Particle spectra and hydro - inspired models

In this talk I present several models which turned out to be quite successful in reproducing the experimentally measured hadron spectra in nucleus-nucleus collisions. The discussed models use concepts borrowed from relativisitic hydrodynamics but they do not include the complete time evolution of the system. For this reason, they may be called the hydro-inspired (freeze-out) models. The measured particle spectra reflect properties of matter at the stage when particles stop to interact. This moment is called the kinetic (thermal) freeze-out. Hydro-inspired models help us to verify the idea that matter, just before the kinetic freeze-out, is locally thermalized and exhibits collective behavior, such as, e.g., the transverse and longitudinal expansion. If this is really the case, i.e., if the hydro-inspired models describe the data well, we may infer the thermodynamic properties of matter at freeze-out, such as the values of the temperature and flow, and request that the advanced hydrodynamic models reproduce this configuration. In my opinion, the real aim of the freeze-out models is to form a simple link between sophisticated hydrodynamic calculations [ 1, 2, 3, 4, 5, 6] describing the full time evolution of matter (with the inclusion of the phase transition) and the rich bulk of the experimental data describing soft phenomena. This is an appealing idea, however, one encounters several problems on the way to achieve this task, since certain features of the hydrodynamic models and the freeze-out models are quite different. For example, at the first sight one can realize that typical shapes of the freeze-out hypersurfaces used in the advanced hydro calculations and in the freeze-out models are quite different. Clearly, further work is necessary to make the connection between the realistic hydro calculations and the freeze-out models more consistent.