Exact Strangeness Conservation Research Articles

Exact strangeness conservation in heavy ion collisions

We investigate the increase in strangeness production with charged particle multiplicity (dNch/dy) seen by the ALICE collaboration at CERN in p-p, p-Pb and Pb-Pb collisions using the hadron resonance gas model. The strangeness canonical ensemble is used taking into account the interactions among hadrons using S-matrix corrections based on known phase shift analyses. We show the essential role of constraints due to the exact conservation of strangeness which is instrumental to describing observed features of strange particle yields and their scaling with dNch/dy. Furthermore, the results on comparing the hadron resonance gas model with and without S-matrix corrections, are presented. We observe that the interactions introduced by the phase shift analysis via the S-matrix formalism are essential for a better description of the yields data independent of collision system. This work is based on our longlasting collaboration and most recent publications with Jean Cleymans.

Hadronic Resonance Gas Model and Multiplicity Dependence in \(p\)–\(p\), \(p\)–Pb, Pb–Pb Collisions: Strangeness Enhancement

Recently the ALICE collaboration has observed an interesting systematic behaviour of ratios of identified particles to pions yields at the LHC, showing that they depend solely on the charged-particle multiplicity in pp, pPb and PbPb collisions. In particular, the yields of (multi)strange particles relative to pions, increases with multiplicity and the enhancement is mode pronounced with increasing strangeness content. We will argue, that such a pattern of arises naturally in the thermal model taking into account exact strangeness conservation. Furthermore, extending the thermal model by including hadron interactions within the S-matrix approach, the ALICE data can be well quantified by the thermal particle yields at the chiral-crossover temperature, as previously found in central Pb-Pb collisions.

Thermodynamic Limit in High-Multiplicity Proton-Proton Collisions at s=7 TeV

An analysis is made of the particle composition in the final state of proton-proton (pp) collisions at 7 TeV as a function of the charged particle multiplicity (dNch/dη). The thermal model is used to determine the chemical freeze-out temperature as well as the radius and strangeness suppression factor γs. Three different ensembles are used in the analysis: the grand canonical ensemble, the canonical ensemble with exact strangeness conservation, and the canonical ensemble with exact baryon number, strangeness, and electric charge conservation. It is shown that for the highest multiplicity class the three ensembles lead to the same result. This allows us to conclude that this multiplicity class is close to the thermodynamic limit. It is estimated that the final state in pp collisions could reach the thermodynamic limit when dNch/dη is larger than twenty per unit of rapidity, corresponding to about 300 particles in the final state when integrated over the full rapidity interval.

Comparison of p−p, p−Pb , and Pb-Pb collisions in the thermal model: Multiplicity dependence of thermal parameters

% An analysis is made of the particle composition (hadrochemistry) of the final state in proton-proton (p-p), proton-lead (p-Pb) and lead-lead (Pb-Pb) collisions as a function of the charged particle multiplicity ($\dNchdeta$). The thermal model is used to determine the chemical freeze-out temperature as well as the radius and strangeness saturation factor $\gamma_s$. Three different ensembles are used in the analysis namely, the grand canonical ensemble, the canonical ensemble with exact strangeness conservation and the canonical ensemble with exact baryon number, strangeness and electric charge conservation. It is shown that for high multiplicities (at least 20 charged hadrons in the mid-rapidity interval considered) the three ensembles lead to the same results.

Particle Transverse Momentum Distributions in p-p Collisions at √sNN=0.9 TeV

The midrapidity transverse momentum spectra of hadrons (p, K+, Ks0, ϕ, Λ, and (Ξ-+Ξ--)) and the available rapidity distributions of the strange hadrons (Ks0, (Λ+Λ-), (Ξ-+Ξ--)) produced in p-p collisions at LHC energy √sNN = 0.9 TeV have been studied using a Unified Statistical Thermal Freeze-out Model (USTFM). The calculated results are found to be in good agreement with the experimental data. The theoretical fits of the transverse momentum spectra using the model calculations provide the thermal freeze-out conditions in terms of the temperature and collective flow parameters for different hadronic species. The study reveals the presence of a significant collective flow and a well-defined temperature in the system thus indicating the formation of a thermally equilibrated hydrodynamic system in p-p collisions at LHC. Moreover, the fits to the available experimental rapidity distributions data of strange hadrons show the effect of almost complete transparency in p-p collisions at LHC. The model incorporates longitudinal as well as a transverse hydrodynamic flow. The contributions from heavier decay resonances have also been taken into account. We have also imposed the criteria of exact strangeness conservation in the system.

Thermal model description of p\u2013Pb collisions at sqrt{s_{NN}} = 5.02\xa0TeV

The ALICE data on light flavor hadron production obtained in p–Pb collisions at sqrt{s_{NN}} = 5.02 TeV are studied in the thermal model using the canonical approach with exact strangeness conservation. The chemical freeze-out temperature is independent of centrality except for the lowest multiplicity bin, with values close to 160 MeV but consistent with those obtained in Pb–Pb collisions at sqrt{s_{NN}} = 2.76 TeV. The value of the strangeness non-equilibrium factor gamma _s is slowly increasing with multiplicity from 0.9 to 0.96, i.e. it is always very close to full chemical equilibrium.

Complete strangeness measurements in heavy-ion collisions

We discuss strangeness production in heavy-ion collisions within and around the energy range of the planned NICA facility. We describe the minimal statistical model, in which the total strangeness yield is fixed by the observed or calculated $K^+$ multiplicity. We show how the exact strangeness conservation can be taken into account on the event-by-event basis in such a model. We argue that from strange particle yields one can reveal information about the collision dynamics and about possible modifications of particle properties in medium. This can be best achieved if the complete strangeness measurement is performed, i.e. kaons, anti-kaons, hyperons and multistrange hyperons are registered in the same experimental setup. In particular the production of hadrons containing two and more strange quarks, like $\Xi$ and $\Omega$ baryons could be of interest.

Statistical Model of the Early Stage of Nucleus--Nucleus Collisions with Exact Strangeness Conservation

The Statistical Model of the Early Stage, SMES, describes a transition between confined and deconfined phases of strongly interacting matter created in nucleus-nucleus collisions. The model was formulated in the late 1990s for central Pb+Pb collisions at the CERN SPS energies. It predicted several signals of the transition (onset of deconfinement) which were later observed by the NA49 experiment. The grand canonical ensemble was used to calculate entropy and strangeness production. This approximation is valid for reactions with mean multiplicities of particles carrying conserved charges being significantly larger than one. Recent results of NA61/SHINE on hadron production in inelastic p+p interactions suggest that the deconfinement may also take place in these reactions. However, in this case mean multiplicity of particles with non-zero strange charge is smaller than one. Thus for the modeling of p+p interactions the exact strangeness conservation has to be implemented in the SMES. This extension of the SMES is presented in the paper.

Strangeness balance in HADES experiments and theΞ−enhancement

The High Acceptance Di-Electron Spectrometer (HADES) data on strangeness production in Ar + KCl collisions at 1.76$A$ GeV are analyzed within a minimal statistical model. In the model the total negative strangeness content is fixed by the observed ${K}^{+}$ multiplicities. Particles with negative strangeness are assumed to remain in chemical equilibrium with themselves and in thermal equilibrium with the environment until a common freeze-out. Exact strangeness conservation in each collision event is explicitly preserved. This implies that $\ensuremath{\Xi}$ baryons can be released only in events where two or more kaons are produced. An increase of the fireball volume due to application of a centrality trigger in HADES experiments is taken into account. We find that experimental ratios of ${K}^{\ensuremath{-}}/{K}^{+}$, $\ensuremath{\Lambda}/{K}^{+}$, and $\ensuremath{\Sigma}/{K}^{+}$ can be satisfactorily described provided in-medium potentials are taken into account. However, the calculated ${\ensuremath{\Xi}}^{\ensuremath{-}}/\ensuremath{\Lambda}/{K}^{+}$ ratio proves to be significantly smaller compared to the measured value (eight times less than the experimental median value and three times less than the lower error bar). Various scenarios to explain observed $\ensuremath{\Xi}$ enhancement are discussed. Arguments are given in favor of the $\ensuremath{\Xi}$ production in direct reactions. The rates of the possible production processes are estimated and compared.

Do small systems equilibrate chemically?

Considering particle production in heavy-ion collisions, a particular role has been attributed to strange particles because strangeness was predicted to be a sensitive probe of the properties of QCD matter. The statistical model is very successful in describing the chemical composition of the final state of collisions over a wide range of incident energies. However, without an additional strangeness undersaturation factor, γS, hadron gas models hardly reproduce the data from small colliding systems nor from reactions at the smaller collision energies. Here we investigate the influence of an alternative assumption, exact strangeness conservation in small subvolumes of the fireball, on the model predictions. Therefore, we introduce strangeness equilibrated subvolumes. The canonical strangeness suppression in these correlated clusters accounts successfully for the smaller production of strange particles. The system size dependence of the correlation volume and of the thermal parameters are presented.

Importance of reaction volume in hadronic collisions: canonical enhancement

We study the canonical flavour enhancement arising from exact conservation of strangeness and charm flavour. Both the theoretical motivation, and the practical consequences are explored. We argue using qualitative theoretical arguments and quantitative evaluation, that this proposal to re-evaluate strangeness signature of quark–gluon plasma is not able to explain the majority of available experimental results.

Review of SIS experimental results on strangeness

A review of meson emission in heavy-ion collisions at incident energiesaround 1-2 A GeV is presented. It is shown how the shape of thespectra and the various particle yields vary with system size, withcentrality and with incident energy. A statistical model assuming thermaland chemical equilibrium and exact strangeness conservation (i.e. strangeness conservation per collision)explains most of the observed features.Emphasis is put on the study of K+ and K- emission. Within theframework of this statistical model it is shown that the experimentallyobserved equality of K+ and K- rates at threshold correctedenergies is due to a crossing of two excitationfunctions. Furthermore, the independence of the K+ to K-ratio of the number of participating nucleons observedbetween 1 and 10 A GeV is consistent with this model.The observed flow effects are beyond the scope of thismodel.

Statistical model description of K+ and K− production between 1–10 A·GeV

The excitation functions of K + and K − mesons in heavy ion collisions are studied within a statistical model assuming chemical and thermal equilibrium with exact strangeness conservation. At low incident energies the associate production of kaons, i.e., the production of a K + together with a hyperon and the production of a K − together with a K +, implies specific features: different threshold energies and different dependences of K + and K − yields on baryon number density. It is shown that the experimentally observed equality of the K + and K − rates at energies s − s th ≤0 is due to a crossing of the two excitation functions. Furthermore, the independence of the K + to K − ratio on the number of participating nucleons observed at 1 and 10 A·GeV is consistent with this model.

On the exact conservation laws in thermal models and the analysis of AGS and SIS experimental results

The production of hadrons in relativistic heavy ion collisions is studied using a statistical ensemble with thermal and chemical equilibrium. Special attention is given to exact conservation laws, i.e. certain charges are treated canonically instead of using the usual grand canonical approach. For small systems, the exact conservation of baryon number, strangeness and electric charge is to be taken into account. We have derived compact, analytical expressions for particle abundances in such ensemble. As an application, the change in ratios in AGS experiments with different interaction system sizes is well reproduced. The canonical treatment of three charges becomes impractical very quickly with increasing system size. Thus, we focus our attention on exact conservation of strangeness, and treat baryon number and electric charge grand canonically. We present expressions for particle abundances in such ensemble as well, and apply them to reproduce the large variety of particle ratios in GSI SIS 2 A GeV Ni-Ni experiments. At the energies considered here, the exact strangeness conservation fully accounts for strange particle suppression, and no extra chemical factor is needed.

Thermal model analysis of particle ratios in Ni+Ni experiments using exact strangeness conservation

The production of hadrons in Ni-Ni at the GSI laboratory is considered in a hadronic gas model with chemical equilibrium. Special attention is given to the abundance of strange particles which are treated using the exact conservation of strangeness. It is found that all the data can be described using a temperature $T=70\ifmmode\pm\else\textpm\fi{}10$ MeV and a baryon chemical potential ${\ensuremath{\mu}}_{B}=720\ifmmode\pm\else\textpm\fi{}30$ MeV.

Multiplicity distribution of strange particles in heavy ion collisions

We study the multiplicity distribution of strange particles in a hadronic gas constrained by exact strangeness conservation. The multiplicity distribution obtained is narrower than both the Poisson and negative binomial distributions. Correlations among strange particles are also discussed. The results presented might be useful in determining the thermodynamic parameters (volume, temperature and baryon density) of a hadronic gas possibly formed in relativistic nuclear collisions.