Particle Production In Heavy-ion Collisions Research Articles

Far-from-equilibrium slow modes and momentum anisotropy in an expanding plasma

The momentum distribution of particle production in heavy-ion collisions encodes information about thermalization processes in the early-stage quark-gluon plasma. We use kinetic theory to study the far-from-equilibrium evolution of an expanding plasma with an anisotropic momentum-space distribution. We identify slow and fast degrees of freedom in the far-from-equilibrium plasma from the evolution of moments of this distribution. At late times, the slow modes correspond to hydrodynamic degrees of freedom and are naturally gapped from the fast modes by the inverse of the relaxation time, τR−1. At early times, however, there are an infinite number of slow modes with a gap inversely proportional to time, τ−1. From the evolution of the slow modes we generalize the paradigm of the far-from-equilibrium attractor to vector and tensor components of the energy-momentum tensor, and even to higher moments of the distribution function that are not part of the hydrodynamic evolution. We predict that initial-state momentum anisotropy decays slowly in the far-from-equilibrium phase and may persist until the relaxation time. Published by the American Physical Society 2024

Study of Isothermal Compressibility and Speed of Sound in the Hadronic Matter Formed in Heavy-Ion Collision Using Unified Formalism

The thermodynamical quantities and response functions are useful to describe the particle production in heavy-ion collisions as they reveal crucial information about the produced system. While the study of isothermal compressibility provides an inference about the viscosity of the medium, speed of sound helps in understanding the equation of state. With an aim towards understanding the system produced in the heavy-ion collision, we have made an attempt to study isothermal compressibility and speed of sound as function of charged particle multiplicity in heavy-ion collisions at sNN = 2.76 TeV, 5.02 TeV, and 5.44 TeV using unified formalism.

QCD equation of state at finite densities for nuclear collisions

We construct the QCD equation of state at finite chemical potentials including net baryon, electric charge, and strangeness based on the results of lattice QCD simulations and the hadron resonance gas model. The situation of strangeness neutrality and a fixed charge-to-baryon ratio, which resembles that of heavy nuclei, is considered for the application to relativistic heavy-ion collisions. This increases the values of baryon chemical potential compared to the case of vanishing strangeness and electric charge chemical potentials, modifying the fireball trajectory in the phase diagram. We perform viscous hydrodynamic simulations and demonstrate the importance of multiple chemical potentials for identified particle production in heavy-ion collisions at the RHIC and SPS beam energy scan energies.

Shape of the quark gluon plasma droplet reflected in the high- p⊥ data

We show, through analytic arguments, numerical calculations, and comparison with experimental data, that the ratio of the high-p_T observables v_2/(1-R_AA) reaches a well-defined saturation value at high p_T, and that this ratio depends only on the spatial anisotropy of the quark gluon plasma (QGP) formed in ultrarelativistic heavy-ion collisions. With expected future reduction of experimental errors, the anisotropy extracted from experimental data will further constrain the calculations of initial particle production in heavy-ion collisions and thus test our understanding of QGP physics.

Thermal-FIST: A package for heavy-ion collisions and hadronic equation of state

Thermal-FIST11Thermal-FIST — Thermal, Fast and Interactive Statistical Toolkit. is a C++ package designed for convenient general-purpose physics analysis within the family of hadron resonance gas (HRG) models. This mainly includes the statistical analysis of particle production in heavy-ion collisions and the phenomenology of hadronic equation of state. Notable features include fluctuations and correlations of conserved charges, effects of probabilistic decay, chemical non-equilibrium, and inclusion of van der Waals hadronic interactions. Calculations are possible within the grand canonical ensemble, the canonical ensemble, as well as in mixed-canonical ensembles combining the canonical treatment of certain conserved charges with the grand-canonical treatment of other conserved charges. The package contains a fast thermal event generator, which generates particle yields in accordance with the HRG chemistry, and particle momenta based on the Blast Wave model. A distinct feature of this package is the presence of the graphical user interface frontend – QtThermalFIST – which is designed for fast and convenient general-purpose HRG model applications. Program summaryProgram Title:Thermal-FIST, version 1.2Program Files doi:http://dx.doi.org/10.17632/pprr8p4fkp.1Licensing provisions: GPLv3Programming language: C++External routines:Eigen template library for the linear algebra routines [1], MINUIT2 package from CERN ROOT [2], Mersenne Twister random number generator [3], Qt5 framework [4] (for the GUI only), QCustomPlot Qt widget [5] (for the GUI only)Nature of problem: The HRG model and its various modifications constitute a common framework used for modeling of the hadronic equation of state and particle production in heavy-ion collisions. Even the simplest versions of the HRG model require careful considerations of the many details, including the resonance decay feed-down, implementation of charge conservation constraints relevant for heavy-ion collisions, chemical non-equilibrium effects. A notable extra effort is required in order to treat the fluctuations and correlations of various charges , which presently are being extensively studied in the heavy-ion collision experiments and lattice QCD calculations. The inclusion of hadronic interactions, modeled by an excluded-volume (EV) or a van der Waals (vdW) type framework, additionally requires a numerical solution to a system of many transcendental equations.Solution method: The Thermal-FIST package contains a class-based library which calculates relevant HRG observables for a specified setup. The setup includes a particle list, usually to be supplied with an external file, an HRG model specification (statistical ensemble, van der Waals interaction parameters, etc.), a set of thermal parameters, and conservation laws constraints. Whenever necessary, the systems of transcendental equations are solved numerically with the Broyden’s method. The package includes a fitter for extracting thermal parameters from hadron yield data through the χ2 minimization. The HRG model based Monte Carlo event generator is a complementary feature to analytic calculations. A general-purpose thermal analysis is made maximally convenient with QtThermalFIST — a GUI frontend based on the Qt framework where all typical calculations, such as the properties of the equation of state or the thermal fits, can be straightforwardly performed.Additional comments: If the EV/vdW interactions are present, exact analytic calculations are presently only possible within the grand canonical ensemble. Approximate calculations are possible for the strangeness-canonical ensemble on the condition that strange particles form a small subsystem relative to the total system. Effects of probabilistic decays on fluctuation observables are generally included only up to the moments of the 2nd order. The only exception is the ideal HRG model in the grand canonical ensemble, where these effects are included up to the moments of the 4th order. On the other hand, the Monte Carlo event generator is not constrained by the above restrictions.

Coulomb Final State Interaction in Heavy Ion Collisions for Lévy Sources

Investigation of momentum space correlations of particles produced in high energy reactions requires taking final state interactions into account, a crucial point of any such analysis. Coulomb interaction between charged particles is the most important such effect. In small systems like those created in e + e - - or p + p collisions, the so-called Gamow factor (valid for a point-like particle source) gives an acceptable description of the Coulomb interaction. However, in larger systems such as central or mid-central heavy ion collisions, more involved approaches are needed. In this paper we investigate the Coulomb final state interaction for Lévy-type source functions that were recently shown to be of much interest for a refined description of the space-time picture of particle production in heavy-ion collisions.

Kinetic Approach to Pair Production in Strong Fields—Two Lessons for Applications to Heavy-Ion Collisions

The kinetic-equation approach to particle production in strong, time-dependent external fields is revisited and three limiting cases are discussed for different field patterns: the Sauter pulse, a harmonic pulse with a Gaussian envelope, and a Poisson-distributed stochastic field. It is shown that for transient subcritical electric fields E ( t ) a finite residual particle number density n ( ∞ ) would be absent if the field-dependence of the dynamical phase in the Schwinger source term would be neglected. In this case the distribution function of created particles follows the law f ( t ) ∼ E 2 ( t ) . Two lessons for particle production in heavy-ion collisions are derived from this exercise. First: the shorter the (Sauter-type) pulse, the higher the residual density of produced particles. Second: although the Schwinger process in a string-type field produces a non-thermal particle spectrum, a Poissonian distribution of the (fluctuating) strings produces a thermal spectrum with an apparent temperature that coincides with the Hawking–Unruh temperature for the mean value of the string tension.

Elliptic flow in Pb+Pb collisions at $\sqrt{s_{{\rm NN}}} = 2.76$ s NN = 2 . 76 TeV at the LHC using Boltzmann transport equation with non-extensive statistics

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 elliptic flow in Pb+Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV at the LHC for different centralities. The elliptic flow ($v_2$) of identified particles seems to be described quite well in the available $p_{\rm T}$ range. An approach, which combines the non-extensive nature of particle production in $p+p$ collisions through an evolution in kinetic theory using BTE, with BGBW equilibrium distribution is successful in describing the spectra and elliptic flow in heavy-ion collisions.

Two components in charged particle production in heavy-ion collisions

Transverse momentum spectra of charged particle production in heavy-ion collisions are considered in terms of a recently introduced Two Component parameterization combining exponential (“soft”) and power-law (“hard”) functional forms. The charged hadron densities calculated separately for them are plotted versus number of participating nucleons, Npart. The obtained dependences are discussed and the possible link between the two component parameterization introduced by the authors and the two component model historically used for the case of heavy-ion collisions is established. Next, the variations of the parameters of the introduced approach with the center of mass energy and centrality are studied using the available data from RHIC and LHC experiments. The spectra shapes are found to show universal dependences on Npart for all investigated collision energies.

Solution of the hyperon puzzle within a relativistic mean-field model

The equation of state of cold baryonic matter is studied within a relativistic mean-field model with hadron masses and coupling constants depending on the scalar field. All hadron masses undergo a universal scaling, whereas the couplings are scaled differently. The appearance of hyperons in dense neutron star interiors is accounted for, however the equation of state remains sufficiently stiff if the reduction of the ϕ meson mass is included. Our equation of state matches well the constraints known from analyses of the astrophysical data and particle production in heavy-ion collisions.

Strangeness production associated to a high-pT particle in Pb-Pb collisions at = 2.76 TeV with ALICE

Particle production in heavy-ion collisions at RHIC and the LHC reveals an enhancement of the baryon-to-meson ratios with respect to pp collisions. The observed suppression of high-pT particles raises the question of how the jet fragments may (re)distribute in ultra-relativistic heavy-ion collisions. With two-hadron correlations, we can study the particle composition in jets in order to get a better understanding of the aforementioned observables and the particle production mechanisms in the dense medium. In these proceedings, we present the status of the current analysis using two-hadron angular correlations for Pb-Pb collisions at = 2.76 TeV using the ALICE detector. We study the two different possibilities, considering the strange particle as either the trigger particle or the associated particle. Results on K0s-h±, (Λ A)-h± and h±-K0S correlations are shown for central collisions.

Transverse energy and charged particle production in heavy-ion collisions: From RHIC to LHC

We study the charged particle and transverse energy production mechanism from AGS, SPS, Relativistic Heavy-Ion Collider (RHIC) to Large Hadron Collider (LHC) energies in the framework of nucleon and quark participants. At RHIC and LHC energies, the number of nucleons-normalized charged particle and transverse energy density in pseudorapidity, which shows a monotonic rise with centrality, turns out to be an almost centrality independent scaling behavior when normalized to the number of participant quarks. A universal function which is a combination of logarithmic and power-law, describes well the charged particle and transverse energy production both at nucleon and quark participant level for the whole range of collision energies. Energy dependent production mechanisms are discussed both for nucleonic and partonic level. Predictions are made for the pseudorapidity densities of transverse energy, charged particle multiplicity and their ratio (the barometric observable, [Formula: see text]) at mid-rapidity for Pb + Pb collisions at [Formula: see text]. A comparison with models based on gluon saturation and statistical hadron gas is made for the energy dependence of [Formula: see text].

P/π Ratio in Di-Hadron Correlations

Particle ratios are important observables used to constrain models of particle production in heavy-ion collisions. In this work we report on a measurement of the p/pi ratio in the transverse momentum range 2.0 < p_{T,assoc} < 4.0 GeV/c, associated with a charged trigger particle of 5.0 < p_{T,trig} < 10.0 GeV/c, in 0-10% central Pb--Pb collisions at sqrt{s_{NN}}=2.76 TeV. The ratio is measured in the jet peak and in a region at large Delta eta separation from the peak (bulk region). The presented results are based on 14M minimum-bias Pb--Pb collisions, recorded by the ALICE detector. It is observed that the p/pi ratio in the bulk region is compatible with the p/pi ratio of an inclusive measurement, and is much larger than the p/pi ratio in the jet peak. The p/pi ratio in the jet peak is compatible with a PYTHIA reference, in which fragmentation in the vacuum is the dominant mechanism of particle production.

Inclusive jet spectra in 2.76 TeV collisions from ALICE

Measurements of high-pT particle production in heavy-ion collisions at RHIC have shown that medium-induced energy loss affects the partons produced in the early stage of a heavy-ion col- lision. The increased initial production cross section for partons at LHC energies makes fully reconstructed jets available in a wide kinematic range, which allows for a more differential in- vestigation of parton energy loss. Partonic energy loss allows us to access key observables of the hot deconfined nuclear matter produced in heavy-ion collisions. The inclusive cross-section of reconstructed jets using the ALICE tracking detectors and electromagnetic calorimeter is pre- sented from data collected during the 2.76 TeV pp runs. The procedures used to reconstruct jets and extract them from a fluctuating background in Pb-Pb collisions are discussed.

Latest results from the PHOBOS experiment

Over the past few years PHOBOS has continued to analyze the large data sets obtained from the first five runs of the relativistic heavy-ion collider (RHIC) at Brookhaven National Laboratory. The two main analysis streams have been pursued. The first one aims to obtain a broad and systematic survey of global properties of particle production in heavy-ion collisions. The second class includes the study of fluctuations and correlations in particle production. Both type of studies have been performed for a variety of the collision systems, covering a wide range in collision energy and centrality. The uniquely large angular coverage of the PHOBOS detector and its ability to measure charged particles down to very low-transverse momentum is exploited. The latest physics results from PHOBOS, as presented at the Quark Matter 2008 Conference, are contained in this paper.

Fluctuations of particle ratios as a freeze-out probe

We explain how event-by-event fluctuations of particle ratios can constrain and falsify the statistical model of particle production in heavy-ion collisions, using K/π fluctuations as an example. We define an observable capable of determining which statistical model, if any, governs freeze-out in ultrarelativistic heavy-ion collisions. We calculate this observable for K/π fluctuations, and show that it should be the same for RHIC and LHC energies, as well as independent of centrality, if the grand canonical statistical model is an appropriate description and chemical equilibrium applies. We describe what happens in case of deviations from this scenario, such as light quark chemical non-equilibrium, strange quark over-saturation and local conservation (canonical ensemble) for strange quarks. We also introduce a similar observable capable, together with the published K*/K measurement, of ascertaining if an interacting hadron gas phase governs the system between thermal and chemical freeze-out, and of ascertaining its duration and impact on hadronic chemistry

Chemical equilibrium in collisions of small systems

The system-size dependence of particle production in heavy-ion collisions at the top energy at the CERN Super Proton Synchrotron is analyzed in terms of the statistical model. A systematic comparison is made of two suppression mechanisms that quantify strange-particle yields in ultrarelativistic heavy-ion collisions: the canonical model with strangeness correlation radius determined from the data and the model formulated in the canonical ensemble using chemical off-equilibrium strangeness suppression factor. The system-size dependence of the correlation radius and the thermal parameters are obtained for p-p, C-C, Si-Si, and Pb-Pb collisions at {radical}(s{sub NN})=17.3A GeV. It is shown that on the basis of a consistent set of data there is no clear difference between the two suppression patterns. In the present study, the strangeness correlation radius was found to exhibit a rather weak dependence on the system size.

Pair production by boost-invariant fields in comoving coordinates

We derive the pair-production probability in a constant electric field in Rindler coordinates in a quasi-classical approximation. Our result is different from the pair-production probability in an inertial frame (Schwinger formula). In particular, it exhibits non-trivial dependence on rapidity and deviation from Gaussian behavior at small transverse momenta. Our results can be important for analysis of particle production in heavy-ion collisions.

From RHIC to LHC: a relativistic diffusion approach

We investigate stopping and particle production in heavy-ion collisions in a Relativistic Diffusion Model (RDM). Using three sources for particle production, the energy- and centrality dependence of rapidity distributions of net protons, and pseudorapidity distributions of charged hadrons in heavy systems at RHIC energies are precisely reproduced in the analytical model. The transport coefficients are then extrapolated from Au + Au at RHIC energies (OsNN=19.6 - 200 GeV) to Pb + Pb at LHC energies of OsNN= 5.52 TeV. Rapidity distributions for net protons, and pseudorapidity spectra for produced charged particles are obtained and discussed in a three-sources model at LHC energies.

From RHIC to LHC: A relativistic diffusion approach

Stopping and particle production in heavy-ion collisions are investigated in a Relativistic Diffusion Model (RDM). Using three sources for particle production, the energy- and centrality dependence of rapidity distributions of net protons, and pseudorapidity distributions of charged hadrons in heavy systems at RHIC energies are precisely reproduced in the analytical model. The gradual approach to local thermal equilibrium is discussed. The transport coefficients are then extrapolated from Au + Au at RHIC energies ( s N N = 19.6 − 200 GeV ) to Pb + Pb at LHC energies of s N N = 5.52 TeV . Rapidity distributions fot net protons, and pseudorapidity spectra for produced charged particles are obtained and discussed in a three-sources model at LHC energies.