energies are analyzed by considering particles to be created from two participant partons, which are assumed to be contributors from the collision system. Each participant (contributor) parton is assumed to contribute to the transverse momentum by a Tsallis-like function. The contributions of the two participant partons are regarded as the two components of transverse momentum of the identified particle. The experimental data measured in high-energy AA collisions by international collaborations are studied. The excitation functions of kinetic freeze-out temperature and transverse flow velocity are extracted. The two parameters increase quickly from ≈3 to ≈10 GeV (exactly from 2.7 to 7.7 GeV) and then slowly at above 10 GeV with the increase of collision energy. In particular, there is a plateau from near 10 GeV to 200 GeV in the excitation function of kinetic freeze-out temperature.

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.