Searching for the Critical Point of QCD: Theoretical Benchmark Calculations

We present a comprehensive study of event-by-event multiplicity fluctuations in nucleon-nucleon and nucleus-nucleus interactions from AGS/FAIR to RHIC energies within the UrQMD transport approach. The scaled variances of negative, positive, and all charged hadrons are analysed. The scaled variance in central Pb+Pb collisions increases with energy and behaves similar to inelastic p+p interactions. We find a non-trivial dependence of multiplicity fluctuations on the rapidity and transverse momentum interval used for the analysis and on the centrality selection procedure. Quantitative predictions for the NA49 experiment are given, taking into account the acceptance of the detector and the selection procedure of central events.Comment: 10 pages, 10 figure

Multiplicity Fluctuations in Limited Segments of Momentum Space in Statistical Models

Multiplicity fluctuations in limited segments of momentum space are calculated for a classical pion gas within the statistical model. Results for the grand canonical, canonical, and micro-canonical ensemble are obtained, compared and discussed. We demonstrate that even in the large volume limit correlations between macroscopic subsystems due to energy and momentum conservation persist. Based on the micro-canonical formulation we make qualitative predictions for the rapidity and transverse momentum dependence of multiplicity fluctuations. The resulting effects are of similar magnitude as the predicted enhancement due to a phase transition from a quark-gluon plasma to a hadron gas phase, or due to the critical point of strongly interacting matter, and qualitatively agree with recently published preliminary multiplicity fluctuation data of the NA49 SPS experiment.Comment: 23 pages, 4 figure

Multiplicity fluctuations in relativistic nuclear collisions: statistical model versus experimental data

The multiplicity distributions of hadrons produced in central nucleus-nucleus collisions are studied within the hadron-resonance gas model in the large volume limit. The microscopic correlator method is used to enforce conservation of three charges - baryon number, electric charge, and strangeness - in the canonical ensemble. In addition, in the micro-canonical ensemble energy conservation is included. An analytical method is used to account for resonance decays. The multiplicity distributions and the scaled variances for negatively, positively, and all charged hadrons are calculated along the chemical freeze-out line of central Pb+Pb (Au+Au) collisions from SIS to LHC energies. Predictions obtained within different statistical ensembles are compared with the preliminary NA49 experimental results on central Pb+Pb collisions in the SPS energy range. The measured fluctuations are significantly narrower than the Poisson ones and clearly favor expectations for the micro-canonical ensemble. Thus this is a first observation of the recently predicted suppression of the multiplicity fluctuations in relativistic gases in the thermodynamical limit due to conservation laws.Comment: 27 pages, 9 figures, corrected reference

Multiplicity fluctuations in relativistic nuclear collisions

Multiplicity distributions of hadrons produced in central nucleus-nucleus collisions are studied within the hadron-resonance gas model in the large volume limit. In the canonical ensemble conservation of three charges (baryon number, electric charge, and strangeness) is enforced. In addition, in the micro-canonical ensemble energy conservation is included. An analytical method is used to account for resonance decays. Multiplicity distributions and scaled variances for negatively charged hadrons are presented along the chemical freeze-out line of central Pb+Pb (Au+Au) collisions from SIS to LHC energies. Predictions obtained within different statistical ensembles are compared with preliminary NA49 experimental results on central Pb+Pb collisions in the SPS energy range. The measured fluctuations are significantly narrower than a Poisson reference distribution, and clearly favor expectations for the micro-canonical ensemble.Comment: 6 pages, 3 figure

Particle number fluctuations in nuclear collisions within excluded volume hadron gas model

The multiplicity fluctuations are studied in the van der Waals excluded volume hadron-resonance gas model. The calculations are done in the grand canonical ensemble within the Boltzmann statistics approximation. The scaled variances for positive, negative and all charged hadrons are calculated along the chemical freeze-out line of nucleus-nucleus collisions at different collision energies. The multiplicity fluctuations are found to be suppressed in the van der Waals gas. The numerical calculations are presented for two values of hard-core hadron radius, $r=0.3$ fm and 0.5 fm, as well as for the upper limit of the excluded volume suppression effects.Comment: 19 pages, 4 figure

Multiplicity Fluctuations in Nucleus-Nucleus Collisions: Dependence on Energy and Atomic Number

Event-by-event multiplicity fluctuations in central C+C, S+S, In+In, and Pb+Pb as well as p+p collisions at bombarding energies from 10 to 160 AGeV are studied within the HSD and UrQMD microscopic transport approaches. Our investigation is directly related to the future experimental program of the NA61 Collaboration at the SPS for a search of the QCD critical point. The dependence on energy and atomic mass number of the scaled variances for negative, positive, and all charged hadrons is presented and compared to the results of the model of independent sources. Furthermore, the nucleus-nucleus results from the transport calculations are compared to inelastic proton-proton collisions for reference. We find a dominant role of the participant number fluctuations in nucleus-nucleus reactions at finite impact parameter $b$. In order to reduce the influence of the participant numbers fluctuations on the charged particle multiplicity fluctuations only the most central events have to be selected. Accordingly, the samples of the 1% most central nucleus-nucleus collisions with the largest numbers of the projectile participants are studied. The results are compared with those for collisions at zero impact parameter. A strong influence of the centrality selection criteria on the multiplicity fluctuations is pointed out. Our findings are essential for an optimal choice of colliding nuclei and bombarding energies for the experimental search of the QCD critical point.Comment: 26 pages, 12 figures, extended version, to be published in Phys. Rev.

Energy dependence of transverse mass spectra of kaons produced in p+p and p+pbar interactions.A compilation

The data on m_T spectra of K0S K+ and K- mesons produced in all inelastic p+p and p+pbar interactions in the energy range sqrt(s)NN=4.7-1800GeV are compiled and analyzed. The spectra are parameterized by a single exponential function, dN/(m_T*dm_T)=C exp(-m_T/T), and the inverse slope parameter T is the main object of study. The T parameter is found to be similar for K0S, K+ and K- mesons. It increases monotonically with collision energy from T~30MeV at sqrt(s)NN=4.7GeV to T~220MeV at sqrt(s)NN=1800GeV. The T parameter measured in p+p and p+pbar interactions is significantly lower than the corresponding parameter obtained for central Pb+Pb collisions at all studied energies. Also the shape of the energy dependence of $T$ is different for central Pb+Pb collisions and p+p(pbar) interactions.Comment: more differential analysis adde

Regional variation in the flexural properties of the equine hoof wall

The equine hoof wall is a hard, keratinous structure that transmits forces generated when the hoof connects the ground to the skeleton of the horse. During locomotion the hoof capsule is known to deform, resulting in an inward curvature of the dorsal wall and expansion of the heels. However, while researchers have studied the tensile and compressive properties, there is a lack of data on the flexural properties of the hoof wall in different locations around the hoof capsule. In this study, the flexural properties and hydration status of the hoof wall were investigated in two orthogonal directions, in different locations around the hoof capsule. The hoof was divided into three regions: the dorsal-most aspect (toe), the medial and lateral regions (quarters) and the heels caudally. Beams were cut both perpendicular (transverse) and parallel (longitudinal) to the orientation of the tubules. Differences in the mechanical properties were then investigated using three-point bending tests. There were considerable differences in the flexural properties around the hoof capsule; transverse beams from the heel were 45% more compliant than those from the toe region. This corresponded with changes in the hydration of the hoof wall; beams from the heel region were more hydrated (28.2 ± 0.60%) than those from the toe (24.2 ± 0.44%; P < 0.01). Regional variation in the water content is thought to help explain differences in the flexural properties. Mechanical data are further discussed in relation to variation in the structure and loading of the hoof wall

Strangeness production time and the K+/pi+ horn

We construct a hadronic kinetic model which describes production of strange particles in ultrarelativistic nuclear collisions in the energy domain of SPS. We test this model on description of the sharp peak in the excitation function of multiplicity ratio K+/pi+ and demonstrate that hadronic model reproduces these data rather well. The model thus must be tested on other types of data in order to verify the hypothesis that deconfinement sets in at lowest SPS energies.Comment: proceedings of Hot Quarks 0

Strangeness and threshold of phase changes

We explore entropy and strangeness as signature of QGP for top AGS energy and the energy scan at SPS. We find that the hadronization dynamics changes between 20 and 30 $A$ GeV projectile energy. The high energy results are consistent with QGP.Comment: Presented at SQM07, to appear in JPG special issu