ar X iv : h ep - p h / 01 03 30 2 v 1 2 8 M ar 2 00 1 1 Models for RHIC and LHC : New Developments

We outline inconsistencies in presently used models for high energy nuclear scattering, which make their application quite unreliable. Many " successes " are essentially based on an artificial freedom of parameters, which does not exist when the models are constructed properly. The problem is the fact that any multiple scattering theory requires an appropriate treatment of the energy sharing between the individual interactions, which is technically very difficult to implement. Lacking a satisfying solution to this problem, it has been simply ignored. We introduce a fully self-consistent formulation of the multiple-scattering scheme. Inclusion of soft and hard components – very crucial at high energies – appears in a " natural way " , providing a smooth transition from soft to hard physics. We can show that the effect of appropriately considering energy conservation has a big influence on the results, and MUST therefore be included in any serious calculation. With the start of the RHIC program to investigate nucleus-nucleus collisions at very high energies, there is an increasing need of computational tools in order to provide a clear interpretation of the data. The situation is not satisfactory in the sense that there exists a nice theory (QCD) but we are not able to treat nuclear collisions strictly within this framework, and on the other hand there are simple models, which can be applied easily but which have no solid theoretical basis. A good compromise is provided by effective theories, which are not derived from first principles, but which are nevertheless self-consistent and calculable. A candidate seems to be the Gribov-Regge approach, and – being formally quite similar – the eikonalized parton model. Here, however, some inconsistencies occur, which we are going to discuss in the following, before we provide a solution to the problem. Gribov-Regge theory [1,2] is by construction a multiple scattering theory. The elementary interactions are realized by complex objects called " Pomerons " , who's precise nature is not known, and which are therefore simply parameterized, with a couple of parameters to be determined by experiment [3]. Even in hadron-hadron scattering, several of these Pomerons are exchanged in parallel (the cross section for exchanging a given number of Pomerons is called " topological cross section "). Simple formulas can be derived for the