The excluded volume hadron gas model and pion production at the SPS

Experimental data for nucleus-nucleus collisions at the CERN SPS suggest that an ideal hadron gas model is unable to account simultaneously (same baryonic chemical potential and temperature at freeze-out) for the strange anti-baryon to baryon ratios and pion abundances. Using a thermodynamically consistent excluded volume model we examine possibilities to account for the observed excess of pions.     

Thermal hadron production in high energy heavy ion collisions

We provide a method to test if hadrons produced in high energy heavy ion collisions were emitted at freeze-out from an equilibrium hadron gas. Our considerations are based on an ideal gas at fixed temperatureT _f , baryon number densityn _B , and vanishing total strangeness. The constituents of this gas are all hadron resonances up to a mass of 2 GeV; they are taken to decay according to the experimentally observed branching ratios. The ratios of the various resulting hadron production rates are tabulated as functions ofT _f andn _B . These tables can be used for the equilibration analysis of any heavy ion data; we illustrate this for some specific cases.     

Quark model for multiparticle and inclusive reactions

The relative multiplicity of different hadrons produced in high-energy collisions is found in the framework of the quark model. Appart from the usual hypothesis about the quark structure of hadrons, two extra assumptions are made. Firstly, produced particles are supposed to be mainly the members of the meson 36-plet and baryon (antibaryon) 56-plet. Secondly, production of strange quarks is assumed to be suppressed relative to non-strange quarks roughly by a factor of three, as taken from experiment. In the small-x region the agreement with experimental data is satisfactory. In the fragmentation region it is necessary to take into account the kinematics of the resonant state's decay. The influence of such decay on the x and p_T² distributions of hadrons is discussed.     

Chemical equilibration of baryons in an expanding fireball

Due to long chemical equilibration times of hadrons in the hadron gas phase in relativistic heavy ion collisions it has been suggested that they are “born" into equilibrium. Here we review reactions that allow for quick equilibration times within the hadron gas phase such as multi-mesonic reactions at SpS and Hagedorn resonances decays at RHIC. The inclusion of a Bjorken expansion reveals that baryon anti-baryon pairs can quickly equilibrate within the hadron gas phase.     

Hadron production in relativistic nuclear collisions: thermal hadron source or hadronizing quark-gluon plasma?

Measured hadron yields from relativistic nuclear collisions can be equally well understood in two physically distinct models, namely a static thermal hadronic source vs. a time-dependent, nonequilibrium hadronization off a quark-gluon plasma droplet. Due to the time-dependent particle evaporation off the hadronic surface in the latter approach the hadron ratios change (by factors of ) in time. Final particle yields reflect time averages over the actual thermodynamic properties of the system at a certain stage of the evolution. Calculated hadron, strangelet and (anti-)cluster yields as well as freeze-out times are presented for different systems. Due to strangeness distillation the system moves rapidly out of the , plane into the -sector. Strangeness to baryon ratios prevail during a considerable fraction (50%) of the time evolution (i.e. -droplets or even -droplets form the system at the late stage: The possibility of observing this time evolution via two-particle correlations is discussed). The observed hadron ratios require MeV and MeV. If the present model is fit to the extrapolated hadron yields, metastable hypermatter can only be produced with a probability for . Received: 15 April 1997 / Revised version: 5 June 1997     

On the possibility of thermalization of heavy mesons in ultrarelativistic nuclear collisions

The phenomenological analysis and interpretation of experimental data from RHIC and LHC on the production of J/ψ and D mesons in heavy-ion collisions are performed within the two-component HYDJET++ model including the thermal and hard mechanisms of hadron production. It is shown that the thermal freeze-out of charmed mesons at RHIC energies occurs earlier than the thermal freeze-out of light hadrons (assumingly, simultaneously with chemical freeze-out), which indicates that J/ψ and D mesons are not in kinetic equilibrium with the formed hadronic matter. At the same time, a significant part of D mesons at LHC energies are in kinetic equilibrium with the formed thermalized matter, but J/ψ mesons are still characterized by early freeze-out.     

Leading particle production in light flavour jets

The energy distribution and type of the particle with the highest momentum in quark jets are determined for each of the five quark flavours making only minimal model assumptions. The analysis is based on a large statistics sample of hadronic decays collected with the OPAL detector at the LEP collider. These results provide a basis for future studies of light flavour production at other centre-of-mass energies. We use our results to study the hadronisation mechanism in light flavour jets and compare the data to the QCD models JETSET and HERWIG. Within the JETSET model we also directly determine the suppression of strange quarks to be by comparing the production of charged and neutral kaons in strange and non-strange light quark events. Finally we study the features of baryon production. Received: 19 November 1999 / Published online: 8 May 2000     

Dynamics of the hadronization phase transition at finite baryon chemical potentials

The dynamics of the expansion (conserving total baryon number and entropy) of a quark-gluon plasma which undergoes a first-order phase transition into a hadron resonance gas is studied. An increase of the temperature and a long lifetime of the system are observed in the two-phase coexistence region. These phenomena may prove to be crucial for the survival of strongly interacting probes which have been proposed as signals for the formation of a quark-gluon plasma.     

Fast chemical equilibration of hadrons in an expanding fireball

The suggestion of hadrons being “born” into equilibrium arose from long chemical equilibration times of hadrons in the hadron gas phase in relativistic heavy ion collisions. Here we consider possible Hagedorn states, which contribute to fast chemical equilibration times of baryon anti-baryon pairs (as well as kaon anti-kaon pairs) inside a hadron gas and just below the critical temperature. Master equations are used to describe the reactions. Within a Bjorken expansion scenario, the kaons and baryons as well as the bath of pions and Hagedorn resonances can indeed quickly chemically equilibrate.     

Topological bootstrap theory of hadrons

A topological framework is constructed for anS-matrix bootstrap theory of particles. Each component of anS-matrix topological expansion is associated with a pair of intersecting “quantum” and “classical” surfaces whose complexity exhibits an entropy property. The bounded classical surface embeds graphs that carry the direct observables — energymomentum, spin and electric charge. The closed quantum surface carries a triangulation whose orientations represent internal quantum numbers — which turn out to be baryon number, lepton number and flavor. A form of “color” automatically appears. All strong-interaction components of the expansion are generated through “Landau connected sums” from “zeroentropy” surface pairs — which are self generating. Elementary particles correspond to triangulated areas on the quantum surface; consistency at zero entropy determines allowed hadrondisks on quantum spheres together with the associated quantum numbers. Elementary topological hadrons turn out to include mesons, baryons and baryoniums, with quarks appearing as “peripheral triangles” (along the perimenters of hadron disks) whose attachments correspond to a total of 8 flavors as well as spin. Individual quarks do not carry momentum and cannot be hadrons; quark confinement is automatic. Also appearing within hadron disks are “core triangles” that carry baryon number and electric charge but no flavor or spin. Hadron disks have quantum numbers that accord with the lowestmass physically-observed mesons and baryons. The relation of topological theory to QCD is discussed.     

Quark condensate in a dilute hadronic gas containing an excess of baryons

We calculate the quark condensate within a simple model for the hadronic phase by evaluating the derivative of the pressure with respect to the quark mass. The corresponding phase diagram for the transition from the hadrons to a quark-gluon plasma is discussed and we also describe the composition of the hadron gas for several temperatures and baryon densities.     

Hagedorn states and thermalization

In recent years Hagedorn states have been used to explain the physics close to the critical temperature within a hadron gas. Because of their large decay widths these massive resonances lower η/s to near the AdS/CFT limit within the hadron gas phase. A comparison of the Hagedorn model to recent lattice results is made and it is found that for both T _c = 176 MeV and T _c = 196 MeV, the hadrons can reach chemical equilibrium almost immediately, well before the chemical freeze-out temperatures found in thermal fits for a hadron gas without Hagedorn states. In this paper we also observe the effects of Hagedorn States on the K ⁺/π⁺ horn seen at AGS, SPS, and RHIC.     

Thermal gas models and particle production in heavy ion collisions

A systematic study of particle production in nuclear S–S and S–W collisions at 200 GeV/A is presented within the context of an equilibrium interacting hadron gas model. It is shown that the results for strange particle multiplicities and for non-strange baryons obtained in the NA35 and WA85 experiments can be well described in terms of the considered model.     

Search for collective transverse flow using particle transverse momentum spectra in relativistic heavy-ion collisions

The particle transverse momentum spectra recently measured in relativistic heavy-ion collisions at CERN and BNL are analysed within an expanding fireball model. All the particle spectra at a given beam energy can be reproduced simultaneously with a single set of intensive parameters for the initial state of the fireball. As typical freeze-out parameters in this beam energy region we find a freeze-out temperatureT _f?110 MeV for most hadrons, and an average transverse expansion velocity at freeze-out of 〈v/c〉?0.4–0.45. The striking enhancement at transverse momentap _T<200 MeV/c in the CERN pion data cannot be fully explained by the existence of transverse flow.     

Equation of state of hadron resonance gas and the phase diagram of strongly interacting matter

The equation of state of hadron resonance gas at finite temperature and baryon density is calculated taking into account finite-size effects within the excluded-volume model. Contributions of known hadrons with masses up to 2 GeV are included in the zero-width approximation. Special attention is paid to the role of strange hadrons in the system with zero total strangeness. A density-dependent mean field is added to guarantee that the nuclear matter has a saturation point and a liquid-gas phase transition. The deconfined phase is described by the bag model with lowest order perturbative corrections. The phasetransition boundaries are found by using the Gibbs conditions with the strangeness neutrality constraint. The sensitivity of the phase diagram to the hadronic excluded volume and to the parametrization of the mean-field is investigated. The possibility of strangeness-antistrangeness separation in the mixed phase is analyzed. It is demonstrated that the peaks in the K/π and Λ/π excitation functions observed at low SPS energies can be explained by a nonmonotonous behavior of the strangeness fugacity along the chemical freeze-out line. The text was submitted by the authors in English.     

From chemical freeze-out to critical conditions in heavy ion collisions

We compare the statistical thermodynamics of hadron resonance gas with recent LGT results at finite chemical potential. We argue that for T≤T _cthe equation of state derived from Monte-Carlo simulations of 2-quark-flavor QCD at finite chemical potential is consistent with that of a hadron resonance gas when applying the same set of approximations as used in LGT calculations. We indicate the relation of chemical freeze-out conditions obtained from a detailed analysis of particle production in heavy ion collisions with the critical conditions required for deconfinement. We argue that the position of a hadron quark-gluon boundary line in temperature chemical potential plane can be determined in terms of the resonance gas model by the condition of fixed energy density.     

Thermodynamics of hadronic matter at high density

We calculate thermodynamics observables for an interacting relativistic hadron gas. Hadronic states are taken into account by the use of a sizeable portion of the experimental hadron spectrum, supplemented in some cases by an exponentially rising continuum. Calculations with non-zero baryon number densities, subject to the additional requirement of zero net strangeness, show structure in the heat capacity per unit volume of the baryon sector at a temperature of approximately 140 MeV. This structure also becomes visible in the total heat capacity per unit volume at large baryon number densities, and provides a signature for the change of the thermal response of the hadron gas from baryon- to meson-dominated, even though the meson number density is lower than the baryon number density. Furthermore, this structure is not seen in calculations with a massless hadron gas. Its origin is therefore associated with information contained in the hadronic mass spectrum, and thus with the sub-hadronic degrees of freedom of the hadrons.