Remarks on the extraction of freeze-out parameters

Collisions of elementary particles, hadrons, and nuclei at ultrarelativistic energies produce a multitude of particles (“multiparticle production”). Final-state interactions between the produced particles determine the dynamical evolution of the system. In ee and hadron-hadron collisions only few particles are produced, and it is unlikely that many final-state interactions occur. The particles decouple (“freeze out”) from the system soon after production. On the other hand, in AA collisions the density of produced particles is sufficiently large over an extended region in space-time, such that the mean free path of produced particles becomes small and many final-state interactions occur. These interactions drive the system towards local thermodynamic, i.e., thermal, mechanical, and chemical equilibrium. In local thermodynamic equilibrium, the evolution of the system is governed by the equations of ideal fluid dynamics [1]. If the system is only thermally and mechanically, i.e., kinetically, but not chemically equilibrated, these equations have to be supplemented by rate equations which determine the chemical composition of the system [2]. In both cases, pressure gradients between dense, equilibrated matter and the vacuum drive collective expansion, which cools and dilutes the system. Freeze-out of particles occurs when microscopic interaction rates become smaller than the macroscopic expansion rate of the system. By definition, after freeze-out the momenta of the produced particles do not change. The experimentally measured spectra of hadronic particles thus reflect the state of the system at freeze-out. The question is whether the spectra can also tell us about the state of the system prior to freeze-out? For instance, can they tell us whether the system was in thermodynamic, or at least kinetic equilibrium? Do they provide information as to whether a quark-gluon plasma (QGP), i.e., an equilibrated state of quarks and gluons, was created at some stage during the evolution of the system?