In high-energy collisions the number of the created particles is far less than the thermodynamic limit, especially in small colliding systems (e.g. proton-proton). Therefore final-state effects and fluctuations in the one-particle energy distribution are appreciable. As a consequence the characterization of identified hadron spectra with the Boltzmann\,--\,Gibbs thermodynamical approach is insufficient. Instead particle spectra measured in high-energy collisions can be described very well with Tsallis\,--\,Pareto distributions, derived from non-extensive thermodynamics. Using the Tsallis q-entropy formula, a generalization of the Boltzmann\,--\,Gibbs entropy, we interpret the microscopical physics by analysing the Tsallis $q$ and $T$ parameters. In this paper we give a quick overview on these parameters, analyzing identified hadron spectra from recent years in a wide center of mass energy range. We demonstrate that the fitted Tsallis-parameters show dependency on this energy and on the particle species. Our findings are described well by a QCD inspired evolution ansatz.
Statistical Coalescence Model Analysis of J/psi Production in Pb+Pb Collisions at 158 A GeV
在统计合并模型中考虑了重离子碰撞中J/π介子的产生。该模型与NA 50协作组在158 A GeV的Pb+Pb碰撞的实验数据在一个很宽的中心度范围内，包括所谓的“双”抑制域是一致的。J/psi数据的模型描述需要，但是，强大的增强中心Pb+Pb碰撞的开放魅力生产。该模型预测可以在未来的SPS运行中进行检查。
This paper discusses a statistical anomaly-detection method for model-independent searches for new physics in collision events produced at the Large Hadron Collider (LHC). The method requires calculations of $Z$-scores for a large number of Lorenz-invariant variables to identify events that deviate from those expected for the Standard Model (SM).
Thermodynamical description of the system created during high energy collision requires a proper thermodynamical framework to study the distribution of particles. In this work, we have attempted to explain the transverse momentum spectra of charged hadrons formed in $pp$ collision at different energies using the Pearson statistical framework. This formalism has been proved to nicely explain the spectra of particles produced in soft processes as well hard scattering processes in a consistent manner. For this analysis, we have used the highest available range of $p_T$ published by experiments to…
Study of the characteristic properties of charged particle production in hadron-nucleus collisions at high energies, by utilising the approaches from different statistical models is performed.~Predictions from different approaches using the Negative Binomial distribution, shifted Gompertz distribution, Weibull distribution and the Krasznovszky-Wagner distribution are utilised for a comparative study of the relative successes of these models.~These distributions derived from a variety of functional forms are based on either phenomenological parameterizations or some model of the underlying dyna…
In high energy nucleus-nucleus collisions, it is difficult to measure the contributions of resonance strong decay and weak decay to the final measured hadrons as well as the corresponding effects on some physical observables. To provide a reference from statistical thermal model, we performed a systematic analysis for the energy dependence of particle yield and yield ratios in Au + Au collisions. We found that the primary fraction of final hadrons decreases with increasing collision energy and somehow saturates around $\sqrt{s_\textrm{NN}}$ = 10 GeV, indicating a limiting temperature in hadron…
The transverse momentum spectra of identified charged hadrons stemming from high energy collisions at different beam energies are described by a new non-extensive distribution, the Kaniadakis $κ$-distribution, with respect to the constraints in non-extensive quantum statistics. All fittings are also compared with the Tsallis distributions as well as the usual Boltzmann-Gibbs one. $χ^2/ndf$ is also used to test the fitting goodness of all functions. Our results show that these different non-extensive approaches can be well applied in high energy collisions rather than the classical one. The Kan…
Transverse spectra of both jets and hadrons obtained in high-energy $pp$ and $p\bar p $ collisions at central rapidity exhibit power-law behavior of $1/p_T^n$ at high $p_T$. The power index $n$ is 4-5 for jet production and is 6-10 for hadron production. Furthermore, the hadron spectra spanning over 14 orders of magnitude down to the lowest $p_T$ region in $pp$ collisions at LHC can be adequately described by a single nonextensive statistical mechanical distribution that is widely used in other branches of science. This suggests indirectly the possible dominance of the hard-scattering process …
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 co…
Predictions on fluctuations of hadron production properties in central heavy ion collisions are presented. They are based on the Statistical Model of the Early Stage and extend previously published results by considering the strongly intensive measures of fluctuations. In several of the considered cases a significant change in collision energy dependence of calculated quantities as a result of the phase transition is predicted. This provides an opportunity to observe new signals of the onset of deconfinement in heavy ion collisions experiments.
Predictions are presented within the framework of the statistical hadronization model for integrated yields of bottomonia in Pb-Pb collisions at the LHC. We investigate the centrality dependence of $Υ$ production and provide predictions for a large set of still-unmeasured open-beauty hadrons.
A brief introduction to the statistical hadronization approach to particle production in relativistic heavy-ion collisions is given. In the context of fluid dynamics modeling various aspects of hadron emission at the freeze-out are discussed. Practical applications of the presented concepts are presented within the THERMINATOR Monte-Carlo hadron generator.
Charm particle production in nucleus-nucleus collisions at the CERN SPS energies is considered within a statistical approach. Namely, the Statistical Model of the Early Stage is used to calculate mean multiplicity of charm particles in central Pb+Pb collisions. A small number of produced charm particles necessitates the use of the exact charm conservation law. The model predicts a rapid increase of mean charm multiplicity as a function of collision energy. The mean multiplicity calculated for central Pb+Pb collisions at the center of mass energy per nucleon pair $\sqrt{s_{NN}}=17.3$ GeV exceed…
We consider a selection of recent experimental results on electroweak $W^{\pm},\,Z$ gauge boson production in $pp$ collisions at BNL RHIC and CERN LHC energies in comparison to prediction of perturbative QCD calculations based on different sets of NLO parton distribution functions including the statistical PDF model known from fits to the DIS data. We show that the current statistical PDF parameterisation (fitted to the DIS data only) underestimates the LHC data on $W^{\pm},\,Z$ gauge boson production cross sections at the NLO by about 20\%. This suggests that there is a need to refit the para…
In a recent analysis of high-statistics $p_t$ spectra from 5 and 13 TeV $p$-$p$ collisions a two-component (soft+hard) model (TCM) of hadron production near midrapidity, based on fixed model functions independent of collision multiplicity $n_{ch}$ or event selection criteria, was employed as a reference to determine data biases induced by the selection criteria. As in previous studies the fixed TCM accurately isolated jet-related and nonjet contributions to spectra. It was observed that two selection criteria (V0M and SPD), based on different pseudorapidity $η$ acceptances, bias the spectrum h…
The analysis of high-energy particle collisions is an excellent testbed for the non-extensive statistical approach. In these reactions we are far from the thermodynamical limit. In small colliding systems, such as electron-positron or nuclear collisions, the number of particles is several orders of magnitude smaller than the Avogadro number; therefore, finite-size and fluctuation effects strongly influence the final-state one-particle energy distributions. Due to the simple characterization, the description of the identified hadron spectra with the Boltzmann-Gibbs thermodynamical approach is i…
Elliptic flow in heavy-ion collisions is an important signature of a possible de-confinement transition from hadronic phase to partonic phase. In the present work, we use non-extensive statistics, which has been used for transverse momentum ($p_{\rm T}$) distribution in proton+proton ($p+p$) collisions, as the initial particle distribution function in Boltzmann Transport Equation (BTE). A Boltzmann-Gibbs Blast Wave (BGBW) function is taken as an equilibrium function to get the final distribution to describe the particle production in heavy-ion collisions. In this formalism, we try to estimate …
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 $p_T^2$…
