ar X iv : h ep - p h / 06 12 02 8 v 1 4 D ec 2 00 6 High energy hadron production

We discuss here Quantum molecular dynamics models (QMD) and Dual Parton Models (DPM and QGSM). We compare RHIC data to DPM–models and we present a (Cosmic ray oriented) model comparison. The emphasis of this contribution is to high energies, therefore, QMD non–relativistic models (E < 2AGeV) are not treated here. The first relativistic QMD model was RQMD [1]. This model is no longer supported since the year 2000 ,RQMD is used in FLUKA for A–A collisions below 5AGeV. A second relativistic model is UrQMD [2], it is used in CORSIKA Cosmic Ray cascade code below 80AGeV. Let me mention some efforts within the FLUKA collaboration which will not be treated here: F.Cerutti et al. add (approximate) energy conservation , evaporation, and residual nuclei to RQMD [3]. M.V.Garzelli et al. construct a low enery QMD for A–A collisions in FLUKA [4]. There are efforts in Milano and Houston to construct a fully relativistic model for A–A collisions to be inserted into FLUKA. A relativistic QMD model is a Lorentz invariant cascade (molecular dynamics) with nucleons of both nuclei and all produced hadrons as participants. Properties of such models are: (i)A formation zone cascade of all produced hadrons. (ii) Elementary interactions used in the models include: (1) h + h −→ resonance; resonance + resonance and resonance decay (similar to HADRIN in FLUKA), (2) high enery: h + h −→ hadronic chain; 2 hadronic chains and Lund like chain fragmentation, (3) chain fusion (called formation of color ropes) in RQMD, (4) empirical parametrization of all cross sections, (5) pQCD description of hard collisions (UrQMD). The model is fully described in [2]. It is based on the covariant propagation of all hadrons on classical trajectories in combination with stochastic binary scatterings, color