abstract

Bose–Einstein correlations of identical charged-pion pairs produced in hadronic Z decays are analyzed in terms of various parametrizations. The \(\tau \)-model with a one-sided Lévy proper-time distribution provides a good description, enabling the source function to be reconstructed.

abstract

We investigate thermalization of a longitudinally expanding color glass condensate with Bjorken boost invariant geometry within microscopical parton cascade BAMPS. Our main focus lies on comparison of thermalization processes, observed in BAMPS with the picture suggested in the “Bottom–Up” scenario. Contrary to the “Bottom–Up” scenario, soft and hard gluons thermalize at the same time. No significant increase of the net gluon number is observed with both RHIC and LHC relevant initial conditions. The time scale of thermal equilibration in BAMPS calculations is of the order of \(\alpha _{\rm s}^{-2} (\ln \, \alpha _{\rm s})^{-2} Q_{\rm s}^{-1}\). After this time the gluon system exhibits nearly hydrodynamical behavior.

abstract

We show effects of the event-by-event fluctuation of the initial conditions (IC) in hydrodynamic description of high-energy nuclear collisions on some observables. Such IC produce not only fluctuations in observables but, due to their bumpy structure, several non-trivial effects appear. They enhance production of isotropically distributed high-\(p_{\rm T}\) particles, making \(v_2\) smaller there. Also, they reduce \(v_2\) in the forward and backward regions where the global matter density is smaller, so where such effects become more efficacious. They may also produce the so-called ridge effect in the two large-\(p_{\rm T}\) particle correlation.

abstract

Collective, explosive flow in central heavy ion collisions manifests itself in the mass dependence of \(p_{\rm T}\) distributions and femtoscopic length scales, measured in the soft sector (\(p_{\rm T}\lesssim 1\) GeV/\(c\)). Measured \(p_{\rm T}\) distributions from proton–proton collisions differ significantly from those from heavy ion collisions. This has been taken as evidence that \(p+p\) collisions generate little collective flow, a conclusion in line with naive expectations. We point out possible hazards of ignoring phase-space restrictions due to conservation laws when comparing high- and low-multiplicity final states. Already in two-particle correlation functions, we see clear signals of such phase-space restrictions in low-multiplicity collisions at RHIC. We discuss how these same effects, then, must appear in the single particle spectra. We argue that the effects of energy and momentum conservation actually dominate the observed systematics, and that \(p+p\) collisions may be much more similar to heavy ion collisions than generally thought.

abstract

A simple kinematic model based on superposition of \(p+p\) collisions, relativistic geometry and final-state hadronic rescattering is used to calculate various hadronic observables in \(\sqrt s = 200\) GeV/nucleon Au+Au collisions and \(\sqrt s = 5.5\) TeV/nucleon Pb+Pb collisions. The model calculations are compared with experimental results from several \(\sqrt s = 200\) GeV/nucleon Au+Au collision studies. If a short hadronization time is assumed in the model, it is found that this model describes the trends of the observables from these experiments surprisingly well considering the model’s simplicity. This also gives more credibility to the model predictions presented for \(\sqrt s = 5.5\) TeV/nucleon Pb+Pb collisions.

abstract

The current status of the modeling of relativistic heavy-ion collisions with 3+1D hydrodynamic and hybrid models is reviewed. Particular emphasis is placed in the use of hydrodynamics as a “standard medium”, enabling the calculation of rare probe — medium interactions in a way consistent with the bulk evolution of the medium.

abstract

In this paper I give an overview of the status of viscous hydrodynamic simulations performed by a number of groups. Also discussed is the use of electromagnetic observables as an alternative probe of the shear viscosity in heavy ion collisions.

abstract

We study the energy dissipation in an one-dimensional expansion of gluon matter with Bjorken boost invariance and the formation of shock waves in viscous gluon matter by employing a microscopic parton cascade as well as by solving the Israel–Stewart hydrodynamic equations. Comparisons between the present results from the two approaches are reported.

abstract

It is shown how the initial azimuthally asymmetric flow develops from the free-streaming + sudden equilibration approximation to the early dynamics in relativistic heavy-ion collisions. Consequences for the hydrodynamics and physical results are discussed.

abstract

A very early start up time of the hydrodynamic evolution is needed in order to reproduce observations from relativistic heavy-ion collisions experiments. At such early times the systems is still not locally equilibrated. Another source of deviations from local equilibrium is the viscosity of the fluid. We study these effects at very early times to obtain a dynamical prescription for the transition from an early 2-dimensional expansion to a nearly equilibrated 3-dimensional expansion at latter stages. The role of viscosity at latter stages of the evolution is also illustrated.

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A comparison is made between results obtained using smooth initial conditions and event-by-event initial conditions in the hydrodynamical description of relativistic nuclear collisions. Some new results on directed flow are also included.

abstract

We present results on strangeness production from a coupled Boltzmann and hydrodynamics approach to relativistic heavy ion reactions. This approach is based on the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) transport model with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. Final particle yields are discussed, putting special attention on the production of multistrange hyperons. We find that the yields for (multi)strange particles are strongly enhanced, due to the inferred local thermal equilibrium in the hydrodynamic evolution, leading to an improved description of experimental yields for these particles.

abstract

We present the status of the description of hadron production in central nucleus–nucleus collisions within the statistical model. Extending previous studies by inclusion of very high-mass resonances (\(m\gt 2\) GeV), and the up-to-now neglected scalar \(\sigma \) meson leads to an improved description of the data. In particular, the hitherto poorly reproduced energy dependence of the \(K^{\,+}\)/\(\pi ^+\) ratio at SPS energies (“the horn”) is now well described through the connection to the hadronic mass spectrum and, implicitly, Hagedorn’s limiting temperature.

abstract

We discuss, in qualitative and quantitative fashion, the yields of hadron resonances. We show that these yields, in general, are not in chemical equi- librium. We evaluate the non-equilibrium abundances in a dynamic model implementing the \(1+2\leftrightarrow 3\) resonance formation reactions. Due to the strength of these reactions, we show the \({\mit \Sigma }(1385)\) enhancement, and the \({\mit \Lambda }(1520)\) suppression explicitly.

abstract

The problem of spectra formation in hydrodynamic approach to \(A+A\) collisions is considered within the Boltzmann equations. It is shown analytically and illustrated by numerical calculations that the particle momentum spectra can be presented in the Cooper–Frye form despite freeze-out is not sharp and has the finite temporal width. The latter is equal to the inverse of the particle collision rate at points \((t_{\sigma }\,({\mathbf r},p),{\mathbf r})\) of the maximal emission at a fixed momentum \(p\). The set of these points forms the hypersurfaces \(t_\sigma \,({\mathbf r},p)\) which strongly depend on the values of \(p\) and typically do not enclose completely the initially dense matter. This is an important difference from the standard Cooper–Frye prescription (CFp), with a common freeze-out hypersurface for all \(p\), that affects significantly the predicted spectra. Also, the well known problem of CFp as for negative contributions to the spectra from non-space-like parts of the freeze-out hypersurface is naturally eliminated in this improved prescription.

abstract

The decoupling and freeze-out of energetic nuclear collisions is analysed in terms of transparent semi-classical decoupling formulae. They provide a smooth transition and generalise frequently employed instantaneous freeze-out procedures. Simple relations between the damping width and the duration of the decoupling process are presented and the implications on various physical phenomena arising from the expansion and decay dynamics of the highly compressed hadronic matter generated in high energy nuclear collisions are discussed.

abstract

Here I discuss some implicit assumptions of modern hydrodynamic models and argue that their accuracy cannot be better then 10–15%. Then I formulate the correct conservation laws for the fluid emitting particles from an arbitrary freeze-out (FO) hypersurface (HS) and show that the derived momentum distribution function of emitted particles does not contain negative contributions which appear in the famous Cooper–Frey formula. Further I analyze the typical pitfalls of some hydro models trying to alternatively resolve the FO problem.

abstract

Overview of event-by-event studies on relativistic heavy-ion collisions is given. I focus on fluctuation measurements and on theoretical ideas which appeared experimentally fruitful.

abstract

Fluctuations of thermodynamic quantities are fundamental for the study of the QGP phase transition. The ALICE experiment is well suited for precise event-by-event measurements of various quantities. In this article, we review the capabilities of ALICE to study the fluctuations of several key observables such as the net charge, the temperature, and the particle ratios. Among the observables related to correlations, we review the balance functions and the long range correlations.

abstract

Recently PHOBOS has focused on the study of fluctuations and correlations in particle production in heavy-ion collisions at the highest energies delivered by the Relativistic Heavy Ion Collider (RHIC). In this report, we present results on event-by-event elliptic flow fluctuations in Au+Au collisions at \(\sqrt {s_{\rm NN}}=\)200 GeV. A data-driven method was used to estimate the dominant contribution from non-flow correlations. Over the broad range of collision centralities, the observed large elliptic flow fluctuations are in agreement with the fluctuations in the initial source eccentricity.

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The PHENIX experiment has conducted searches for the QCD critical point with measurements of multiplicity fluctuations, transverse momentum fluctuations, event-by-event kaon-to-pion ratios, and azimuthal correlations. Measurements have been made in several collision systems as a function of centrality and transverse momentum. The results do not show significant evidence of critical behavior in the collision systems and energies studied, although several interesting features are discussed.

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We show that a consistent hydrodynamic description of soft-hadronic one- and two-particle observables (the HBT radii) studied in the relativistic heavy-ion collisions at RHIC may be obtained if one uses the Gaussian energy density profile as the initial condition. The transverse-momentum spectra, the elliptic flow coefficient \(v_2\), and the pionic azimuthally sensitive HBT radii are successfully reproduced, which hints that the long standing HBT puzzle has been solved.

abstract

An overview of the present status in particle femtoscopy applied to heavy-ion collisions at intermediate energies is presented. Information about dynamics of particle emission can be obtained by means of two-particle correlation functions constructed with protons, intermediate mass fragments and complex light particles. The latter are more difficult to be treated due to the complexity of final state interactions and the effects induced by the interplay between thermal and collective motion. Some source size measurements with two-proton and deuteron–alpha correlation functions are presented. Correlation techniques are also used to study sequential emissions of light particles by unbound states in \(^{12}\)C and \(^{10}\)C, showing that femtoscopic techniques can provide tools to explore spectroscopy as well as dynamics.

abstract

In this note we review our ideas, first published in year 2006, and corresponding results, including the new ones, which show that whereas the assumption of (partial) thermalization in relativistic \(A+A\) collisions is really crucial to explain soft physics observables, the hypotheses of early thermalization at times less than 1 fm/\(c\) is not necessary. The reason for the later conclusion is that the initial transverse flow in thermal matter as well as its anisotropy, leading to asymmetry of the transverse momentum spectra, could be developed at pre-thermal, either partonic or classical field — Glasma, stage with even more efficiency than in the case of very early perfect hydrodynamics. Such radial and elliptic flows develop no matter whether a pressure already established. The general reason for them is an essential finiteness of the system in transverse direction.

abstract

Femtoscopic measurements at a variety of facilities have established a clear dependence of spatial scales with event multiplicity and particle transverse mass (\(m_{\rm T}\)) in heavy ion collisions from \(\sqrt {s}_{\rm NN}\sim 2\)–200 GeV. The \(m_{\rm T}\)-dependence is thought to arise from collective, explosive flow of the system, as probed by independent measurements, while the multiplicity dependence reflects the increased spatial extent of the final state with decreasing impact parameter. Qualitatively similar dependences have been reported from high energy hadron and lepton collisions, where the conceptual validity of an impact parameter or collective flow are less clear. We focus on results from elementary particle collisions, identify trends seen in the experimental data and compare them to those from heavy ion collisions.

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Recent results of identical pion correlations from the NA45/CERES, NA49, and NA57 CERN SPS experiments are discussed including their beam energy and transverse momentum dependence. The emphasis is put on the Hanbury–Brown Twiss (HBT) pion correlations analyzed with respect to the reaction plane orientation reported by the CERES Collaboration D. Adamova et al., Phys. Rev. C78, 064901 (2008). The mean free path of pions at freeze-out D. Adamova et al., Phys. Rev. Lett. 90, 022301 (2003) is presented updated by the recent results from the SPS experiments.

abstract

The formalism and assumptions behind the correlation femtoscopy are briefly reviewed. The femtoscopy techniques, with the emphasis on correlations of nonidentical particles, are discussed.

abstract

Non-identical particle femtoscopy is sensitive to relative emission asymmetries between particles of different masses. In heavy ion collisions observation of such asymmetries has been interpreted as a strong evidence of the collective behavior of matter. However, decays of resonances are also known to affect the asymmetries, mainly because they introduce a difference in average emission time, which is indistinguishable from the spatial shift coming from collective flow. We show that the effect of resonance decay processes on asymmetries are more complicated than the simple picture above. We show how resonance decay can result in the enhancement of the flow asymmetries, rather than its dilution.

abstract

Correlations between non-identical particles at small relative velocity probe asymmetries in the average space-time emission points at freeze-out. Such asymmetries may arise from long-lived resonances, bulk collective effects, or differences in the freeze-out scenario for the different particle species. STAR has extracted pion–proton correlation functions from a high-statistics dataset of Au+Au collisions at \(\sqrt {s_{\rm NN}}=200\) GeV. We present a femtoscopic analysis (including spherical-harmonics decomposition) of pions and (anti-)protons for collisions of different centrality. Our results suggest that pions and protons have relatively shifted average space-time emission points. At the end we show THERMINATOR simulations which look quantitatively similar to the data.

abstract

We report preliminary data on proton–lambda correlations at small relative momentum \(q\) in the \(e^3\)He(\(^4\)He)\(\rightarrow \!e'p {\mit \Lambda } X\) reaction at \(E_0\! =\! 4.7\)(4.46) GeV using the CLAS detector at Jefferson Lab. The enhancement of the correlation function at small \(q\) was found to be in qualitative agreement with theoretical expectations. The size of emission region about 1.5 fm was estimated using Lednický–Lyuboshitz analytical model. The experimental correlation function is compatible with the \(P\)-matrix fit of the hyperon–nucleon data. Small relative momentum proton–lambda correlations both for He target and for electroproduction reaction were studied for the first time.

abstract

Different decay modes ratio study for \(\varphi \) and \(\omega \) mesons are proposed to estimate the nuclear density integral along meson trajectory within strongly interacting matter between hadronization point and kinetic freeze-out.

abstract

Predictions of hydrodynamics-parametrized statistical hadronization model HYDJET++ are compared to the STAR Collaboration preliminary \(\pi {\mit \Xi }\) data. We demonstrate how decay of resonances and collective flow affect shift between the average freeze-out space-time points of \({\mit \Xi }\) and \(\pi \). We study how different freeze-out scenarios: single freeze-out at \(T_{\rm th}=T_{\rm ch}=0.165\) GeV; thermal freeze-out at \(T_{\rm th}=0.1\) GeV; combined scenario when \({\mit \Xi }\) and \({\mit \Xi }^{*}(1530)\) are emitted at chemical freeze-out while all other particles are emitted at the thermal freeze-out influence this shift. We study influence of the relative contribution of \({\mit \Xi }\) from \({\mit \Xi }^{*}(1530)\) resonance decay on the \(\pi {\mit \Xi }\) emission asymmetries. We show that the best description of \(m_{\rm t}\)-spectra and space-time differences is achieved within the combined scenario.

abstract

In this paper we present properties of relativistic and non-relativistic perfect hydrodynamical models. In particular we show illustrations of the fact that different initial conditions and equations of state can lead to the same hadronic final state. This means that alone from the hadronic observables one cannot determine either of the above, one needs for example penetrating probes that inherit their properties from each timeslice of the evolution of the fireball.

abstract

For fragments emitted in the reactions \(^{124}\)Sn + \(^{64}\)Ni and \(^{112}\)Sn + \(^{58}\)Ni at 35 \(A\) MeV, isotopic composition and velocity correlations have been studied as a function of the centrality of the collision, using the 4\(\pi \) Chimera multidetector. We have investigated the time scale for fragments formation, in order to distinguish between prompt dynamical and sequential statistical emission. Promptly emitted light fragments (\(Z\leq \)9) produced in the mid-rapidity domain are characterised by larger \(N\) / \(Z\) ratio and stronger angular anisotropies than those produced in sequential statistical emission. Results are compared with stochastic BNV code simulations obtained for primary fragments. Valuable information on the symmetry term of the nuclear equation of state at sub-saturation densities are obtained.

abstract

The systematic study of shape in non-Gaussian HBT distributions requires a systematic understanding of the underlying mathematical structures. Gram–Charlier series as the statistics approach to their systematic description have elegant series and good properties but do not converge uniformly. Extensions and relationships to other systems are briefly outlined.

abstract

The UrQMD results of the HBT correlation of two-identical particles (pions, kaons, and Lambdas) at freeze-out in heavy ion collisions (HICs) from AGS to RHIC energies are shown. When the cascade mode is considered, the “lifetime” of the emission source is larger than the experimentally observed values at all investigated energies. After the mean-field potentials for both confined and “pre-formed” hadrons are considered, it is found that the inclusion of potential interactions pushes down the HBT \(R_{\rm O}\) and pulls up the \(R_{\rm S}\) so that the HBT time-related puzzle disappears and the HBT radii of pions and kaons and even those of \({\mit \Lambda }\)s with large transverse momenta follow the \(m_{\rm T}\)-scaling fairly well. Furthermore, it is seen to reproduce the proper stopping power for net protons and to improve the elliptic flow at large transverse momenta.

abstract

A novel type of correlation involving particle–antiparticle pairs was found out in the 1990’s. Currently known as squeezed or Back-to-Back Correlations (BBC), they should be present if the hadronic masses are modified in the hot and dense medium formed in high energy heavy ion collisions. Although well-established theoretically, such hadronic correlations have not yet been observed experimentally. In this phenomenological study we suggest a promising way to search for the BBC signal, by looking into the squeezed correlation function of \(\phi \phi \) and \(K^{\,+} K^{\,-}\) pairs at RHIC energies, as function of the pair average momentum, \(\mathbf {K_{12}}=(\mathbf {k_1}+\mathbf {k_2})/2\). The effects of in-medium mass-shift on the identical particle correlations (Hanbury–Brown and Twiss effect) are also discussed.

abstract

The Bowler–Sinyukov method to eliminate Coulomb interaction from a two-particle correlation function is discussed and tested.

abstract

The QCD phase diagram appears to be the most important single figure of our field. While recent progress in Lattice QCD (LQCD) and model calculations is impressive, the location of phase boundaries and the exact position of the hypothetical critical point (CP) remains unknown. The available theoretical estimates, however, indicate that the critical point might be in the region of the phase diagram probed by current heavy ion experiments. The Beam Energy Scan (BES) program at RHIC, described in this paper, was launched to expand the experimental study where theory cannot yet reach. Both large RHIC experiments, STAR and PHENIX, are in the process of preparing for the first run. Particularly STAR with its large, uniform acceptance and excellent particle identification capabilities, is uniquely positioned to cover this physics in unprecedented depth and detail.

abstract

I report on a two-particle analysis package in which the algorithmic part is strictly separated from the input data format such that it can be used to analyze data from different experiments. After introducing the analysis scheme and briefly discussing some aspects of the implementation I go through a collection of histograms obtained by running the package on data from three heavy-ion experiments.

abstract

Femtoscopic measurements at RHIC have been hailed as a source of insight into the bulk properties of QCD matter. However, hydrodynamic models, which have been successful in reproducing other observables have failed to satisfactorily explain femtoscopic two-particle correlation measurements. This failure has been labeled the “HBT puzzle”. In this paper, I present correlations using a hybrid model composed of a viscous hydrodynamic module and a hadronic cascade. After incorporating early acceleration, viscosity and a stiffer equation of state, the extracted source sizes come much closer to experiment.