Statistical Hadronization Model Research Articles

Strangeness production with ALICE at the LHC

The main goal of the ALICE experiment is to study the physics of strongly interacting matter under extremely high temperature and energy density conditions to investigate the properties of the Quark-Gluon plasma (QGP). The enhanced production of strange hadrons with respect to non-strange particles was historically considered as one of the signatures of QGP formation during the evolution of the system created in heavy-ion collisions. The excellent tracking and particle identification capabilities of the ALICE experiment allow the reconstruction of multi-strange baryons via their weak decay channels over a large range of transverse momentum. The yields and the relative production rates of strange and multi-strange particles normalized to pions measured in pp, p–Pb, Pb–Pb and Xe–Xe collisions are presented as a function of particle multiplicity. The strangeness production dependence on the collision energy is also shown. Results are compared to QCD-inspired and statistical hadronization model predictions.

Probing QCD critical fluctuations from the yield ratio of strange hadrons in relativistic heavy-ion collisions

By analyzing the available data on strange hadrons in central Pb+Pb collisions from the NA49 Collaboration at the Super Proton Synchrotron (SPS) and in central Au+Au collisions from the STAR Collaboration at the Relativistic Heavy-Ion Collider (RHIC) in a wide collision energy range from sNN=6.3 GeV to 200 GeV, we find a possible non-monotonic behavior in the ratio OK-Ξ-ϕ-Λ=N(K+)N(Ξ−)N(ϕ)N(Λ) of K+, Ξ−, ϕ, and Λ yields as a function of sNN. Based on the quark coalescence model, which can take into account the effect of quark density fluctuations on hadron production, a possible non-monotonic behavior in the dependence of the strange quark density fluctuation on sNN is obtained. This is in contrast to the coalescence model that does not include quark density fluctuations and also to the statistical hadronization model as both fail to describe even qualitatively the collision energy dependence of the ratio OK-Ξ-ϕ-Λ. Our findings thus suggest that the signal and location of a possible critical endpoint in the QCD phase diagram, which is expected to result in large quark density fluctuations, can be found in the on-going Bean Energy Scan program at RHIC.

Yields of weakly bound light nuclei as a probe of the statistical hadronization model

The statistical hadronization model is a simple and efficient phenomenological framework in which the relative yields for very high energy heavy ion collisions are essentially determined by a single model parameter---the chemical freeze-out temperature. Recent measurements of yields of hadrons and light nuclei covering over 9 orders of magnitudes from the ALICE collaboration at the LHC were described by the model with remarkable accuracy with a chemical freeze-out temperature of 156.5 $\pm$ 1.5 MeV. A key physical question is whether the freeze-out temperature can be understood, literally, as the temperature at which the various species of an equilibrated gas of hadrons (including resonances) and nuclei chemically freeze out as the model assumes, or whether it successfully parametrizes the yield data for a different reason. The yields of weakly-bound light nuclei---the deuteron and the hypertriton---provide insights into this issue. The analysis indicates that a key assumption underlying the model---that hadrons (and nuclei), just prior to chemical freeze-out temperature, are in thermal equilibrium and are sufficiently dilute as to have particle distributions accurately described statistically by a nearly ideal gas of hadrons and nuclei with masses given by their free space values---appears to be inconsistent with the chemical freeze-out temperature output by the model, at least for these weakly-bound nuclei.

Transverse momentum distributions of charmonium states with the statistical hadronization model

Calculations and predictions are presented within the framework of the statistical hadronization model for transverse momentum spectra of the charmonium states J/ψ, ψ(2S) and X(3872) produced in nucleus-nucleus collisions at LHC energies. The results are confronted with available data and exhibit very good agreement by using particle flow profiles from state-of-the-art hydrodynamic calculations. For X(3872) production in Pb–Pb collisions we predict a transverse momentum distribution similar in shape to that for J/ψ with a strong enhancement at low transverse momenta and a production yield of about 1% relative to that for J/ψ.

Charm-baryon production in proton-proton collisions

Recent measurements of charm-hadron production in proton-proton collisions at the LHC have found a surprisingly large baryon to meson ratio. We propose that this observation can be explained by the statistical hadronization model (SHM), by employing a largely augmented set of charm-baryon states beyond the current listings of the particle data group. We estimate the additional states using guidance from the relativistic quark model and from lattice QCD. Using charm- and strange-quark fugacity factors to account for the well-known suppression of heavy flavor in elementary collisions, we compute the yields and spectra of D, Ds and Λc hadrons in proton-proton collisions at s=5 TeV. Our main finding is that the enhanced feeddown from excited charm baryons can account for the Λc/D0 ratio measured by ALICE at midrapidity, with some caveat for the forward-rapidity LHCb data. Furthermore, assuming independent fragmentation of charm quarks but with the hadronic ratios fixed by the SHM, the measured transverse-momentum (pT) spectra of D-mesons and Λc can also be described; in particular, the low-pT enhancement in the observed Λc/D0 ratio is attributed to the enhanced feeddown from “missing” charm-baryon states. We comment on the implications of these findings for measurements of Ds and Λc in heavy-ion collisions.

The thermal proton yield anomaly in Pb-Pb collisions at the LHC and its resolution

We propose a resolution of the discrepancy between the proton yield predicted by the statistical hadronization approach and data on hadron production in ultra-relativistic nuclear collisions at the LHC. Applying the S-matrix formulation of statistical mechanics to include pion-nucleon interactions, we reexamine their contribution to the proton yield, taking resonance widths and the presence of nonresonant correlations into account. The effect of multi-pion-nucleon interactions is estimated using lattice QCD results on the baryon-charge susceptibility. We show that a consistent implementation of these features in the statistical hadronization model, leads to a reduction of the predicted proton yield, which then quantitatively matches data of the ALICE collaboration for Pb-Pb collisions at the LHC.

Suppression of Λ(1520) resonance production in central Pb-Pb collisions at sNN=2.76 TeV

The production yield of the $\Lambda(1520)$ baryon resonance is measured at mid-rapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV with the ALICE detector at the LHC. The measurement is performed in the $\Lambda(1520)\rightarrow {\rm pK}^{-}$ (and charge conjugate) hadronic decay channel as a function of the transverse momentum ($p_{\rm T}$) and collision centrality. The $p_{\rm T}$-integrated production rate of $\Lambda(1520)$ relative to $\Lambda$ in central collisions is suppressed by about a factor of 2 with respect to peripheral collisions. This is the first observation of the suppression of a baryonic resonance at the LHC and the first 3$\sigma$ evidence of $\Lambda(1520)$ suppression within a single collision system. The measured $\Lambda(1520)/\Lambda$ ratio in central collisions is smaller than the value predicted by the statistical hadronisation model calculations. The shape of the measured $p_{\rm T}$ distribution and the centrality dependence of the suppression are reproduced by the EPOS3 Monte Carlo event generator. The measurement adds further support to the formation of a dense hadronic phase in the final stages of the evolution of the fireball created in heavy-ion collisions, lasting long enough to cause a significant reduction in the observable yield of short-lived resonances.

The QCD Phase Diagram from Statistical Model Analysis

In high multiplicity nucleus-nucleus collisions baryon-antibaryon annihilation and regeneration occur during the final hadronic expansion phase, thus distorting the initial equilibrium multiplicity ratios. We quantify the modifications employing the hybrid UrQMD transport model and apply them to the grand canonical partition functions of the Statistical Hadronization Model(SHM). We analyze minimum bias and central Pb+Pb collision data at SPS and LHC energy. We explain the Pion to Proton ratio puzzle. We also reproduce the deuteron to proton ratio at LHC energy by the SHM, and by UrQMD after attaching a phase space coalescence process. We discuss the resulting (T,μB) diagram.

Testing charm quark thermalisation within the Statistical Hadronisation Model

A wealth of data on charmonium production in Pb-Pb collisions from the LHC experiments has provided strong evidence for (re-)generation as a dominant production mechanism at low transverse momentum. We present an important extension of the statistical hadronisation model to describe J/ψ transverse momentum distributions based on input parameters from hydrodynamical simulations. Comparison to the data allows the testing of the degree of thermalisation of charm quarks in the quark-gluon plasma. To this end we will report analyses of the J/ψ transverse momentum spectra in Pb-Pb collisions at sNN=2.76and5.02TeV.

Baryon-antibaryon dynamics in relativistic heavy-ion collisions

The dynamics of baryon-antibaryon annihilation and reproduction ($B{\bar B} \leftrightarrow 3 M$) is studied within the Parton-Hadron-String Dynamics (PHSD) transport approach for Pb+Pb and Au+Au collisions as a function of centrality from lower Super Proton Synchrotron (SPS) up to Large Hadron Collider (LHC) energies on the basis of the quark rearrangement model (QRM). At Relativistic Heavy-Ion Collider (RHIC) energies we find a small net reduction of baryon-antibaryon ($B {\bar B}$) pairs while for the LHC energy of $\sqrt{s_{NN}}$ = 2.76 GeV a small net enhancement is found relative to calculations without annihilation (and reproduction) channels. Accordingly, the sizeable difference between data and statistical calculations in Pb+Pb collisions at $\sqrt{s_{NN}}$= 2.76 TeV for proton and antiproton yields \cite{53}, where a deviation of 2.7 $\sigma$ was claimed by the ALICE Collaboration, should not be attributed to a net antiproton annihilation. This is in line with the observation that no substantial deviation between the data and statistical hadronization model (SHM) calculations is seen for antihyperons, since according to the PHSD analysis the antihyperons should be modified by the same amount as antiprotons. As the PHSD results for particle ratios are in line with the ALICE data (within error bars) this might point towards a deviation from statistical equilibrium in the hadronization (at least for protons/antiprotons). Furthermore, we find that the $B {\bar B} \leftrightarrow 3 M$ reactions are more effective at lower SPS energies where a net suppression for antiprotons and antihyperons up to a factor of 2 -- 2.5 can be extracted from the PHSD calculations for central Au+Au collisions.

Reduction of the K* meson abundance in heavy ion collisions

We study the $K^*$ meson reduction in heavy ion collisions by focusing on the hadronic effects on the $K^*$ meson abundance. We evaluate the absorption cross sections of the $K^*$ and $K$ meson by light mesons in the hadronic matter, and further investigate the variation in the meson abundances for both particles during the hadronic stage of heavy ion collisions. We show how the interplay between the interaction of the $K^*$ meson and kaon with light mesons in the hadronic medium determines the final yield difference of the statistical hadronization model to the experimental measurements. For the central Au+Au collision at $\sqrt{s_{NN}}=200$ GeV, we find that the $K^*/K$ yield ratio at chemical freeze-out decreases by $36\%$ during the expansion of the hadronic matter, resulting in the final ratio comparable to STAR measurements of 0.23 $\pm0.05$.

Kinetic freeze-out conditions for the production of resonances, hadronic molecules, and light nuclei

We investigate the freeze-out conditions of a particle in an expanding system of interacting particles in order to understand the productions of resonances, hadronic molecules and light nuclei in heavy ion collisions. Applying the kinetic freeze-out condition with explicit hydrodynamic calculations for the expanding hadronic phase to the daughter particles of $K^*$ mesons, we find that the larger suppression of the yield ratio of $K^*/K$ at LHC than at RHIC compared to the expectations from the statistical hadronization model based on chemical freeze-out parameters reflects the lower kinetic freeze-out temperature at LHC than at RHIC. Furthermore, we point out that for the light nuclei or hadronic molecules that are bound, the yields are affected by the freeze-out condition of the respective particle in the hadronic matter, which leads to the observation that the deuteron production yields are independent of the size of deuteron, and depend only on the number of ground state constituents.

Strangeness production in Pb-Pb collisions at LHC energies with ALICE

The results on the production of strange and multi-strange hadrons (K0S, Λ, Ξ and Ω) measured with ALICE in Pb-Pb collisions at the top LHC energy of [see formula in PDF] = 5.02 TeV are reported. Thanks to its excellent tracking and particle identification capabilities, ALICE is able to measure weakly decaying particles through the topological reconstruction of the identified hadronic decay products. Results are presented as a function of centrality and include transverse momentum spectra measured at central rapidity, pT-dependent Λ/K0S ratios and integrated yields. A systematic study of strangeness production is of fundamental importance for determining the thermal properties of the system created in ultrarelativistic heavy ion collisions. In order to study strangeness enhancement, the yields of studied particles are normalised to the corresponding measurement of pion production in the various centrality classes. The results are compared to measurements performed at lower energies, as well as to different systems and to predictions from statistical hadronization models.

Studying Strangeness Production with HADES

The High-Acceptance DiElectron Spectrometer (HADES) operates in the 1 - 2A GeV energy regime in fixed target experiments to explore baryon-rich strongly interacting matter in heavy-ion collisions at moderate temperatures with rare and penetrating probes. We present results on the production of strange hadrons below their respective NN threshold energy in Au+Au collisions at 1.23A GeV ([see formula in PDF] = 2.4 GeV). Special emphasis is put on the enhanced feed-down contribution of ϕ mesons to the inclusive yield of K- and its implication on the measured spectral shape of K-. Furthermore, we investigate global properties of the system, confronting the measured hadron yields and transverse mass spectra with a Statistical Hadronization Model (SHM) and a blastwave parameterization, respectively. These supplement the world data of the chemical and kinetic freeze-out temperatures.

Production of Σ(1385)± and Ξ(1530)0 measured by ALICE in pp, p–Pb and Pb–Pb collisions at the LHC

The measurement of resonances in ultra-relativistic heavy-ion collisions allows one to study the properties of the hadronic medium. Resonances with short lifetimes compared to the duration of the time span between chemical and kinetic freeze out are good candidates to probe the interplay of particle re-scattering and regeneration in the hadronic phase, which result in a modification of their measured yields. Measurements of Σ(1385)± and Ξ(1530)0 have been performed with the ALICE detector in pp, p–Pb and Pb–Pb collisions at LHC energies. We report on pT-integrated yield ratios as function of charged-particle multiplicity density, 〈dNch/dηlab〉, which is used as a proxy for the size of collision system. These results complement the information derived from the measurement of other resonances such as K⁎(892)0 and ϕ(1020). The system size dependence of the yield ratio of short-lived resonances to longer-lived particles with the same strangeness content is discussed and compared to predictions from pQCD-inspired models, statistical hadronization models and EPOS.

Production of Σ(1385)± and Ξ(1530)0 in p–Pb collisions at measured by ALICE at the LHC

In order to study the hot hadronic matter created in heavy-ion collisions, it is important to compare particle production in large systems to that in smaller systems, such as proton-proton (pp) and proton-lead (p–Pb) collisions. In particular, resonances with different lifetimes are good candidates to probe the interplay of particle re-scattering and regeneration in the hadronic phase. The yields of the strange and double-strange hyperon resonances Σ(1385)± and Ξ(1530)0 are measured in the rapidity range −0.5 < yCMS < 0 in p–Pb collisions at with the ALICE detector at the LHC. We report on the transverse momentum distributions and mean transverse momentum as a function of the charged-particle multiplicity. These results complement the information derived from the measurements of other resonances such as K*(892)0 and ˚(1020). The multiplicity dependence of the integrated yield ratios of excited hyperons to longer-lived particles is discussed and compared to model predictions from pQCD-inspired models such as PYTHIA8 as well as statistical hadronization models.

Jet mass dependence of fragmentation in positron-proton collisions

We propose the characterization of fragmentation functions by the energy fraction x, a hadron takes away from the energy of the jet measured in the frame co-moving with the jet. Besides, we propose the usage of the jet mass as the fragmentation scale Q. We show that these two Lorentz-invariant variables emerge naturally in a microcanonical ensemble with conserved fourmomentum. Then, we construct a statistical hadronisation model, in which, two features of the hadronic final states in various high-energy reactions (power law spectra and negative-binomial multiplicity distributions) can be connected simply. Finally, we analyse the scale dependence of the parameters of the model (power of the spectrum and mean energy per hadron) in the phi^3 theory. Fitting fragmentation functions in diffractive positron-proton collisions, we obtain a prediction for the jet mass dependence of the hadron multiplicity distribution inside jets.

The Mar(e)k of QGP: Strangeness

Strangeness signature of of quark-gluon plasma (QGP) is central to the exploration of baryon-dense matter: the search for the critical point and onset of deconfinement. I report on the discovery of QGP by means of strangeness: The key historical figures and their roles in this quest are introduced and the experimental results obtained are discussed. The important role of antihyperons is emphasized. The statistical hadronization model, and sudden hadronization are described. Results of present day data analysis: strangeness and entropy content of a large fireball, and the universal hadronization condition describing key features of all explored collision systems are presented.

Hadron yields, the chemical freeze-out and the QCD phase diagram

We present the status of the chemical freeze-out, determined from fits of hadron yields with the statistical hadronization (thermal) model, with focus on the data at the LHC. A description of the yields of hadrons containing light quarks as well as the application of the model for the production of the J/ψ meson is presented. The implications for the QCD phase diagram are discussed.

Jet Mass Fluctuations and Fragmentation Functions

The effect of jet mass fluctuations on the fragmentation process is examined in the framework of a statistical hadronisation model. In this model, the fragmentation scale Q is taken to be the virtuality of the leading parton, and jet mass fluctuations are accounted for through this quantity. The scale evolution of the model is treated in the phi^3 theory with leading-order splitting function and one-loop coupling.