Average transverse expansion velocities and global freeze-out temperatures in central Cu + Cu, Au + Au, and Pb + Pb collisions at high energies at RHIC and LHC

Abstract

The experimental invariant transverse momentum [Formula: see text] spectra of the charged pions and kaons, protons and antiprotons, produced at midrapidity in central (0–10%) Au[Formula: see text]Au collisions at [Formula: see text], central (0–10%) Cu[Formula: see text]Cu collisions at [Formula: see text], central (0–10%) Au[Formula: see text]Au collisions at [Formula: see text], and central (0–5%) Pb[Formula: see text]Pb collisions at [Formula: see text], measured by BRAHMS, STAR and ALICE collaborations, were analyzed using three different transverse expansion (blast-wave) models: Siemens–Rasmussen blast-wave model, Simple transverse flow model, and Simplified (hydro-inspired) blast-wave model of Schnedermann et al. Combined (simultaneous) minimum [Formula: see text] fits of the experimental invariant [Formula: see text] spectra of the charged pions and kaons, protons and antiprotons with the above three model functions were conducted, using the identical selected optimal fitting ranges in [Formula: see text] in each studied collision system, and the values of the average transverse expansion velocity [Formula: see text] and global kinetic freeze-out temperature [Formula: see text] and their dependencies on the collision system [Formula: see text] and [Formula: see text] were extracted. The combined (simultaneous) fits using Hagedorn formula with the (embedded) simple transverse flow describe well the experimental invariant [Formula: see text] spectra of the charged pions, kaons, protons and antiprotons in the whole measured range in region [Formula: see text] in the analyzed central heavy ion collisions at RHIC and LHC, reproducing qualitatively well all the established dependencies of the parameters [Formula: see text] and [Formula: see text] on the collision system [Formula: see text] and [Formula: see text]. The obtained results were compared with those of the previous analyses of high energy heavy ion collisions.

Initial- and Final-State Temperatures of Emission Source from Differential Cross-Section in Squared Momentum Transfer in High-Energy Collisions

“…The extraction of final-state temperature T 0 is more complex than that of the initial temperature T i . Generally, one may introduce the transverse flow velocity β T in the considered function and obtain T 0 and β T simultaneously [49][50][51][52][53][54][55][56][57], in which the effective temperature T no longer appears. Alternatively, the intercept in T versus m 0 is assumed to be T 0 [50,[58][59][60][61][62][63], and the slope in hp T i versus m is assumed to be β T [62][63][64][65][66], where m denotes the average energy.…”

Multiplicity Dependencies of Midrapidity Transverse Momentum Distributions of Identified Charged Particles in Proton-Proton Collisions at (s)1/2 = 7 TeV at the LHC

“…In the present work, we include the transverse flow into Equation (4) by using the transformation m t → γ t (m t − p t β t ) , as also performed in [11,15,16,21,33]. Then, Equation (4) is modified to:…”

“…We call the function in Equation ( 5) the Hagedorn function with included transverse flow in the present work. Successful analysis, using the function in Equation ( 5), of p t distributions of particles in collisions at high energies has been performed in [11,15,16,21,33]. The model represented by the function in Equation ( 5) is a powerful tool, which probes the long p t ranges of particles, allowing to compare different collision systems using few parameters [15,16,21,33].…”

“…The different transverse flow models have been incorporated into Tsallis statistics to describe the p t distributions of hadrons in high-energy heavy-ion and proton-proton collisions at the RHIC and LHC. In most cases, the Blast-Wave model with Boltzmann-Gibbs statistics (the BGBW model) [26][27][28], the Blast-Wave model with Tsallis statistics (the TBW model) [29,30], the Tsallis distribution with transverse flow effect-improved Tsallis distribution [30][31][32], and the Hagedorn formula (function) with transverse flow [11,16,21,33] have been used to estimate the kinetic freeze-out temperature and transverse expansion velocity.…”

“…However, as indicated in [34], it is not feasible to assign the physical meaning to collective properties, such as kinetic freeze-out temperature or radial transverse flow velocity, extracted from separate model fits to each particle type. The simultaneous model fits to p t distributions of various particle species in a studied collision system, performed by keeping the temperature and transverse flow velocity as the common (shared) fitted parameters for all particle species, can produce the physically meaningful collective parameters of a collision system [16,21,33,34]. The combined (global) fits have proved to be quite efficient for the extraction of collective properties and the comparison of different collision systems with the help of few parameters [16,21,33,34].…”