Abstract
Dependencies of midrapidity pt distributions of the charged pions and kaons, protons and antiprotons on charged-particle multiplicity density (<dNch/dη>) in inelastic proton-proton collisions at (s)1/2 = 7 TeV at the LHC, measured by ALICE Collaboration, are investigated. The simultaneous minimum χ2 fits with the Tsallis function with thermodynamical consistence and the Hagedorn function with included transverse flow have well-described the pt spectra of the particle species in the ten studied groups of charged-particle multiplicity density. The effective temperatures, T, of the Tsallis function with thermodynamical consistence have shown a steady rise with increasing the charged-particle multiplicity in proton-proton collisions at (s)1/2 = 7 TeV, in agreement with the similar result obtained recently in proton-proton collisions at (s)1/2 = 13 TeV at the LHC. The respective T versus <dNch/dη> dependence in proton-proton collisions at (s)1/2 = 7 TeV is reproduced quite well by the simple power function with the same value (≈ 1/3) of the exponent parameter as that extracted in proton-proton collisions at (s)1/2 = 13 TeV. The identical power dependence T~ε1/3 between the initial energy density and effective temperature of the system has been observed in proton-proton collisions at (s)1/2 = 7 and 13 TeV. We have observed that the transverse radial flow emerges at <dNch/dη> ≈ 6 and then increases, becoming substantial at larger multiplicity events in proton-proton collisions at (s)1/2 = 7 TeV. We have estimated, analyzing T0 and ⟨βt⟩ versus <dNch/dη> dependencies, that the possible onset of deconfinement phase transition in proton-proton collisions at (s)1/2 = 7 TeV occurs at <dNch/dη> ≈ 6.1 ± 0.3, which is close to the corresponding recent estimate (<dNch/dη> ≈ 7.1 ± 0.2) in proton-proton collisions at (s)1/2 = 13 TeV. The corresponding critical energy densities for probable onset of deconfinement phase transition in proton-proton collisions at (s)1/2 = 7 and 13 TeV at the LHC have been estimated to be 0.67 ± 0.03 and 0.76 ± 0.02 GeV/fm3, respectively.
Highlights
The widespread use [1–25] of the Tsallis distribution function in high-energy protonproton collisions is explained by its very good parameterization of the experimental pt spectra of hadrons with just a few parameters: the first one—effective temperature (T), the second one—parameter of non-extensivity, q, which accounts for deviation of pt distribution from the Boltzmann–Gibbs exponential distribution, and the third parameter—the fitting constant, assumed to be proportional to the system volume
The different transverse flow models have been incorporated into Tsallis statistics to describe the pt distributions of hadrons in high-energy heavy-ion and proton-proton collisions at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC)
We have studied the change of collective characteristics of the collision system with varying through combined minimum χ2 model fits of pt distributions of identified charged particles, using the Tsallis distribution function with thermodynamical consistence and the Hagedorn function with included transverse flow
Summary
The widespread use [1–25] of the Tsallis distribution function in high-energy protonproton collisions is explained by its very good parameterization of the experimental pt spectra of hadrons with just a few parameters: the first one—effective temperature (T), the second one—parameter of non-extensivity, q, which accounts for deviation of pt distribution from the Boltzmann–Gibbs exponential distribution, and the third parameter—the fitting constant, assumed to be proportional to the system volume. There are various modifications of the Tsallis function, which have welldescribed the pt distributions of final hadrons in proton-proton collisions up to the largest available pt values at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) experiments [3–10,15]. The non-extensivity parameter, q, of the Tsallis function has shown quite noticeable sensitivity to the large pt region (pt > 3 GeV/c) of the invariant pt distributions of hadrons, suggesting the necessity of analyzing the longer pt intervals for extracting the more correct q values [22–24]. The different transverse flow models have been incorporated into Tsallis statistics to describe the pt distributions of hadrons in high-energy heavy-ion and proton-proton collisions at the RHIC and LHC. The Blast-Wave model with Boltzmann–Gibbs statistics (the BGBW model) [26–28], the Blast-Wave model with Tsallis statistics (the TBW model) [29,30], the Tsallis distribution with transverse flow effect—improved Tsallis distribution [30–32], and the Hagedorn formula (function) with transverse flow [11,16,21,33]
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