The QCD confinement transition: hadron formation
We review the foundations and the applications of the statistical and the quark recombination model as hadronization models.
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arXiv subjects
F. Becattini
Publications and source records attributed to F. Becattini.
An introduction to the Statistical Hadronization Model
In these lectures I review the foundations and the applications of the statistical hadronization model to elementary and relativistic heavy ion collisions. The role of strangeness production and the general interpretation of results is addressed.
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Centrality dependence of strangeness production in heavy-ion collisions as a geometrical effect of core-corona superposition
It is shown that data on strange particle production as a function of centrality in Au-Au collisions at \sqrt(s)_{NN}= 200 GeV can be explained with a superposition of emission from a hadron gas at full chemical equilibrium (core) and from nucleon-nucleon collisions at the boundary (corona) of the overlapping region of the two colliding nuclei. This model nicely accounts for the enhancement of phi meson and strange particle production as a function of centrality observed in relativistic heavy ion collisions at that energy. The enhancement is mainly a geometrical effect, that is the increasing weight of the core with respect to corona for higher centrality, while strangeness canonical suppression in the core seems to play a role only in very peripheral collisions. This model, if confirmed at lower energy, would settle the long-standing problem of strangeness under-saturation in relativistic heavy ion collisions, parametrized by $\gs$. Furthermore, it would give a unique tool to locate the onset of deconfinement in nuclear collisions both as a function of energy and centrality if this is to be associated to the onset of the formation of a fully equilibrated core.
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Chemical freeze-out in ultra-relativistic heavy ion collisions at sqrt(s)_NN = 130 and 200 GeV
A comprehensive and detailed analysis of hadronic abundances measured in Au-Au collisions at RHIC at sqrt(s)_NN = 130 and 200 GeV is presented. The rapidity densities measured in the central rapidity region have been fitted to the statistical hadronization model and the chemical freeze-out parameters determined as a function of centrality, using data from experiments BRAHMS, PHENIX and STAR. The chemical freeze-out temperature turns out to be independent of centrality to a few percent accuracy, whereas the strangeness under-saturation parameter gamma_S decreases from almost unity in central collisions to a significantly lower value in peripheral collisions. Our results are in essential agreement with previous analyses, with the exception that fit quality at sqrt(s)_NN = 200 GeV is not as good as previously found. From the comparison of the two different energies, we conclude that the difference in fit quality, as described by chi2 values, is owing to the improved resolution of measurements which has probably exceeded the intrinsic accuracy of the simplified theoretical formula used in the fits.
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Strangeness production from SPS to LHC
Global strangeness production in relativistic heavy ion collisions at SPS and RHIC is reviewed. Special emphasis is put on the comparison with the statistical model and the canonical suppression mechanism. It is shown that recent RHIC data on strange particle production as a function of centrality can be explained by a superposition of a fully equilibrated hadron gas and particle emission from single independent nucleon-nucleon collisions in the outer corona.
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The Thermal Production of Strange and Non-Strange Hadrons in e+e- Collisions
The thermal multihadron production observed in different high energy collisions poses two basic problems: (1) why do even elementary collisions with comparatively few secondaries (e+e- annihilation) show thermal behaviour, and 2) why is there in such interactions a suppression of strange particle production? We show that the recently proposed mechanism of thermal hadron production through Hawking-Unruh radiation can naturally account for both. The event horizon of colour confinement leads to thermal behaviour, but the resulting temperature depends on the strange quark content of the produced hadrons, causing a deviation from full equilibrium and hence a suppression of strange particle production. We apply the resulting formalism to multihadron production in e+e- annihilation over a wide energy range and make a comprehensive analysis of the data in the conventional statistical hadronization model and the modified Hawking-Unruh formulation. We show that this formulation provides a very good description of the measured hadronic abundances, fully determined in terms of the string tension and the bare strange quark mass; it contains no adjustable parameters.
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The ideal relativistic spinning gas: polarization and spectra
We study the physics of the ideal relativistic rotating gas at thermodynamical equilibrium and provide analytical expressions of the momentum spectra and polarization vector for the case of massive particles with spin 1/2 and 1. We show that the finite angular momentum J entails an anisotropy in momentum spectra, with particles emitted orthogonally to J having, on average, a larger momentum than along its direction. Unlike in the non-relativistic case, the proper polarization vector turns out not to be aligned with the total angular momentum with a non-trivial momentum dependence.
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Angular momentum conservation in heavy ion collisions at very high energy
The effects of angular momentum conservation in peripheral heavy ion collisions at very high energy are investigated. It is shown that the initial angular momentum of the quark-gluon plasma should enhance the azimuthal anisotropy of particle spectra (elliptic flow) with respect to the usual picture where only the initial geometrical eccentricity of the nuclear overlap region is responsible for the anisotropy. In hydrodynamical terms, the initial angular momentum entails a non trivial dependence of the initial longitudinal flow velocity on the transverse coordinates. This gives rise to a non-vanishing vorticity in the equations of motion which enhances the expansion rate of the supposedly created fluid compensating for the possible quenching effect of viscosity. A distinctive signature of the vorticity in the plasma is the generation of an average polarization of the emitted hadrons, for which we provide analytical expressions. These phenomena might be better observed at LHC, where the initial angular momentum density will be larger and where we envisage an increase of the elliptic flow coefficient v_2 with respect to RHIC energies.
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The microcanonical ensemble of the ideal relativistic quantum gas with angular momentum conservation
We derive the microcanonical partition function of the ideal relativistic quantum gas with fixed intrinsic angular momentum as an expansion over fixed multiplicities. We developed a group theoretical approach by generalizing known projection techniques to the Poincare' group. Our calculation is carried out in a quantum field framework and applies to particles with any spin. It extends known results in literature in that it does not introduce any large volume approximation and it takes particle spin fully into account. We provide expressions of the microcanonical partition function at fixed multiplicities in the limiting classical case of large volumes and large angular momenta and in the grand-canonical ensemble. We also derive the microcanonical partition function of the ideal relativistic quantum gas with fixed parity.
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The microcanonical ensemble of the ideal relativistic quantum gas
We derive the microcanonical partition function of the ideal relativistic quantum gas of spinless bosons in a quantum field framework as an expansion over fixed multiplicities. Our calculation generalizes well known expressions in literature in that it does not introduce any large volume approximation and it is valid at any volume. We discuss the issues concerned with the definition of the microcanonical ensemble for a free quantum field at volumes comparable with the Compton wavelength and provide a consistent prescription of calculating the microcanonical partition function, which is finite at finite volume and yielding the correct thermodynamic limit. Besides an immaterial overall factor, the obtained expression turns out to be the same as in the non-relativistic multi-particle approach. This work is introductory to derive the most general expression of the microcanonical partition function fixing the maximal set of observables of the Poincare' group.
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Rapidity Variation of Thermal Parameters at SPS and RHIC
The rapidity dependence of the chemical freeze-out thermal parameters $T$ and $μ_B$ are determined at the highest RHIC and SPS energies. These show a systematic behavior towards an increase in $μ_B$ away from mid-rapidity and a corresponding decrease in the temperature $T$.
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Remark on statistical model fits to particle ratios in relativistic heavy ion collisions
In order to determine the chemical freeze-out parameters of the hadron-emitting source in relativistic heavy ion collisions some studies in literature perform fits by using as data input a subsample of ratios calculated out of experimentally measured hadron yields instead of yields themselves. We show that this is a statistically incorrect method fit, implying a bias in the extracted parameters.
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Thermal Dileptons at LHC
We predict dilepton invariant-mass spectra for central 5.5 ATeV Pb-Pb collisions at LHC. Hadronic emission in the low-mass region is calculated using in-medium spectral functions of light vector mesons within hadronic many-body theory. In the intermediate-mass region thermal radiation from the Quark-Gluon Plasma, evaluated perturbatively with hard-thermal loop corrections, takes over. An important source over the entire mass range are decays of correlated open-charm hadrons, rendering the nuclear modification of charm and bottom spectra a critical ingredient.
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Chemical Equilibrium in Heavy Ion Collisions: Rapidity Dependence
Particle yields in heavy ion collisions show an overwhelming evidence for chemical or relative chemical equilibrium at all beam energies. The rapidity dependence of the thermal parameters $T$ and $μ_B$ can now be determined over a wide range of rapidities and show a systematic behavior towards an increase in $μ_B$ away from mid-rapidity.
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Threshold effects in relativistic gases
Particle multiplicities and ratios in the microcanonical ensemble of relativistic gases near production thresholds are studied. It is shown that the ratio of heavy to light particle multiplicity may be enhanced in comparison to its thermodynamic limit.
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Energy and system size dependence of chemical freeze-out in relativistic nuclear collisions
We present a detailed study of chemical freeze-out in p-p, C-C, Si-Si and Pb-Pb collisions at beam momenta of 158A GeV as well as Pb-Pb collisions at beam momenta of 20A, 30A, 40A and 80A GeV. By analyzing hadronic multiplicities within the statistical hadronization model, we have studied the parameters of the source as a function of the number of the participating nucleons and the beam energy. We observe a nice smooth behaviour of temperature, baryon chemical potential and strangeness under-saturation parameter as a function of energy and nucleus size. Interpolating formulas are provided which allow to predict the chemical freeze-out parameters in central collisions at centre-of-mass energies > 4.5 GeV and for any colliding ions. Specific discrepancies between data and model emerge in particle ratios in Pb-Pb collisions at SPS between 20A and 40A GeV of beam energy which cannot be accounted for in the considered model schemes.
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Correlating Strangeness Enhancement and J/psi Suppression in Heavy Ion Collisions at sqrt(s)_NN = 17.2 GeV
It is shown that the strangeness enhancement and the J/psi anomalous suppression patterns observed in heavy ion collisions at top SPS energy, sqrt(s)_NN = 17.2 GeV, exhibit an interesting correlation if studied as a function of the transverse size of the interaction region. The onset of both phenomena seems to occur when the size exceeds \approx 4 fm. Strangeness enhancement is defined in terms of the strangeness undersaturation factor gamma_S and J/psi anomalous suppression in terms of the deviation from the absorption expected in a purely hadronic scenario.
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Multiplicity fluctuations in the hadron gas with exact conservation laws
The study of fluctuations of particle multiplicities in relativistic heavy-ion reactions has drawn much attention in recent years, because they have been proposed as a probe for underlying dynamics and possible formation of quark-gluon plasma. Thus, it is of uttermost importance to describe the baseline of statistical fluctuations in the hadron gas phase in a correct way. We have performed a comprehensive study of multiplicity distributions in the full ideal hadron-resonance gas in different ensembles, namely grand-canonical, canonical and microcanonical, using two different methods: asymptotic expansions and full Monte Carlo simulations. The method based on asymptotic expansion allows a quick numerical calculation of dispersions in the hadron gas with three conserved charges at primary hadron level, while the Monte-Carlo simulation is suitable to study the effect of resonance decays. Even though mean multiplicities converge to the same values, major differences in fluctuations for these ensembles persist in the thermodynamic limit, as pointed out in recent studies. We observe that this difference is ultimately related to the non-additivity of the variances in the ensembles with exact conservation of extensive quantities.
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