Multi Module Model for the ultra-relativistic heavy ion collisions

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Main points

The realistic and detailed description of an energetic heavy ion reaction requires a Multi Module Model, where the different stages of the reaction are each described with a suitable theoretical approach [14,17,18,p2,p3,p9,p11,p12,p14,p19,a1,w1-w3 (see CV )]. It is important that these Modules are coupled to each other correctly: at the interface, which is a 3 dimensional hyper-surface in space-time, all conservation laws should be satisfied, and entropy should not decrease. In energetic collisions of large heavy ions, especially if Quark-Gluon Plasma (QGP) is formed in the collision, one-fluid dynamics is a valid and good description for the intermediate stages of the reaction. Here, interactions are strong and frequent, so that other models (e.g. transport models, string models, etc., assuming binary collisions, with free propagation of constituents between collisions) have limited validity. On the other hand, the initial and final, post Freeze-Out (FO), stages of the reaction are outside the domain of applicability of the fluid dynamical model. After hadronization and FO matter is already dilute and can be described well with kinetic models, while the initial state is more problematic. The FO process and the matching conditions on the interface between different Modules (different phases of matter) have been studied in the Refs. [4-7,9,20,21 (see CV)].

Recently, in collaboration with L.P. Csernai and D.D. Strottman, we developed Effective String Rope Model (ESRM) to describe initial stages of ultra-relativistic heavy ion collisions [14,17,18,p2,p3,p9,p11,p12,p14,p19,a1,w1-w3(see CV)]. One important conclusion of heavy ion research in the last decade is that standard 'hadronic' string models fail to describe heavy ion experiments. All string models had to introduce new energetic objects like string ropes in order to describe the abundant formation of massive particles like strange antibaryons. Based on this, we describe the initial moments of the reaction in the framework of classical Yang-Mills theory, assuming larger field strength (string tension) than in ordinary hadron-hadron collisions. The single phenomenological parameter describing our effective field must be fixed from comparison with experimental data.

The results show that QGP forms a tilted disk, such that the direction of the largest pressure gradient stays in the reaction plane, but deviates from both the beam and the usual transverse flow directions. Such initial conditions lead to creation of the third flow component [p9,p11,w3 (see CV)].

In present only the first step is done - Two Module Model [p9,p11,w3 (see CV)], - but very important one, since the ESRM has been developed for the most problematic module - module describing the initial stages of collisions. Thus, in our Two Module Model the output of ESRM is used like an initial state for further hydrodynamical evolution. The hydrodymanical calculations are perform with the Los Alamos Particle-in-Cell (PIC) one fluid code. The hydro evolution stops at the FO hypersurface. We present a version of the code assuming that FO (simultaneous chemical and thermal) happens on the simplified toothed hypersurface, where it's normal vector is parallel to the flow velocity for every cell. On average this hypersurface approximates the constant time hypersurface. Therefore the flow velocity does not change during the FO process, and the calculations can be done in local rest frame of the matter. Such a surface is also completely timelike, what let us avoid the problems discussed in Refs. [4-7,9 (see CV)]. The more advanced description of the FO process is planned to be separated into the Third Module.

The EoS presently used in the code
A) takes the phenomenological EoS for hadronic matter in a simple form, which nevertheless allows to check different parameterization discussed in the literature;
B) uses the Bag model EoS to describe QGP;
C) creates a complete EoS, containing pure phases and a region where they coexist, by the Maxwell construction.

The model is still raw and a lot of further work in necessary. We are not yet ready to present the quantitative calculations to be compared with data. Nevertheless preliminary results show that our expectation to generate third flow component became true [p9,p11 (see CV)] . Our initial state generated by ESRM indeed produces a strong antiflow in semi-central collisions. The directed V1 component appeared to be is very small, as it was expected for RHIC energies. The peaks in V1 (actually V3) around |y|=0.3 look very high, but this is typical for calculations without thermal smearing. Including of thermal smearing will lead to smaller and wider peaks. To evaluate all the observables a third, FO module is going to be attached to the model. Here the widely used Cooper-Frye model should be essentially improved and modified. First of all conservation laws and the requirement of increasing entropy should be enforced in the module. In addition, particularly for FO across space-like hypersurfaces, realistic, non-equilibrium post FO phase space distributions will have to be used to avoid negative contributions occuring in the naive use of the Cooper-Frye model [4-7,9 (see CV)].