Multiplicities,p T distributions and the expected hadron → quark-gluon phase transition

Extracting the speed of sound in quark-gluon plasma with ultrarelativistic lead-lead collisions at the LHC

Ultrarelativistic nuclear collisions create a strongly interacting state of hot and dense quark-gluon matter that exhibits a remarkable collective flow behavior with minimal viscous dissipation. To gain deeper insights into its intrinsic nature and fundamental degrees of freedom, we determine the speed of sound in an extended volume of quark-gluon plasma using lead-lead (PbPb) collisions at a center-of-mass energy per nucleon pair of 5.02 TeV. The data were recorded by the CMS experiment at the CERN LHC and correspond to an integrated luminosity of 0.607 nb-1. The measurement is performed by studying the multiplicity dependence of the average transverse momentum of charged particles emitted in head-on PbPb collisions. Our findings reveal that the speed of sound in this matter is nearly half the speed of light, with a squared value of0.241±0.002(stat)±0.016(syst)in natural units. The effective medium temperature, estimated using the mean transverse momentum, is219±8(syst)MeV. The measured squared speed of sound at this temperature aligns precisely with predictions from lattice quantum chromodynamic (QCD) calculations. This result provides a stringent constraint on the equation of state of the created medium and direct evidence for a deconfined QCD phase being attained in relativistic nuclear collisions.

Centrality and System Size Dependence among Freezeout Parameters and the Implications for EOS and QGP in High-Energy Collisions

Utilizing the Modified Hagedorn function with embedded flow, we analyze the transverse momenta (pT) and transverse mass (mT) spectra of π+ in Au-Au, Cu-Cu, and d-Au collisions at sNN = 200 GeV across various centrality bins. Our study reveals the centrality and system size dependence of key freezeout parameters, including kinetic freezeout temperature (T0), transverse flow velocity (βT), entropy-related parameter (n), and kinetic freezeout volume (V). Specifically, T0 and n increase from central to peripheral collisions, while βT and V show the opposite trend. These parameters also exhibit system size dependence; T0 and βT are smaller in larger collision systems, whereas V is larger. Importantly, central collisions correspond to a stiffer Equation of State (EOS), characterized by larger βT and smaller T0, while peripheral collisions indicate a softer EOS. These insights are crucial for understanding the properties of Quark-Gluon Plasma (QGP) and offer valuable constraints for Quantum Chromodynamics (QCD) models at high temperatures and densities.

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.

Some Non-Obvious Consequences of Non-Extensiveness of Entropy

Non-additive (or non-extensive) entropies have long been intensively studied and used in various fields of scientific research. This was due to the desire to describe the commonly observed quasi-power rather than the exponential nature of various distributions of the variables of interest when considered in the full available space of their variability. In this work we will concentrate on the example of high energy multiparticle production processes and will limit ourselves to only one form of non-extensive entropy, namely the Tsallis entropy. We will discuss some points not yet fully clarified and present some non-obvious consequences of non-extensiveness of entropy when applied to production processes.

Simulation Studies of Track-Based Analysis of Charged Particles in Symmetric Hadron–Hadron Collisions at 7 TeV

This manuscript presents a simulation study of a track-based analysis of the multiplicity distributions of the primary charged particle compared to experimental measurements in symmetric hadron–hadron collisions acquiring maximum energy for the new particle production. The data are compared to the simulations of EPOS, PYTHIA8, Sibyll, and QGSJET under the same conditions. The event generators in the current study are simple parton-based models that incorporate the Reggie–Gribov theory. The latter is a field theory based on the QCD that uses the mechanism of multiple parton interactions. It has been found that the PYTHIA8 model chases the data well in most of the distributions but depends on the momentum and the requirement of charged particles in a given track, due to its feature-like color reshuffling of quarks and gluons through the color re-connection modes and initial and final state radiations by incorporating the parton showers. The EPOS model could also reproduce some spectral regions and presents a good comparison after the PYTHIA8. All the other models could not produce most of the spectra except for the limited region, which also depends on the analysis’s cuts. Besides the model’s prediction, we used Tsallis–Pareto and Hagedorn functions to fit the aforementioned spectra of the charged particles. The fit is applied to the data and models, and their results are compared. We extract the temperature parameter T01 (effective temperature (Teff)) from the Tsallis–Pareto-kind function and T02 (kinetic freezeout temperature) from the Hagedorn function. The temperatures are affected by pT as well Nch cuts.

Study of Bulk Properties of Strange Particles in Au+Au Collisions at sNN = 54.4 GeV

We analyzed the transverse momentum pT spectra of various strange hadrons KS0, Λ(Λ¯) and Ξ-(Ξ¯+) at mid-rapidity (y) in different centrality intervals from Au+Au collisions at sNN= 54.4 GeV. The pT spectra of these strange hadrons are investigated by the Tsallis-like distribution, which satisfactorily fits the experimental data. The bulk properties of the medium produced in ultra-relativistic heavy-ion collisions at the kinetic freeze-out are reflected by measuring the hadron spectra. The effective temperature T, transverse flow velocity βT, and mean pT along with other parameters that are strongly dependent on centrality and particle specie are extracted. The effective temperature of multi-strange particle (Ξ-(Ξ¯+)) is larger as compared to singly-strange particles Λ(Λ¯) and KS0. Furthermore, the kinetic freeze-out temperature T, transverse flow velocity βT. and mean pT (⟨pT⟩) show a decreasing trend towards lower centrality, while the entropy parameter q increases from central to peripheral collisions. In addition, a positive correlation of ⟨pT⟩ and T and a negative correlation of q and T are also reported.

Pseudorapidity dependence of the bulk properties of hadronic medium in pp collisions at 7 TeV

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The EPOS–LHC model underpredicts the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_T$$\end{document}pT spectra from 0.1 to 2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {GeV/}c$$\end{document}GeV/c in all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}η bins for about 20% and the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_T$$\end{document}pT spectrum from 0.1 to 4.2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {GeV/}c$$\end{document}GeV/c for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|$$\end{document}|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|$$\end{document}| < 2.4 by about 15% while reasonably predicts well for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_T$$\end{document}pT > 4.2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {GeV/}c$$\end{document}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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi ^2/ndf$$\end{document}χ2/ndf show that the functions fit the data and simulation results well. The parameter extracted by the functions: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _T$$\end{document}βT, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_0$$\end{document}T0, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{eff}$$\end{document}Teff decreases with increasing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}η. The decrease in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _T$$\end{document}βT with increasing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_0$$\end{document}T0 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{eff}$$\end{document}Teff. The values of the fit constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_0$$\end{document}N0 increase with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}η where the values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_0$$\end{document}N0 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.

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

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.

Excitation Function of Kinetic Freeze-Out Parameters at 6.3, 17.3, 31, 900 and 7000 GeV

The transverse momentum spectra of π+ (π−)(π++π−) at 6.3, 17.3, 31, 900 and 7000 GeV are analyzed by the blast-wave model with Tsallis statistics (TBW) in proton-proton collisions. We took the value of flow profile n0 = 1 and 2 in order to see the difference in the results of the extracted parameters in the two cases. Different rapidity slices at 31 GeV are also analyzed, and the values of the related parameters, such as kinetic freeze-out temperature, transverse flow velocity and kinetic freeze-out volume, are obtained. The above parameters rise with the increase of collision energy, while at 31 GeV, they decrease with increasing rapidity, except for the kinetic freeze-out volume, which increases. We also extracted the parameter q, which is an entropy-based parameter, and its rising trend is noticed with increasing collision energy, while at 31 GeV, no specific dependence of q is observed on rapidity. In addition, the multiplicity parameter N0 and mean transverse momentum are extracted, which increase with increasing collision energy and decrease with increasing rapidity. We notice that the kinetic freeze-out temperature and mean transverse momentum are slightly larger with n0 = 2, while the transverse flow velocity is larger in the case of n0 = 1, but the difference is very small and hence insignificant.

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.

Fractal Structures of Yang–Mills Fields and Non-Extensive Statistics: Applications to High Energy Physics

In this work, we provide an overview of the recent investigations on the non-extensive Tsallis statistics and its applications to high energy physics and astrophysics, including physics at the Large Hadron Collider (LHC), hadron physics, and neutron stars. We review some recent investigations on the power-law distributions arising in high energy physics experiments focusing on a thermodynamic description of the system formed, which could explain the power-law behavior. The possible connections with a fractal structure of hadrons is also discussed. The main objective of the present work is to delineate the state-of-the-art of those studies and show some open issues that deserve more careful investigation. We propose several possibilities to test the theory through analyses of experimental data.

Similarities in Multiparticle Production Processes in pp Collisions as Imprints of Nonextensive Statistics

The transverse momentum pT spectra of both hadrons and jets produced in pp collisions at beam energies from hundreds GeV to a few TeV exhibit power-law behavior of 1/pTn at high pT, with similar power indices n. The respective nonextensivity parameters for transverse momenta distributions and the global nonextensivity parameter obtained from multiplicities are compared. In particular, data on kaon to pion (charged particles) multiplicity ratio are analyzed, assuming that the reaction occurs in some nonextensive environment. The values of the corresponding nonextensivity parameters were found to be similar, strongly indicating the existence of a common mechanism behind all these observables.

Kinetic Freeze-Out Properties from Transverse Momentum Spectra of Pions in High Energy Proton-Proton Collisions

Transverse momentum spectra of negative and positive pions produced at mid-(pseudo)rapidity in inelastic or non-single-diffractive proton-proton collisions over a center-of-mass energy, s , range from a few GeV to above 10 TeV are analyzed by the blast-wave fit with Boltzmann (Tsallis) distribution. The blast-wave fit results are well fitting to the experimental data measured by several collaborations. In a particular superposition with Hagedorn function, both the excitation functions of kinetic freeze-out temperature ( T 0 ) of emission source and transverse flow velocity ( β T ) of produced particles obtained from a given selection in the blast-wave fit with Boltzmann distribution have a hill at s ≈ 10 GeV, a drop at dozens of GeV, and then an increase from dozens of GeV to above 10 TeV. However, both the excitation functions of T 0 and β T obtained in the blast-wave fit with Tsallis distribution do not show such a complex structure, but a very low hill. In another selection for the parameters or in the superposition with the usual step function, T 0 and β T increase generally quickly from a few GeV to about 10 GeV and then slightly at above 10 GeV, there is no such the complex structure, when also studying nucleus-nucleus collisions.

Aspects of Relativistic Heavy-Ion Collisions

The rapid thermalization of quarks and gluons in the initial stages of relativistic heavy-ion collisions is treated using analytic solutions of a nonlinear diffusion equation with schematic initial conditions, and for gluons with boundary conditions at the singularity. On a similarly short time scale of t ≤ 1 fm/c, the stopping of baryons is accounted for through a QCD-inspired approach based on the parton distribution functions of valence quarks, and gluons. Charged-hadron production is considered phenomenologically using a linear relativistic diffusion model with two fragmentation sources, and a central gluonic source that rises with ln 3 ( s N N ) . The limiting-fragmentation conjecture that agrees with data at energies reached at the Relativistic Heavy-Ion Collider (RHIC) is found to be consistent with Large Hadron Collider (LHC) data for Pb-Pb at s N N = 2.76 and 5.02 TeV. Quarkonia are used as hard probes for the properties of the quark-gluon plasma (QGP) through a comparison of theoretical predictions with recent CMS, ALICE and LHCb data for Pb-Pb and p-Pb collisions.

Hadron Spectra Parameters within the Non-Extensive Approach

We investigate how the non-extensive approach works in high-energy physics. Transverse momentum ( p T ) spectra of several hadrons are fitted by various non-extensive momentum distributions and by the Boltzmann–Gibbs statistics. It is shown that some non-extensive distributions can be transferred one into another. We find explicit hadron mass and center-of-mass energy scaling both in the temperature and in the non-extensive parameter, q, in proton–proton and heavy-ion collisions. We find that the temperature depends linearly, but the Tsallis q follows a logarithmic dependence on the collision energy in proton–proton collisions. In the nucleus–nucleus collisions, on the other hand, T and q correlate linearly, as was predicted in our previous work.

Atmospheric Muons Measured with IceCube

IceCube is a cubic-kilometer Cherenkov detector in the deep ice at the geographic South Pole. The dominant event yield is produced by penetrating atmospheric muons with energies above several 100 GeV. Due to its large detector volume, IceCube provides unique opportunities to study atmospheric muons with large statistics in detail. Measurements of the energy spectrum and the lateral separation distribution of muons offer insights into hadronic interactions during the air shower development and can be used to test hadronic models. We will present an overview of various measurements of atmospheric muons in IceCube, including the energy spectrum of muons between 10 TeV and 1 PeV. This is used to derive an estimate of the prompt contribution of muons, originating from the decay of heavy (mainly charmed) hadrons and unflavored mesons. We will also present measurements of the lateral separation distributions of TeV muons between 150m and 450m for several initial cosmic ray energies between 1 PeV and 16 PeV. Finally, the angular distribution of atmospheric muons in IceCube will be discussed.

Testing nonextensive statistics in relativistic heavy-ion collisions

Numerical solutions of the nonlinear Fokker-Planck equation (FPE) which has been associated with nonextensive q-statistics show that the available data on rapidity distributions for stopping in relativistic heavy-ion collisions cannot be reproduced with any permitted value of the nonextensivity parameter (1 < q < 1.5). This casts doubt on the nonextensivity concept that is widely used in relativistic heavy-ion physics.

Describing phase transitions in field theory by self-similar approximants

Self-similar approximation theory is shown to be a powerful tool for describing phase transitions in quantum field theory. Self-similar approximants present the extrapolation of asymptotic series in powers of small variables to the arbitrary values of the latter, including the variables tending to infinity. The approach is illustrated by considering three problems: (i) The influence of the coupling parameter strength on the critical temperature of the O(N)-symmetric multicomponent field theory. (ii) The calculation of critical exponents for the phase transition in the O(N)-symmetric field theory. (iii) The evaluation of deconfinement temperature in quantum chromodynamics. The results are in good agreement with the available numerical calculations, such as Monte Carlo simulations, Padé-Borel summation, and lattice data.

Generalized statistical mechanics of cosmic rays: Application to positron-electron spectral indices

Cosmic ray energy spectra exhibit power law distributions over many orders of magnitude that are very well described by the predictions of q-generalized statistical mechanics, based on a q-generalized Hagedorn theory for transverse momentum spectra and hard QCD scattering processes. QCD at largest center of mass energies predicts the entropic index to be [Formula: see text]. Here we show that the escort duality of the nonextensive thermodynamic formalism predicts an energy split of effective temperature given by Δ [Formula: see text] MeV, where T H is the Hagedorn temperature. We carefully analyse the measured data of the AMS-02 collaboration and provide evidence that the predicted temperature split is indeed observed, leading to a different energy dependence of the e+ and e- spectral indices. We also observe a distinguished energy scale E* ≈ 50 GeV where the e+ and e- spectral indices differ the most. Linear combinations of the escort and non-escort q-generalized canonical distributions yield excellent agreement with the measured AMS-02 data in the entire energy range.

Energy dependence of the transverse momentum distributions of charged particles in pp collisions measured by ALICE

Differential cross sections of charged particles in inelastic pp collisions as a function of p_T have been measured at [Formula: see text] at the LHC. The p_T spectra are compared to NLO-pQCD calculations. Though the differential cross section for an individual [Formula: see text] cannot be described by NLO-pQCD, the relative increase of cross section with [Formula: see text] is in agreement with NLO-pQCD. Based on these measurements and observations, procedures are discussed to construct pp reference spectra at [Formula: see text] up to p_T=50 GeV/c as required for the calculation of the nuclear modification factor in nucleus-nucleus and proton-nucleus collisions.