S. Wheaton

THERMUS—A thermal model package for ROOT ✩

THERMUS is a package of C++ classes and functions allowing statistical-thermal model analyses of particle production in relativistic heavy-ion collisions to be performed within the ROOT framework of analysis. Calculations are possible within three statistical ensembles; a grand-canonical treatment of the conserved charges B, S and Q, a fully canonical treatment of the conserved charges, and a mixed-canonical ensemble combining a canonical treatment of strangeness with a grand-canonical treatment of baryon number and electric charge. THERMUS allows for the assignment of decay chains and detector efficiencies specific to each particle yield, which enables sensible fitting of model parameters to experimental data.

Transition from baryonic to mesonic freeze-out

Abstract The recently discovered sharp peak in the K + / π + ratio in relativistic heavy-ion collisions is discussed in the framework of the statistical model. In this model a rapid change is expected as the hadronic gas undergoes a transition from a baryon-dominated to a meson-dominated gas. The transition occurs at a temperature T = 140 MeV and baryon chemical potential μ B = 410 MeV corresponding to an incident energy of s N N = 8.2 GeV . The maximum in the Λ / π ratio is well reproduced by the statistical model, but the change in the K + / π + ratio is much less pronounced than the one observed by the NA49 Collaboration. The calculated smooth increase of the K − / π − ratio and the shape of the Ξ − / π + and Ω − / π + ratios exhibiting maxima at different incident energies is consistent with the presently available experimental data. We conclude that the measured particle ratios with 20–30% deviations agree with a hadronic freeze-out scenario. These deviations seem to occur just in the transition from baryon-dominated to meson-dominated freeze-out.

Transverse Energy per Charged Particle and Freeze-Out Criteria in Heavy-Ion Collisions

Abstract In relativistic nucleus–nucleus collisions the transverse energy per charged particle, E T / N ch , increases rapidly with beam energy and remains approximately constant at about 800 MeV for beam energies from SPS to RHIC. It is shown that the hadron resonance gas model describes the energy dependence, as well as the lack of centrality dependence, qualitatively. The values of E T / N ch are related to the chemical freeze-out criterium E / N ≈ 1 GeV valid for primordial hadrons.

Saturation of ET /Nch and freeze-out criteria in heavy-ion collisions

The pseudorapidity densities of transverse energy, the charged particle multiplicity and their ratios, E T /N ch , are estimated at mid-rapidity, in a statistical-thermal model based on chemical freeze-out criteria, for a wide range of energies from GSI-AGS-SPS to RHIC. It has been observed that in nucleus-nucleus collisions, E T /N ch increases rapidly with beam energy and remains approximately constant at about a value of 800 MeV for beam energies from SPS to RHIC. E T /N ch has been observed to be almost independent of centrality at all measured energies. The statistical-thermal model describes the energy dependence as well as the centrality independence, qualitatively well. The values of E T /N ch are related to the chemical freeze-out criterium, E/N ≈ 1 GeV valid for primordial hadrons.

Saturation of transverse energy per charged hadron and freeze-out criteria in heavy-ion collisions

Abstract.nFor beam energies from SPS to RHIC, nthe transverse energy per charged particle, ET/Nch,nsaturates at a value of approximately 0.8u2009GeV. nA direct connection between this value and nthe freeze-out criterium E/N ≈1u2009GeV for the primordial energynand particle number in the hadronic resonance gas model is established.

The thermal model and the transition from baryonic to mesonic freeze-out

Abstract.The present status of the thermal model is reviewed and the recently discovered sharp peak in the K+/π+ ratio is discussed in this framework. It is shown that the rapid change is related to a transition from a baryon-dominated hadronic gas to a meson-dominated one. Further experimental tests to clarify the nature of the transition are discussed. In the thermal model the corresponding maxima in the Ξ/π and Ω/π ratios occur at slightly different beam energies.

Transition from baryon-to meson-dominated freeze-out—early decoupling around 30 A GeV?

The recently discovered sharp peak in the excitation function of the K+/?+ ratio around 30 A GeV in relativistic heavy-ion collisions is discussed in the framework of the statistical model. In this model, the freeze-out of an ideal hadron gas changes from a situation where baryons dominate to one with mainly mesons. This transition occurs at a temperature T = 140 MeV and a baryon chemical potential ?B = 410 MeV corresponding to an energy of . The calculated maximum in the K+/?+ ratio is, however, much less pronounced than that observed by the NA49 Collaboration. The smooth increase of the K?/?? ratio with incident energy and the shape of the excitation functions of the ?/?+, ??/?+ and ??/?+ ratios all exhibiting maxima at different incident energies is consistent with the presently available experimental data. The measured K+/?+ ratio exceeds the calculated one just at the incident energy when the freeze-out condition is changing. We speculate that at this point freeze-out might occur in a modified way. We discuss a scenario of an early freeze-out which indeed increases the K+/?+ ratio while most other particle ratios remain essentially unchanged. Such an early freeze-out is supported by results from HBT studies.

The Horn and the Thermal Model.

The recently discovered sharp peak in the K + /π + ratio in relativistic heavy-ion collisions is discussed in the framework of the thermal model. In this model a rapid change is expected as the hadronic gas undergoes a transition from a baryon-dominated to a meson- dominated gas. The transition occurs at a temperature T = 140 MeV and baryon chemical potential µB = 410 MeV corresponding to an incident energy of √ sNN = 8.2 GeV. The thermal model has been extremely successful in bringing order to a very large number of experimental results on particle yields in relativistic heavy-ion collisions. The results for the temperature and baryon chemical potential have been found to be consistent with having E/N = 1 GeV from the lowest beam energies up to the highest ones. This is illustrated in Fig. 1 which combines results from SIS up to RHIC. The NA49 Collaboration has recently performed a series of measurements of Pb-Pb collisions at 20, 30, 40, 80 and 158 AGeV beam energies. When these results are combined with measurements at lower beam energies from the AGS and SIS they reveal an unusually sharp variation with beam energy in the Λ/ � π� ,w ith� π �≡ 3/2(π + + π � ), and in the K + /π + ratios. Such a strong variation with energy does not occur in pp collisions and therefore indicates a major difference in heavy-ion collisions. This transition has been referred to in Ref. (1) as the horn. A strong variation with energy of the Λ/ � π� ratio has been predicted on the basis of arguments put forward in (2). In (3) another, less spectacular, possibility for the origin of the sharp maximum, namely as being due to the transition from a baryon-dominated to a meson-dominated hadronic gas has been suggested; the distinction being based on whether the entropy of the hadronic gas is dominated by baryons or by mesons. For this purpose various quantities along the freeze-out

Statistical model predictions for Pb–Pb collisions at LHC

The systematics of statistical model parameters extracted from heavy-ion collisions at lower energies are exploited to extrapolate in the LHC regime. Predictions of various particle ratios are presented and particle production in central Pb–Pb collisions at LHC is discussed in the context of the statistical model. The sensitivity of several ratios on the temperature and the baryon chemical potential is studied in detail, and some of them, which are particularly appropriate to determine the chemical freeze-out point experimentally, are indicated. The impact of feed-down contributions from resonances, especially to light hadrons, is illustrated.

Comparison of chemical freeze-out criteria in heavy-ion collisions

One of the most remarkable results to emerge from heavy-ion collisions over the past two decades is the striking regularity shown by particle yields at all energies. This has led to several very successful proposals describing particle yields over a very wide range of beam energies, reaching from 1 A GeV up to 200 A GeV, using only one or two parameters. A systematic comparison of these proposals is presented here. The conditions of fixed energy per particle, baryon+anti-baryon density, normalized entropy density as well as percolation model are investigated. The results are compared with the most recent chemical freeze-out parameters obtained in the thermal-statistical analysis of particle yields. The sensitivity and dependence of the results on parameters is analyzed and discussed. It is shown that in the energy range above the top AGS energy, within present accuracies, all chemical freeze-out criteria give a fairly good description of the particle yields. However, the low energy heavy-ion data favor the constant energy per particle as a unified condition of chemical particle freeze-out. This condition also shows the weakest sensitivity on model assumptions and parameters.