A study of vorticity formation in high energy nuclear collisions

We present a quantitative study of vorticity formation in peripheral ultrarelativistic heavy ion collisions at sqrt(s)NN = 200 GeV by using the ECHO-QGP numerical code, implementing relativistic dissipative hydrodynamics in the causal Israel-Stewart framework in 3+1 dimensions with an initial Bjorken flow profile. We consider and discuss different definitions of vorticity which are relevant in relativistic hydrodynamics. After demonstrating the excellent capabilities of our code, which proves to be able to reproduce Gubser flow up to 8 fm/c, we show that, with the initial conditions needed to reproduce the measured directed flow in peripheral collisions corresponding to an average impact parameter b=11.6 fm and with the Bjorken flow profile for a viscous Quark Gluon Plasma with eta/s=0.1 fixed, a vorticity of the order of some 10^{-2} c/fm can develop at freezeout. The ensuing polarization of Lambda baryons does not exceed 1.4% at midrapidity. We show that the amount of developed directed flow is sensitive to both the initial angular momentum of the plasma and its viscosity.

Centrality dependence of hadronization and chemical freeze-out conditions in heavy ion collisions at sqrt s_{NN} = 2.76 TeV

We present an analysis of hadronic multiplicities measured in Pb-Pb collisions at sqrt s_{NN} = 2.76 TeV as a function of the collision centrality within the statistical hadronization model. Evidence is found of a dependence of the chemical freeze-out temperature as a function of centrality, with a slow rise from central to peripheral collisions, which we interpret as an effect of post-hadronization inelastic scatterings. Using correction factors calculated by means of a simulation based on the UrQMD model, we are able to obtain a significant improvement in the statitical model fit quality and to reconstruct the primordial chemical equilibrium configuration. This is characterized by a nearly constant temperature of about 164 MeV which we interpret as the actual hadronization temperature.

Local thermodynamical equilibrium and the beta frame for a quantum relativistic fluid

We discuss the concept of local thermodynamical equilibrium in relativistic hydrodynamics in flat spacetime in a quantum statistical framework without an underlying kinetic description, suitable for strongly interacting fluids. We show that the appropriate definition of local equilibrium naturally leads to the introduction of a relativistic hydrodynamical frame in which the four-velocity vector is the one of a relativistic thermometer at equilibrium with the fluid, parallel to the inverse temperature four-vector beta, which then becomes a primary quantity. We show that this frame is the most appropriate for the expansion of stress-energy tensor from local thermodynamical equilibrium and that therein the local laws of thermodynamics take on their simplest form. We discuss the difference between the beta frame and Landau frame and present an instance where they differ.

Nonequilibrium Thermodynamical Inequivalence of Quantum Stress-energy and Spin Tensors

It is shown that different pairs of stress-energy and spin tensors of quantum relativistic fields related by a pseudo-gauge transformation, i.e. differing by a divergence, imply different mean values of physical quantities in thermodynamical nonequilibrium situations. Most notably, transport coefficients and the total entropy production rate are affected by the choice of the spin tensor of the relativistic quantum field theory under consideration. Therefore, at least in principle, it should be possible to disprove a fundamental stress-energy tensor and/or to show that a fundamental spin tensor exists by means of a dissipative thermodynamical experiment.

Covariant statistical mechanics and the stress-energy tensor

After recapitulating the covariant formalism of equilibrium statistical mechanics in special relativity and extending it to the case of a non-vanishing spin tensor, we show that the relativistic stress-energy tensor at thermodynamical equilibrium can be obtained from a functional derivative of the partition function with respect to the inverse temperature four-vector beta. For usual thermodynamical equilibrium, the stress-energy tensor turns out to be the derivative of the relativistic thermodynamic potential current with respect to the four-vector beta, i.e. T^{mu u} = - partial Phi^mu/partial beta_ u. This formula establishes a relation between stress-energy tensor and entropy current at equilibrium possibly extendable to non-equilibrium hydrodynamics.

Statistical hadronization with exclusive channels in e+e- annihilation

We perform a systematic analysis of exclusive hadronic channels in e+e- collisions at centre-of-mass energies between 2.1 and 2.6 GeV within the statistical hadronization model. Because of the low multiplicities involved, calculations have been carried out in the full microcanonical ensemble, including conservation of energy-momentum, angular momentum, parity, isospin, and all relevant charges. We show that the data is in an overall good agreement with the model for an energy density of about 0.5 GeV/fm^3 and an extra strangeness suppression parameter gamma_S ~ 0.7, essentially the same values found with fits to inclusive multiplicities at higher energy.

Validity of the Hadronic Freeze-Out Curve

We analyze hadro-chemical freeze-out in central Pb+Pb collisions at CERN SPS energies, employing the hybrid version of UrQMD which models hadronization by the Cooper-Frye mechanism, and matches to a final hadron-resonance cascade. We fit the results both before and after the cascade stage using the Statistical Hadronization Model, to assess the effect of the cascade phase. We observe a strong effect on antibaryon yields except anti-{Omega}, resulting in a shift in T and {mu}_B. We discuss the implications for the freeze-out curve.

Centrality dependence of strangeness production in heavy-ion collisions as a geometrical effect of core-corona superposition

It is shown that data on strange particle production as a function of centrality in Au-Au collisions at sqrt(s)_{NN}= 200 GeV can be explained with a superposition of emission from a hadron gas at full chemical equilibrium (core) and from nucleon-nucleon collisions at the boundary (corona) of the overlapping region of the two colliding nuclei. This model nicely accounts for the enhancement of phi meson and strange particle production as a function of centrality observed in relativistic heavy ion collisions at that energy. The enhancement is mainly a geometrical effect, that is the increasing weight of the core with respect to corona for higher centrality, while strangeness canonical suppression in the core seems to play a role only in very peripheral collisions. This model, if confirmed at lower energy, would settle the long-standing problem of strangeness under-saturation in relativistic heavy ion collisions, parametrized by $gs$. Furthermore, it would give a unique tool to locate the onset of deconfinement in nuclear collisions both as a function of energy and centrality if this is to be associated to the onset of the formation of a fully equilibrated core.

Chemical freeze-out in ultra-relativistic heavy ion collisions at sqrt(s)_NN = 130 and 200 GeV

A comprehensive and detailed analysis of hadronic abundances measured in Au-Au collisions at RHIC at sqrt(s)_NN = 130 and 200 GeV is presented. The rapidity densities measured in the central rapidity region have been fitted to the statistical hadronization model and the chemical freeze-out parameters determined as a function of centrality, using data from experiments BRAHMS, PHENIX and STAR. The chemical freeze-out temperature turns out to be independent of centrality to a few percent accuracy, whereas the strangeness under-saturation parameter gamma_S decreases from almost unity in central collisions to a significantly lower value in peripheral collisions. Our results are in essential agreement with previous analyses, with the exception that fit quality at sqrt(s)_NN = 200 GeV is not as good as previously found. From the comparison of the two different energies, we conclude that the difference in fit quality, as described by chi2 values, is owing to the improved resolution of measurements which has probably exceeded the intrinsic accuracy of the simplified theoretical formula used in the fits.

Strangeness production from SPS to LHC

Global strangeness production in relativistic heavy ion collisions at SPS and RHIC is reviewed. Special emphasis is put on the comparison with the statistical model and the canonical suppression mechanism. It is shown that recent RHIC data on strange particle production as a function of centrality can be explained by a superposition of a fully equilibrated hadron gas and particle emission from single independent nucleon-nucleon collisions in the outer corona.