We present a coupled Boltzmann and hydrodynamics approach to relativistic heavy ion reactions. This hybrid approach is based on the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. Event-by-event fluctuations are directly taken into account via the non-equilibrium initial conditions generated by the initial collisions and string fragmentations in the microscopic UrQMD model. After a (3+1)-dimensional ideal hydrodynamic evolution, the hydrodynamical fields are mapped to hadrons via the Cooper-Frye equation and the subsequent hadronic cascade calculation within UrQMD proceeds to incorporate the important final state effects for a realistic freeze-out. This implementation allows to compare pure microscopic transport calculations with hydrodynamic calculations using exactly the same initial conditions and freeze-out procedure. The effects of the change in the underlying dynamics -ideal fluid dynamics vs. non-equilibrium transport theory -will be explored. The freeze-out and initial state parameter dependences are investigated for different observables. Furthermore, the time evolution of the baryon density and particle yields are discussed. We find that the final pion and proton multiplicities are lower in the hybrid model calculation due to the isentropic hydrodynamic expansion while the yields for strange particles are enhanced due to the local equilibrium in the hydrodynamic evolution. The results of the different calculations for the mean transverse mass excitation function, rapidity and transverse mass spectra for different particle species at three different beam energies are discussed in the context of the available data.

The microscopic description of heavy-ion reactions at low beam energies is achieved within hadronic transport approaches. In this article a new approach SMASH (Simulating Many Accelerated Strongly-interacting Hadrons) is introduced and applied to study the production of non-strange particles in heavy-ion reactions at E kin = 0.4 − 2A GeV. First, the model is described including details about the collision criterion, the initial conditions and the resonance formation and decays. To validate the approach, equilibrium properties such as detailed balance are presented and the results are compared to experimental data for elementary cross sections. Finally results for pion and proton production in C+C and Au+Au collisions is confronted with HADES and FOPI data. Predictions for particle production in π + A collisions are made.

We develop a systematic framework for the study of the initial collision geometry fluctuations in relativistic heavy-ion collisions and investigate how they evolve through different stages of the fireball history and translate into final particle momentum anisotropies. We find in our event-by-event analysis that only the few lowest momentum anisotropy parameters survive after the hydrodynamical evolution of the system. The geometry of the produced medium is found to be affected by the preequilibrium evolution of the medium and the thermal smearing of the discretized event-by-event initial conditions, both of which tend to smear out the spatial anisotropies. We find such effects to be more prominent for higher moments than for lower moments. The correlations between odd and even spatial anisotropy parameters during the pre-equilibrium expansion are quantitatively studied and found to be small. Our study provides a theoretical foundation for the understanding of initial state fluctuations and the collective expansion dynamics in relativistic heavy-ion collisions.

Abstract. We review the phenomenology and theory of bulk observables in ultrarelativistic heavy-ion collisions, focussing on recent developments involving event-byevent fluctuations in the initial stages of a heavy ion collision, and how they manifest in observed correlations. We first define the relevant observables and show how each measurement is related to underlying theoretical quantities. Then we review the prevailing picture of the various stages of a collision, including the state-of-the-art modeling of the initial stages of a collision and subsequent hydrodynamic evolution, as well as hadronic scattering and freeze-out in the later stages. We then discuss the recent results that have shaped our current understanding and identify the challenges that remain. Finally, we point out open issues and the potential for progress in the field.PACS numbers: 25.75.Ag,24

Simulations by transport codes are indispensable to extract valuable physical information from heavy-ion collisions. In order to understand the origins of discrepancies among different widely used transport codes, we compare 15 such codes under controlled conditions of a system confined to a box with periodic boundary, initialized with Fermi-Dirac distributions at saturation density and temperatures of either 0 or 5 MeV. In such calculations, one is able to check separately the different ingredients of a transport code. In this second publication of the code evaluation project, we only consider the two-body collision term; i.e., we perform cascade calculations. When the Pauli blocking is artificially suppressed, the collision rates are found to be consistent for most codes (to within 1% or better) with analytical results, or completely controlled results of a basic cascade code. PHYSICAL REVIEW C 97, 034625 (2018) to reach that goal, it was necessary to eliminate correlations within the same pair of colliding particles that can be present depending on the adopted collision prescription. In calculations with active Pauli blocking, the blocking probability was found to deviate from the expected reference values. The reason is found in substantial phase-space fluctuations and smearing tied to numerical algorithms and model assumptions in the representation of phase space. This results in the reduction of the blocking probability in most transport codes, so that the simulated system gradually evolves away from the Fermi-Dirac toward a Boltzmann distribution. Since the numerical fluctuations are weaker in the Boltzmann-Uehling-Uhlenbeck codes, the Fermi-Dirac statistics is maintained there for a longer time than in the quantum molecular dynamics codes. As a result of this investigation, we are able to make judgements about the most effective strategies in transport simulations for determining the collision probabilities and the Pauli blocking. Investigation in a similar vein of other ingredients in transport calculations, like the mean-field propagation or the production of nucleon resonances and mesons, will be discussed in the future publications.

Abstract. In hybrid models, which combine hydrodynamical and transport approaches to describe different stages of heavy-ion collisions, conversion of fluid to individual particles, particlization, is a non-trivial technical problem. We describe in detail how to find the particlization hypersurface in a 3+1 dimensional model, and how to sample the particle distributions evaluated using the Cooper-Frye procedure to create an ensemble of particles as an initial state for the transport stage. We also discuss the role and magnitude of the negative contributions in the Cooper-Frye procedure.

Hybrid approaches based on relativistic hydrodynamics and transport theory have been successfully applied for many years for the dynamical description of heavy ion collisions at ultrarelativistic energies. In this work a new viscous hybrid model employing the hadron transport approach UrQMD for the early and late non-equilibrium stages of the reaction, and 3+1 dimensional viscous hydrodynamics for the hot and dense quark-gluon plasma stage is introduced. This approach includes the equation of motion for finite baryon number, and employs an equation of state with finite net-baryon density to allow for calculations in a large range of beam energies. The parameter space of the model is explored, and constrained by comparison with the experimental data for bulk observables from SPS and the phase I beam energy scan at RHIC. The favored parameter values depend on energy, but allow to extract the effective value of the shear viscosity coefficient over entropy density ratio η/s in the fluid phase for the whole energy region under investigation. The estimated value of η/s increases with decreasing collision energy, which may indicate that η/s of the quark-gluon plasma depends on baryochemical potential µB.

Fermions become polarized in a vortical fluid due to spin-vorticity coupling. The spin polarization density is proportional to the local fluid vorticity at the next-to-leading order of a gradient expansion in a quantum kinetic theory. Spin correlations of two Λ-hyperons can therefore reveal the vortical structure of the dense matter in high-energy heavy-ion collisions. We employ a (3+1)D viscous hydrodynamic model with event-by-event fluctuating initial conditions from A MultiPhase Transport (AMPT) model to calculate the vorticity distributions and Λ spin correlations. The azimuthal correlation of the transverse spin is shown to have a cosine form plus an offset due to a circular structure of the transverse vorticity around the beam direction and global spin polarization. The longitudinal spin correlation shows a structure of vortex-pairing in the transverse plane due to the convective flow of hot spots in the radial direction. The dependence on colliding energy, rapidity, centrality and sensitivity to the shear viscosity are also investigated. Introduction. -Low-energy nuclear reactions can create rotating and deformed compound nuclei that carry a large amount of orbital angular momentum of the colliding nuclei [1]. The large orbital angular momentum in non-central high-energy heavy-ion collisions cannot produce a rotating quark-gluon plasma because of the soft equation of state (EoS). It should instead lead to fluid shear and non-vanishing local fluid vorticity [2][3][4][5][6][7][8][9][10][11][12][13][14]. In such a vorticular fluid, the spin-orbital coupling polarizes the spin of fermions (quarks and baryons) [2][3][4][5][6][7][8][9][10][11][12] along the direction of the vorticity.