We show that the transverse-mass and rapidity spectra of protons and pions produced in Au-Au collisions at sqrt(sNN) = 2.4 GeV can be well reproduced in a thermodynamic model assuming single freeze-out of particles from a spherically symmetric hypersurface. This scenario corresponds to a physical picture used by Siemens and Rasmussen in the original formulation of the blast-wave model. Our framework modifies and extends this approach by incorporation of a Hubble-like expansion of QCD matter and inclusion of resonance decays. In particular, the Delta(1232) resonance is taken into account, with a width obtained from the virial expansion. Altogether, our results bring evidence for substantial thermalization of the matter produced in heavy-ion collisions in a few GeV energy regime and its nearly spherical expansion.
We obtain a detailed description of all available hadron multiplicity yields in central Pb--Pb collisions at LHC measured in the rapidity interval $|y|<0.5$. We find that the hadronization of the fireball at LHC occurs at nearly identical intensive physical bulk conditions for all centralities similar to those seen already at RHIC.
We obtain within the statistical hadronization model the hadron yields $dh/dy$ in heavy ion reactions at $\sqrt{s_{NN}} = 2.76$ TeV. We discuss the dependence both on hadronization temperature $T$, and on critical hadronization pressure $P$. We consider observables distinguishing the hadronization models and conditions.
Recent data on hadron multiplicities in central Pb+Pb collisions at 158A GeV/c at mid-rapidity are analyzed within the concept of chemical freeze-out. A non-uniformity of the baryon chemical potential along the beam axis is taken into account. An approximate analytical solution of the hydrodynamic equations for a chemically frozen Boltzmann-like gas is found. The Cauchy conditions for hydrodynamic evolution of the hadron resonance gas are fixed at the thermal freeze-out hypersurface from analysis of one-particle momentum spectra and HBT correlations. The proper time of chemical freeze-out and …
The widths of charge balance function in high energy hadron-hadron and relativistic heavy ion collisions are studied using the Monte Carlo generators PYTHIA and AMPT, respectively. The narrowing of balance function as the increase of multiplicity is found in both cases. The mean parton-freeze-out time of a heavy-ion-collision event is used as the characteristic hadronization time of the event. It turns out that for a fixed multiplicity interval the width of balance function is consistent with being independent of hadronization time.
We show that hadron production in relativistic heavy ion collisions at transverse momenta larger than 2 GeV/c can be explained by the competition of two different hadronization mechanisms. Above 5 GeV/c hadron production can be described by fragmentation of partons that are created perturbatively. Below 5 GeV/c recombination of partons from the dense and hot fireball dominates. This can explain some of the surprising features of RHIC data like the constant baryon-to-meson ratio of about one and the small nuclear suppression for baryons between 2 to 4 GeV/c.
A transport model is developed to describe hadron emission from a strongly coupled quark-gluon plasma formed in relativistic heavy ion collisions. The quark-gluon plasma is controlled by ideal hydrodynamics, and the hadron motion is characterized by a transport equation with loss and gain terms. The two sets of equations are coupled to each other, and the hadronization hypersurface is determined by both the hydrodynamic evolution and the hadron emission. The model is applied to calculate the transverse momentum distributions of mesons and baryons, and most of the results agree well with the ex…
Using QCD-inspired time dependent cross sections for pre-hadrons we provide a combined analysis of available experimental data on hadron attenuation in DIS off nuclei as measured by HERMES with 12 and 27 GeV and by EMC with 100 and 280 GeV lepton beam energies. We extract the complete four-dimensional evolution of the pre-hadrons using the JETSET-part of PYTHIA. We find a remarkable sensitivity of nuclear attenuation data to the details of the time-evolution of cross sections. Only cross sections evolving linearly in time describe the available data in a wide kinematical regime. Predictions fo…
A novel state of matter has been hypothesized to exist during the early stage of relativistic heavy ion collisions, with normal hadrons not appearing until several fm/c after the start of the reaction. To test this hypothesis, correlations between charges and their associated anticharges are evaluated with the use of balance functions. It is shown that late-stage hadronization is characterized by tightly correlated charge/anticharge pairs when measured as a function of relative rapidity.
Heavy flavor supplies a chance to constrain and improve the hadronization mechanism. We have established a sequential coalescence model with charm conservation and applied it to the charmed hadron production in heavy ion collisions. The charm conservation enhances the earlier hadron production and suppresses the later production. This relative enhancement (suppression) changes significantly the ratios between charmed hadrons in heavy ion collisions.
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.
Within the key issues of hadronic physics one of the interesting issues in nuclear physics is whether there is a transition region between meson-nucleon and quark-gluon degrees of freedom in the NN interaction. This question is relevant for pairs of free nucleons as well as for nucleon pairs immersed in nuclear matter. From NN phase shifts we deduce a dibaryonic scale of 1 GeV for the soft core NN potential strengths at nucleon separation r equal 0.25 to 0.5 fm. A short range intermediate transition, with fusion and fission of the two scattered nucleons into a dibaryon with prevailing quark-gl…
Chemical non-equilibrium version of the statistical hadronization model combined with a single-freeze-out scenario is used to analyze the transverse-momentum spectra of pions, kaons and protons produced in heavy-ion collisions at sqrt(sNN) = 2.76 TeV. With the statistical parameters found in earlier studies of hadronic ratios and two new geometric parameters determined by the absolute normalization and slopes of the spectra, we obtain a very good agreement between the data and the model predictions. In particular, the enhancement of pions observed at the very low transverse-momenta is very wel…
We introduce the Statistical Hadronization with Resonances (SHARE) suite of programs and perform a study of particle multiplicities as well as bulk thermodynamic quantities for the RHIC Au--Au reactions at $\sqrt{s_{NN}}=130$ GeV. We also show that the statistical hadronization model, with parameters fitted to match pion, proton and hyperon ratios, in turn correctly and consistently reproduces rapidity particle multiplicity.
We calculate the charge balance function of the bulk quark system before hadronization and those for the directly produced and the final hadron system in high energy heavy ion collisions. We use the covariance coefficient to describe the strength of the correlation between the momentum of the quark and that of the anti-quark if they are produced in a pair and fix the parameter by comparing the results for hadrons with the available data. We study the hadronization effects and decay contributions by comparing the results for hadrons with those for the bulk quark system. Our results show that wh…
We study the dynamics of energy loss and flow of heavy quarks produced in ultra-relativistic heavy-ion collisions within the framework of a Langevin equation coupled to a (2+1)-dimensional viscous hydrodynamic model that simulates the space-time evolution of the produced hot and dense QCD matter. The classical Langevin approach is improved such that, apart from quasi-elastic scatterings, radiative energy loss is incorporated by treating gluon radiation as an additional force term. The hadronization of emitted heavy quarks is simulated via a hybrid fragmentation plus recombination model. Our ca…
The unified set of yields of particles produced in proton-proton collisions at $\sqrt{s}$ = 17.3 GeV (laboratory beam momentum 158 GeV/c) is evaluated, combining the experimental results of the NA49 and NA61/SHINE collaborations at the CERN SPS. With the statistical hadronization code Thermal-Fist we confirm the unacceptably high value of $χ^2$, both in the canonical and grand canonical - strangeness canonical approach, and the common volume for all the hadrons. The use of the energy-dependent width of the Breit-Wigner parametrization for the mass distributions of unstable particles improves t…
We study multistrange hadrons produced in NA49 and STAR experiments at center of mass energies varying from \sqrt{s_{NN}} = 7.61 GeV to 200 GeV. We show that the yields of Ξ, Ξ-bar and ϕ can help to constrain the physical conditions present in the hot dense fireball source of these multistrange hadrons created in heavy ion collision. We address the question of chemical equilibrium of individual quark flavors before and after hadronization and offer a few predictions for LHC.
The effects of color screening on the hadronization of a parton plasma into a hadron gas are examined at the energies of the relativistic heavy ion collider. It is found to have the tendency to prevent hadronization and therefore delaying the conversion of the partons into a hadron gas. Because of the continual expansion, the resulting hadron gas number densities are lower when screening is included. This should reduce the hadronic noise to genuine signals of the quark-gluon plasma. In this sense, color screening is favorable and should be included in numerical models. In any case, we advocate…
We present additions to the MARTINI event generator for examining heavy quarks and quarkonia in heavy-ion collisions. All stages of a heavy-ion collision affect the observables associated with heavy quarks: the initial phase space of the heavy quarks are sampled with PYTHIA8.1, the heavy quarks are evolved using Langevin dynamics and a 3+1-dimensional hydrodynamical description of the heavy-ion collision, and are fragmented and hadronized using a modified version of the color evaporation model that takes into account non-trivial evolution in position space, as well as the possibility of recomb…
We construct a theoretical framework to describe the evolution of heavy flavors produced in relativistic heavy-ion collisions. The in-medium energy loss of heavy quarks is described using our modified Langevin equation that incorporates both quasi-elastic scatterings and the medium-induced gluon radiation. The space-time profiles of the fireball is described by a (2+1)-dimensional hydrodynamics simulation. A hybrid model of fragmentation and coalescence is utilized for heavy quark hadronization, after which the produced heavy mesons together with the soft hadrons produced from the bulk QGP are…
We perform a systematic analysis of exclusive hadronic channels in e+e- collisions at centre-of-mass energies between 2.1 and 2.6 GeV within the statistical hadronization model. Because of the low multiplicities involved, calculations have been carried out in the full microcanonical ensemble, including conservation of energy-momentum, angular momentum, parity, isospin, and all relevant charges. We show that the data is in an overall good agreement with the model for an energy density of about 0.5 GeV/fm^3 and an extra strangeness suppression parameter gamma_S ~ 0.7, essentially the same values…
Heavy flavor production at the future Electron-Ion Collider (EIC) will allow us to precisely determine the quark/gluon fragmentation processes in vacuum and the nuclear medium especially within the poorly constrained kinematic region. Heavy flavor hadron and jet reconstruction with the recent EIC detector design have been studies in simulation. Results of corresponding physics projections such as the flavor dependent hadron nuclear modification factor $R_{eA}$ in electron+nucleus collisions will be shown. The statistical precision obtained by these proposed heavy flavor measurements for the fu…
Three possible scenarios of the statistical hadronization model are reexamined with the use of the $p_{T}$ spectra of the PHENIX and very low $p_{T}$ PHOBOS measurements at $\sqrt{s_{NN}}=200$ GeV. These scenarios are: (\textit{a}) full chemical non-equilibrium, (\textit{b}) strangeness chemical non-equilibrium and (\textit{c}) chemical equilibrium. Fits to the spectra are done within the Cracow single-freeze-out model, which takes into account both the expansion and resonance decays. Predictions for spectra of $ϕ$, $K(892)^{\ast 0}$ and $π^{0}$ are also given. The global variables like the tr…
We present an analysis of hadronic multiplicities measured in Pb-Pb collisions at \sqrt s_{NN} = 2.76 TeV as a function of the collision centrality within the statistical hadronization model. Evidence is found of a dependence of the chemical freeze-out temperature as a function of centrality, with a slow rise from central to peripheral collisions, which we interpret as an effect of post-hadronization inelastic scatterings. Using correction factors calculated by means of a simulation based on the UrQMD model, we are able to obtain a significant improvement in the statitical model fit quality an…
We formulate and study a mechanical instability criterion for sudden hadronization of dense matter fireballs formed in 158A GeV Pb--Pb collisions. Considering properties of quark-gluon matter and hadron gas we obtain the phase boundary between these two phases and demonstrate that the required deep QGP supercooling prior to sudden hadronization has occurred.
We study the production of charmonia and charmed hadrons in nucleus-nucleus collisions at SPS, RHIC, and LHC energies within the framework of the statistical hadronization model. Results from this model are compared to the measured yields and centrality dependence of J/psi production at SPS and RHIC energies. We explore and contrast the centrality dependence of the production of mesons with open and hidden charm at SPS, RHIC, and LHC. The sensitivity of the results to various input parameters is analyzed in detail for RHIC energy.
Understanding the hadronization of the quark-gluon plasma (QGP) remains a challenging problem in the study of strong-interaction matter as produced in ultrarelativistic heavy-ion collisions (URHICs). The large mass of heavy quarks renders them excellent tracers of the color neutralization process of the QGP when they convert into various heavy-flavor (HF) hadrons. We develop a 4-momentum conserving recombination model for HF mesons and baryons that recovers the thermal and chemical equilibrium limits and accounts for space-momentum correlations (SMCs) of heavy quarks with partons of the hydrod…
We present an analysis of $Ω$, $Ξ$, $Λ$ and $ϕ$ spectra from Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV in terms of distributions of effective constituent quarks at hadronization. Consistency in quark ratios derived from various hadron spectra provides clear evidence for hadron formation dynamics as suggested by quark coalescence or recombination models. We argue that the constituent quark distribution reflects properties of the effective partonic degrees of freedom at hadronization. Experimental data indicate that strange quarks have a transverse momentum distribution flatter than that of up…
Applying a quark combination model for the hadronization of Quark Gluon Plasma (QGP) and A Relativistic Transport (ART) model for the subsequent hadronic rescattering process, we investigate the production of $K^{*0}$ and $Σ^*$ resonances in central Au+Au collisions at $\sqrt{s_{NN}}=$ 200 GeV and 62.4 GeV. The initial $K^{*0}$ produced via hadronization is higher than the experimental data in the low $p_T$ region and is close to the data at 2-3 GeV/c. We take into account the hadronic rescattering effects which lead to a strong suppression of $K^{*0}$ with low $p_T$, and find that the $p_T$ s…
We analyze event-by-event fluctuations of the transverse momentum in relativistic heavy-ion collisions at RHIC in the framework based on the fluctuating Glauber-model initial conditions, event-by-event (3+1)-dimensional viscous hydrodynamics, and statistical hadronization. We use the scaled fluctuation measure < Delta p_Ti Delta p_Tj > / << p_T >>. The identified "geometric" mechanism of generating the transverse-momentum fluctuations from the initial size fluctuations, transmitted to the final statistical-hadronization phase with hydrodynamics, is capable of easily reproducing the magnitude o…
A detailed study of chemical freeze-out in nucleus-nucleus collisions at beam energy 158A GeV is presented. By analyzing hadronic multiplicities within the statistical hadronization approach, the chemical equilibration of p-p, C-C, Si-Si and Pb-Pb systems is studied as a function of the number of participating nucleons in the system. Additionally, Two Component statistical hadronization model is applied to the data and is found to be able to explain the observed strangeness hadronic phase space under-saturation.
We review the quark coalescence model for hadronization in relativistic heavy ion collisions and show how it can explain the observed large baryon to meson ratio at intermediate transverse momentum and scaling of the elliptic flows of identified hadrons. We also show its predictions on higher-order anisotropic flows and discuss how quark coalescence applied to open- and hidden-charm mesons can give insight to charm quark interactions in the quark-gluon plasma and $J/Ψ$ production in heavy ion collisions.
We argue that the emission of hadrons with transverse momentum up to about 5 GeV/c in central relativistic heavy ion collisions is dominated by recombination, rather than fragmentation of partons. This mechanism provides a natural explanation for the observed constant baryon-to-meson ratio of about one and the apparent lack of a nuclear suppression of the baryon yield in this momentum range. Fragmentation becomes dominant at higher transverse momentum, but the transition point is delayed by the energy loss of fast partons in dense matter.
We study heavy flavor evolution and hadronization in relativistic heavy-ion collisions. The in-medium evolution of heavy quarks is described using our modified Langevin framework that incorporates both collisional and radiative energy loss mechanisms. The subsequent hadronization process for heavy quarks is calculated with a fragmentation plus recombination model. We find significant contribution from gluon radiation to heavy quark energy loss at high $p_T$; the recombination mechanism can greatly enhance D meson production at medium $p_T$. Our calculation provides a good description of D meso…
We discuss experimental features of identified particle production from nucleus-nucleus collisions. These features reflect hadronization from a deconfined partonic matter whose particle formation scheme is distinctly different from fragmentation phenomenology in elementary collisions. Multi-parton dynamics, such as quark coalescences or recombinations, appear to be essential to explain the experimental measurements at the intermediate transverse momentum of 2--5 GeV/c. Constituent quarks seem to be the dominant degrees of freedom at hadronization. Heavy quark production should help quantify de…
We address the principles governing QGP hadronization and particle production in relativistic heavy-ion collisions. We argue that chemical non-equilibrium is required and show that once this condition is assumed a very good description of hadron production in collider RHIC and at LHC heavy ion experiments follows. We present results of our analysis as a function of centrality. Comparing most extreme experimental conditions we show that only the reaction volume and degree of strangeness phase space saturation change. We determine the universal QGP fireball hadronization conditions.
Core-corona procedure and microcanonical hadronization to understand strangeness enhancement in proton-proton and heavy ion collisions in the EPOS4 framework
We study the rapidity spectra in ultra-relativistic heavy ion collisions in the framework of the Landau hydrodynamical model. We find that thermal smearing effects improve the agreement with experimental results on pion rapidity spectra. We describe a simple model of the hadronization and discuss its consequences regarding the pion multiplicity and the increasing entropy condition.
The fast simultaneous hadronization and chemical freeze out of supercooled quark-gluon plasma, created in relativistic heavy ion collisions, leads to the re-heating of the expanding matter and to the change in a collective flow profile. We use the assumption of statistical nature of the hadronization process, and study quantitatively the freeze out in the framework of hydrodynamical Bjorken model with different quark-gluon plasma equations of state.
The rapidity densities in Au-Au collisions at center-of-mass energies 200 and 130 A GeV measured at Relativistic Heavy-Ion Collider by STAR and PHENIX collaborations are analyzed within the statistical hadronization model at chemical freeze-out. We find that the model can describe the experimental rapidity densities well. The corresponding chemical freeze-out parameters are determined and they are seen to be in agreement with what we expect from our previous analyzes at lower beam energies at AGS and SPS.
We show that all central rapidity hadron yields measured in Pb--Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV are well described by the chemical non-equilibrium statistical hadronization model (SHM), where the chemically equilibrated QGP source breaks up directly into hadrons. SHM parameters are obtained as a function of centrality of colliding ions, and we compare CERN Large Hadron Collider (LHC) with Brookhaven National Laboratory Relativistic Heavy Ion Collider (RHIC) results. We predict yields of unobserved hadrons and address anti-matter production. The physical properties of the quark--gluon…
We obtain strangeness production as function of centrality in a statistical hadronization model analysis of all experimental hadron production data in Au--Au collisions at $\sqrt{s_{NN}}=62.4\GeV$. Our analysis describes successfully the yield of strange and multi-strange hadrons recently published. We explore condition of hadronization as a function of centrality and find universality for the case of chemical non-equilibrium in the hadron phase space corresponding to quark--gluon plasma (QGP) in chemical equilibrium.
We study the mechanism and probability of in-medium hadronization in the deconfined medium produced in heavy-ion collisions at RHIC and LHC. We show the likelihood of color-neutral objects to be formed inside the partonic fireball and the probability of these states to escape the medium with reduced interaction strength and energy loss. We will suggest specific measurements that are sensitive to the early degrees of freedom and show predictions for these measurements at RHIC and the LHC
In the string melting version of a multiphase transport model, the hadronization algorithm has been improved by favoring parton combinations close in not only coordinate space but also momentum space. Formation probabilities of mesons, baryons, and antibaryons during hadronization are determined by their corresponding Wigner functions for the valence parton combinations with no free parameters, and the net baryon, electric, and strangeness charges are conserved during quark coalescence. Effects of the hadronization on anisotropic flows, collision energy dependence of the proton directed flow, …
We calculate diffusion and hadronization of heavy quarks in high-energy heavy-ion collisions implementing the notion of a strongly coupled quark-gluon plasma in both micro- and macroscopic components. The diffusion process is simulated using relativistic Fokker-Planck dynamics for elastic scattering in a hydrodynamic background. The heavy-quark transport coefficients in the medium are obtained from non-perturbative $T$-matrix interactions which build up resonant correlations close to the transition temperature. The latter also form the basis for hadronization of heavy quarks into heavy-flavor …
The parton recombination model has turned out to be a valuable tool to describe hadronization in high energy heavy ion collisions. I review the model and revisit recent progress in our understanding of hadron correlations. I also discuss higher Fock states in the hadrons, possible violations of the elliptic flow scaling and recombination effects in more dilute systems.
The integrated HydroKinetic Model (iHKM) is applied to analyse the results of direct photon spectra as well as elliptic and triangular flow measurements in 200A GeV Au+Au collisions at RHIC for different centrality bins. Experiments detect the strong centrality dependence of photon elliptic and triangular flow as increasing $v_n(p_T)$-coefficients towards peripheral collisions. The photon production in the model is accumulated from the different sources along with the process of relativistic heavy ion collision developing. Those include the primary hard photons from the parton collisions at th…
The hypothesis of statistical production of J/psi mesons at hadronization is formulated and checked against experimental data. It explains in the natural way the observed scaling behavior of the J/psi to pion ratio at the CERN SPS energies. Using the multiplicities of J/psi and eta mesons the hadronization temperature T_H = 175 MeV is found, which agrees with the previous estimates of the temperature parameter based on the analysis of the hadron yield systematics.
The recombination model as a model for hadronization from a quark-gluon plasma has been recently revived since it has advantages in explaining several important features of the final state produced in heavy-ion collisions at RHIC, such as the constituent quark number scaling of the elliptic coefficient versus the transverse energy of identified hadrons, the bending shape of the $p_T$ spectrum of hadrons near 5 GeV/c, and the measured large value of baryon to meson ratio(of the order of unity) in the same $p_T$ range. We have developed a dynamic simulation model of heavy-ion collisions in which…
Hydrodynamics merged with single-freeze-out statistical hadronization is used to describe the midrapidity hadron production in relativistic heavy-ion collisions at the highest RHIC energies and to make predictions for the LHC. Thermodynamic properties of the quark-gluon plasma are taken from lattice simulations, at low temperatures the hadron-gas equation of state is used, while in the cross-over region an interpolation between the two equations of state is constructed. The initial condition for hydrodynamics is obtained from a Glauber profile for the entropy, with the initial central temperat…
The description of hadron production in relativistic heavy-ion collisions in the statistical hadronization model is very good, over a broad range of collision energy. We outline this both for the light (u, d, s) and heavy (charm) quarks and discuss the connection it brings to the phase diagram of QCD.
We compare the distortion effects of three popular final-state hadronization schemes. We show how hadronization modifies the initial-state gluon correlations in high energy p+A collisions. The three models considered are (1) LPH: local parton-hadron duality, (2) CPR: collinear parton- hadron resonance independent fragmentation, and (3) LUND: color string hadronization. The strong initial-state azimuthal asymmetries are generated using the GLVB model for non-abelian gluon bremsstrahlung, assuming a saturation scale Qsat = 2 GeV. Long-range elliptic and triangular harmonics for the final hadron …
We present a new model for the description of heavy-quark hadronization in relativistic heavy-ion collisions in the presence of a reservoir of lighter thermal particles with which recombination can occur leading to the formation of color-singlet clusters. Color neutralization is assumed to occur locally, within the same fluid cell occupied by the heavy quark and it proceeds via the recombination of the latter with light antiquarks (quarks) or diquarks (anti-diquarks), which are assumed to be present in the medium with thermal abundance as effective degrees of freedom around the QCD crossover t…
Based on a multi-phase transport model, the measured jet fragmentation function ratio of Pb+Pb collisions to p+p collisions in CERN Large Hadron Collider experiments is decomposed into two parts, corresponding to the two contributions of jet hadronization from fragmentation and coalescence. The results suggest an existence of distinct competitions between two jet hadronization mechanisms for different $ξ$=ln(1/$z$) ranges in different centrality bins. The jet fragmentation functions for different types of hadrons (mesons and baryons) are proposed as a good probe to study the competition betwee…
