Hadron yields in high energy heavy ion collisions have been fitted and reproduced by thermal models using standard statistical distributions. These models give insight into the freeze-out conditions at varying beam energies. In this paper we investigate changes to this analysis when the statistical distributions are replaced by Tsallis distributions for hadrons. We investigate the appearance of near-thermal equilibrium state at SPS and RHIC energies. We obtain better fits with smaller chi^2 for the same hadron data, as applied earlier in the thermal fits for SPS energies but not for RHIC energies. This result indicates that at RHIC energies the final state is very well described by a single freeze-out temperature with very little room for fluctuations.
The transverse momentum $(p_T)$ spectra of charged particles measured in Au + Au collisions from the beam energy scan (BES) program, Cu + Cu collisions at $\sqrt{s_{NN}}=62.4$, 200 GeV at the RHIC and Pb + Pb, Xe + Xe collisions at the LHC are investigated in the framework of Tsallis thermodynamics. The theory can describe the experimental data well for all the collision systems, energies and centralities investigated. The collision energy and centrality dependence of the Tsallis distribution parameters, i.e., the temperature $T$ and the nonextensive parameter $q$, for the \mbox{A + A} collisi…
Nonextensive statistics has attracted attention as a description of particle spectra in nuclear collisions at QCD energies. First, we construct the equation of state by incorporating Tsallis statistics based on the hadron resonance gas and parton gas models. Thermodynamic conditions are found to impose constraints on the $q$-parameter of Tsallis distribution. Next, we apply the equation of state to the relativistic hydrodynamic modeling of nuclear collisions. The Cooper-Frye prescription is consistently modified. Numerical demonstrations indicate that the model may describe charged particle sp…
The thermodynamic properties of matter created in high-energy heavy-ion collisions have been studied in the framework of the non-extensive Tsallis statistics. The transverse momentum ($p_{\rm T}$)~spectra of identified charged particles (pions, kaons, protons) and all charged particles from the available experimental data of Au-Au collisions at the Relativistic Heavy Ion Collider (RHIC) energies and Pb-Pb collisions at the Large Hadron Collider (LHC) energies are fitted by the Tsallis distribution. The fit parameters, $q$ and $T$ measure the degree of deviation from an equilibrium state and th…
The Tsallis distribution has been used recently to fit the transverse momentum distributions of identified particles by the STAR and PHENIX collaborations at the Relativistic Heavy Ion Collider and by the ALICE and CMS collaborations at the Large Hadron Collider. Theoretical issues are clarified concerning the thermodynamic consistency of the Tsallis distribution in the particular case of relativistic high energy quantum distributions. An improved form is proposed for describing the transverse momentum distribution and fits are presented together with estimates of the parameter $q$ and the tem…
We obtain within Fokker-Planck dynamics an explicit generalization of Einstein's relation between drag, diffusion and equilibrium distribution for a spatially homogeneous system, considering both the transverse and longitudinal diffusion for dimension n>1. We then provide a complete characterization of when the equilibrium distribution becomes a Boltzmann/J"uttner distribution, and when it satisfies the more general Tsallis distribution. We apply this analysis to recent calculations of drag and diffusion of a charm quark in a thermal plasma, and show that only a Tsallis distribution describes …
We present a study of transverse momentum ($p_{T}$) spectra of unidentified charged particles in pp collisions at RHIC and LHC energies from $\sqrt{s}$ = 62.4 GeV to 13 TeV using Tsallis/Hagedorn function. The power law of Tsallis/Hagedorn form gives excellent description of the hadron spectra in $p_{T}$ range from 0.2 to 300 GeV/$c$. The power index $n$ of the $p_T$ distributions is found to follow a function of the type $a+b/\sqrt {s}$ with asymptotic value $a = 5.72$. The parameter $T$ governing the soft bulk contribution to the spectra remains almost same over wide range of collision energ…
We consider the Tsallis distribution as the source of the apparent slope of one-particle spectra in heavy-ion collisions and investigate the equation of state of this special quark matter in the framework of non-extensive thermodynamics.
The Tsallis distribution has been used recently to fit the transverse momentum distributions of identified particles by the STAR collaboration \cite{Abelev:2006cs} at the Relativistic Heavy Ion Collider and by the ALICE \cite{Aamodt:2011zj} and CMS \cite{Khachatryan:2011tm} collaborations at the Large Hadron Collider. Theoretical issues are clarified concerning the thermodynamic consistency of the Tsallis distribution in the particular case of relativistic high energy quantum distributions. An improved form is proposed for describing the transverse momentum distribution and fits are presented …
We have implemented the Tsallis q-statistics in the Weibull model of particle production known as the q-Weibull distribution to describe the transverse-momentum (pT ) distribution of the charged hadrons at mid-rapidity measured at RHIC and LHC energies. The model describes the data remarkably well for the entire pT range measured in nucleus-nucleus and nucleon-nucleon collisions. The proposed distribution is based on the non-extensive Tsallis q-statistics which replaces the usual thermal equilibrium assumption of hydrodynamical models. The parameters of the distribution can be related to the v…
In this paper, the experimental (simulated) transverse momentum spectra of negatively charged pions produced at mid-rapidity in central nucleus-nucleus collisions at the Heavy Ion Synchrotron (SIS), Relativistic Heavy Ion Collider (RHIC), and Large Hadron Collider (LHC) energies obtained by different collaborations are selected by us to investigate, where a few simulated data are taken from the results of FOPI Collaboration who uses the IQMD transport code based on Quantum Molecular Dynamics. A two-component standard distribution and the Tsallis form of standard distribution are used to fit th…
We explore a hadron resonance gas model using Tsallis non-extensive distribution to study the energy dependence of the product of the moments, $Sσ$ and $κσ^2$ of net-proton multiplicity distributions of published STAR data in \auau collisions at relativistic heavy-ion collider (RHIC) energies. While excellent agreements are found between model predictions and measurements of $Sσ$ and $κσ^2$ of most peripheral collisions and $Sσ$ of most central collisions, the $κσ^2$ for most central collisions deviates significantly from the predictions particularly at \sqsn = 19.6 GeV and $27$ GeV. This coul…
The latest, high-accuracy identified hadron spectra measurements in high-energy nuclear collisions led us to the investigation of the strongly interacting particles and collective effects in small systems. Since microscopical processes result in a statistical Tsallis-Pareto distribution, the fit parameters $q$ and $T$ are well suited for identifying system size scalings and initial conditions. Moreover, parameter values provide information on the deviation from the extensive, Boltzmann-Gibbs statistics in finite-volumes. We apply here the fit procedure developed in our earlier study for proton…
Experimental results of the transverse momentum distributions of phi mesons and $Ω$ hyperons produced in gold-gold (Au-Au) collisions with different centrality intervals, measured by the STAR Collaboration at different energies (7.7, 11.5, 19.6, 27, and 39 GeV) in the beam energy scan (BES) program at the relativistic heavy ion collider (RHIC), are approximately described by the single Erlang distribution and the two-component Schwinger mechanism. Meanwhile, the STAR experimental transverse momentum distributions of negatively charged particles, produced in Au-Au collisions at RHIC BES energie…
Results related to the possible chemical equilibration of hadrons in heavy ion collisions are reviewed. Overall the evidence is very strong with a few clear and well-documented deviations, especially concerning multi-strange hadrons. Two effects are considered in some detail. Firstly, the neglect of (possibly an infinite number) of heavy resonances is investigated with the help of the Hagedorn model. Secondly, possible deviations from the standard statistical distributions are investigated by considering in detail results obtained using the Tsallis distribution.
The speed of sound ($c_s$) is studied to understand the hydrodynamical evolution of the matter created in heavy-ion collisions. The quark-gluon plasma (QGP) formed in heavy-ion collisions evolves from an initial QGP to the hadronic phase via a possible mixed phase. Due to the system expansion in a first order phase transition scenario, the speed of sound reduces to zero as the specific heat diverges. We study the speed of sound for systems, which deviate from a thermalized Boltzmann distribution using non-extensive Tsallis statistics. In the present work, we calculate the speed of sound as a f…
The transverse momentum ($p_{T}$) distribution of strange hadrons ($K_{S}^{0}$ and $Λ$) and multi-strange hadrons( $Ξ$ and $Ω$) measured in p$-$p, p$-$Pb, and Pb$-$Pb collisions at LHC energies have been studied for different multiplicity classes using Tsallis-Weibull (or q$-$Weibull)formalism. The distribution describes the measured $p_{T}$ spectra for all multiplicity (or centrality)classes. The multiplicity dependence of the extracted parameters are studied for the mentioned collisions systems. The $λ$ parameter was observed to increase systematically with the collision multiplicity and fol…
The experimental data from the RHIC and LHC experiments of invariant pT spectra in A+A and p + p collisions are analysed with Tsallis distributions in different approaches. The information about the freeze-out surface in terms of freeze-out volume, temperature, chemical potential and radial flow velocity for different particle species are obtained. Further, these parameters are studied as a function of the mass of the secondary particles. A mass-dependent differential freeze-out is observed which does not seem to distinguish between particles and their antiparticles. Further a mass-hierarchy i…
We demonstrate that charged pion spectra in central and peripheral PbPb collisions at $\sqrt{s}$ = 2.76 ATeV obtained via perturbative quantum chromodynamics improved parton model calculations [17] can be approximated by the Tsallis distribution for transverse momenta $p_T \geq$ 4 GeV/c. Then, we propose a model in which, hadrons produced in heavy-ion collisions stem either from "soft" or "hard" processes, and are distributed according to the Tsallis distribution in both types of yields. We describe transverse spectra as well as azimuthal anisotropy ($v_2$) of charged hadrons stemming from var…
We present a model for radiative energy loss of heavy quarks in quark gluon plasma which incorporates coherence effects. We then study its consequences on the radiation spectra as well as on the nuclear modification factor of open heavy mesons produced in ultrarelativistic heavy ion collisions.
The estimate based on the parton model is made on the rate of production of Super Heavy Particle ( SHP ) in subthreshold collision of heavy ions at LHC. For the one month run of lead-lead collision the yield of 16 TeV particle is of the order of 70 per year.
Some recent experimental results obtained in collisions of heavy nuclei ($\sqrt{s}=200$ GeV) at BNL Relativistic Heavy-Ion Collider (RHIC) are discussed. The probes of dense matter created in heavy-ion collision by quarkonia, $D$ and $B$ mesons containing heavy charm and beauty quarks are considered. The centrality, rapidity and transverse momentum dependences of the nuclear modification factor and elliptic flow coefficient are presented and their possible theoretical interpretation is provided.
We review from the point of view of nonextensive statistics the ubiquitous presence in elementary and heavy-ion collisions of power-law distributions. Special emphasis is placed on the conjecture that this is just a reflection of some intrinsic fluctuations existing in the hadronic systems considered. These systems summarily described by a single parameter q playing the role of a nonextensivity measure in the nonextensive statistical models based on Tsallis entropy.
We review various production mechanisms of photons and small mass dileptons at large transverse momentum in heavy ion collisions at the LHC. Their relevance as a signal for quark-gluon plasma formation is discussed.
A simple geometrical model (often quoted in literature as the Glauber model) of heavy ion collisions is recapitulated. It is shown that the transverse energy distribution of heavy ion collisions follow the geometry of the collision. An extension of the model to include rapidity and transverse mass particle spectra is discussed.
From existing hadron and heavy ion collisions data on \bar{p}/p central production we estimate the value of the percolation parameter at RHIC energies.
Recent work on chemical equilibrium in heavy ion collisions is reviewed. The energy dependence of thermal parameters is discussed. The centrality dependence of thermal parameters at SPS energies is presented.
We point out that exponential shape of transverse spectra can be obtained as the Fourier transform of the limiting distribution of randomly positioned partons with power law spectra given by pQCD, which actually realize Tsallis distributions. Such spectra were used to obtain hadron yields by recombination in relativistic heavy-ion collisions at RHIC energies.
Selected topics in the field of relativistic heavy-ion collisions are reviewed f rom the 15 year research programme at the SPS at CERN and the AGS at BNL, and from the first run of the Relativistic Heavy-Ion Collider at BNL.
We discuss the model predictions for antibaryon/baryon production ratios in high energy heavy ion collisions. The role of string junction mechanism of baryon number transfer seems to be very important here and we consider some quantitative results.
We calculate the centrality dependence for coherent photoproduction of very low-$p_{T}$ $J/ψ$ at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies within the impact parameter dependent saturated color dipole model. By using the large equivalent photon fluxes, we present the differential cross section of very low-$p_{T}$ $J/ψ$ produced by coherent photonuclear in peripheral heavy-ion collisions. The numerical results demonstrate that our calculation are agree with $J/ψ$ data in peripheral heavy ion collisions at Relativistic Heavy Ion Collider (RHIC) energies.
We consider (anti-)baryons production in heavy ion collisions as production of topological defects during the chiral phase transition. Non-zero quark masses which explicitly break chiral symmetry supress the (anti-)baryon density. Hardly any (anti-)baryons will be produced in the central rapidity region of a heavy ion collision.
We study the effect of energy loss on charm and bottom quarks in high-energy heavy-ion collisions including hadronization, longitudinal expansion and partial thermalization. We consider in detail the detector geometry and single lepton energy cuts of the ALICE and CMS detectors at the Large Hadron Collider (LHC) to show the large suppression of high $p_T$ heavy quarks and the consequences of their semileptonic decays.
The simple method for simulation of ``thermal'' hadron spectra in ultrarelativistic heavy ion collisions including longitudinal, transverse and elliptic flow is developed. The model is realized as fast Monte-Carlo event generator.
Some topics on heavy-ion collisions are reviewed with emphasis on those which are expected to be specially relevant at the Large Hadron Collider programme.
We estimate the production rates of supersymmetric particles in central heavy-ion collisions at LHC. The parton cascade model is used to seek for possible collective phenomena which enlarge the production probability of very heavy particles. Even if there is some indication of such cooperative effects, higher energy and higher luminosity of proton beams at LHC disfavor heavy-ion reactions in the search for supersymmetric particles.
Various forms of matter may be produced in ultra-relativistic heavy ion collisions. These are the Quark Gluon Plasma, the Color Glass Condensate, the Glasma and Quarkyonic Matter. A novel effect that may be associated with topological charge fluctuations is the Chiral Magnetic Effect. I explain these concepts and explain how they may be seen in ultra-relativistic heavy ion collisions.
We describe updated calculations of $Q \bar Q$ production in $pp$ and $π^- p$ interactions. We compare these results to total cross section data and discuss how the baseline cross sections extrapolate to heavy ion collider energies. We touch upon the differences between leading and next-to-leading order heavy quark production. Finally, we discuss the implications of our calculations for quarkonium production. Our discussion here focuses on bottom quarks.
The method for simulation of medium-induced rescattering and energy loss of hard partons in ultrarelativistic heavy ion collisions is developed. The model is realized as fast Monte-Carlo tool implemented to modify standard PYTHIA jet event.
We analyse the cluster structure of the final multihadron states resulting from heavy ion collisions using the concept of Jaynes - Shannon entropy. Further evidence for an interesting differentiation of events is provided.
The mid-rapidity transverse-momentum spectra of charmed meson in Pb-Pb and pp($\overline{\text{p}}$) collisions are analyzed by Tsallis-Pareto distribution derived from non-extensive statistics. We perform uniform descriptions for both small and large systems over a wide range of collision energy and hadron transverse momentum. By establishing the relation between the event multiplicity and the Tsallis parameters, we observe that there is significant linearity between thermal temperature and Tsallis-q parameter in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV and 5.02 TeV. And the slope of th…
The transverse momentum ($p_T$) spectra from heavy-ion collisions at intermediate momenta are described by non-extensive statistical models. Assuming a fixed relative variance of the temperature fluctuating event by event or alternatively a fixed mean multiplicity in a negative binomial distribution (NBD), two different linear relations emerge between the temperature, $T$, and the Tsallis parameter $q-1$. Our results qualitatively agree with that of G.~Wilk. Furthermore we revisit the "Soft+Hard" model, proposed recently by G.~G.~Barnaföldi \textit{et.al.}, by a $T$-independent average $p_T^2$…
Comparing effective temperatures in standard, Tsallis, and q-dual statistics from transverse momentum spectra of identified light charged hadrons produced in gold--gold collisions at RHIC energies
We analyze the transverse momentum ($p_T$) spectra of identified particles ($π^{\pm}$, $K^{\pm}$, $p$, and $\bar p$) produced in gold-gold (Au-Au) and lead-lead (Pb-Pb) collisions over a $\sqrt{s_{NN}}$ (center-of-mass energy per nucleon pair) range from 14.5 GeV [one of the Relativistic Heavy Ion Collider (RHIC) energies] to 2.76 TeV [one of the Large Hadron Collider (LHC) energies]. For the spectra with a narrow $p_T$ range, an improved Tsallis distribution which is in fact the Tsallis distribution with radial flow is used. For the spectra with a wide $p_T$ range, a superposition of the impr…
A discussion is presented of results with identified particles at the Large Hadron Collider. Possible deviations from the standard statistical distributions are investigated by considering in detail results obtained using the Tsallis distribution. Matter-antimatter production is discussed within the framework of chemical equilibrium in \pp and heavy ion collisions.
Comparing effective temperatures in standard and Tsallis distributions from transverse momentum spectra in small collision systems
Shanxi University（山西大学）；Xinzhou Normal University（忻州师范学院）；Physical-Technical Institute of Uzbekistan Academy of Sciences（乌兹别克斯坦科学院物理技术研究所）；National University of Science and Technology MISIS (NUST MISIS), Almalyk Branch（国立科技大学MISIS阿拉木克分校）
The possibility of formation of Bose-Einstein Condensation (BEC) is studied in $pp$ collisions at $\sqrt s$ = 7 TeV at the Large Hadron Collider. A thermodynamically consistent non-extensive formulation of the identified hadron transverse momentum distributions is used to estimate the critical temperature required to form BEC of charged pions, which are the most abundant species in a multi-particle production process in hadronic and nuclear collisions. The obtained results have been contrasted with the systems produced in Pb-Pb collisions to have a better understanding. We observe an explicit …
