3-D hydro + cascade model at RHIC

Hydrodynamic models have been very successful in describing the collective behavior of matter at RHIC, such as single particle spectra and elliptic flow. In particular the strong elliptic flow which, for the first time, reaches the hydrodynamic limit at RHIC, provides us with a new understanding of the nature of the quark-gluon plasma (QGP) created at RHIC as strongly interacting or correlated QGP [ 1]. However there exist a number of experimental observations that contradict ideal hydrodynamic models: transverse momentum spectra above 2 GeV, elliptic flow at large pseudo-rapdities η and Hanbury Brown Twiss (HBT) interferometry. These observations suggest that there exist limitations to the application of a simple ideal hydrodynamic model to RHIC physics and that an improvement on an ideal hydrodynamic model is needed in order to obtain a comprehensive and unified description of the data from the point of view of hydrodynamics. In general, hydrodynamic models require initial conditions, an equations of state (EoS) and freezeout conditions as parameters besides the relativistic hydrodynamic equation. One of the main advantages of the hydrodynamic model lies in its ability to investigate the relation between the EoS and physical observables via comparison to experimental data. However, it has been pointed out repeatedly, e.g. by Hirano [ 2], that details of the treatment of the freeze-out process can have large effects on physical observables. For example, the data on PT spectra and elliptic flow show that the assumption of chemical equilibrium [ 3] or partial chemical equilibrium [ 4] in the freezeout process is not realistic [ 2]. In addition, studies of collective flow at AGS, SPS and RHIC based on both of hydrodynamic models and cascade models suggest that the effects of viscosity are not negligible [ 5]. Therefore we construct a hybrid 3-D hydro + cascade model to include a realistic treatment of the freezeout process and viscosity in the hadronic phase. Such hybrid models have been implemented in the past, however with reduced dimensionality in the hydrodynamic component and thus with restrictions to observables at mid-rapidity [ 6]. As a cascade model we use UrQMD in which final state interactions are included correctly [ 7].