Understanding of the freeze-out in ultra-relativistic heavy-ion collisions

Hadronic single-particle spectra and correlations carry information about the freeze-out state of the fireball which results from the collective expansion of the strongly interacting matter. Often, the freeze-out state is being modelled in framework of the Cooper-Frye [7] mechanism where all particles − regardless of their identity and/or momentum − are emitted from a single sharp three-dimensional freeze-out hypersurface. This is the case for most hydrodynamic simulations. A question appears: does the assumption of a common sharp three-dimensional freezeout still provide reliable approximation of the real process? In case of a sharp freeze-out, the freeze-out hypersurface is usually characterised by some prescription. There were some attempts to identify a universal freeze-out criterion [1, 8], i.e., a condition which determines the freeze-out hypersurface for heavy-ion collisions of any size and at any ultrarelativistic energy. In case of the continuous gradual decoupling, there is no hypersurface to be determined and the concept of a universal freeze-out criterion is not applicable. I will focus on gradual decoupling since the sharp freeze-out can be defined as its limiting case. Let me focus on the mechanism of freeze-out and identify the important effects and quantities. Freeze-out occurs when scattering ceases. It has been suggested that the mean-free path is the relevant quantity to look at [1, 11]. Here, densities of the individual species are weighted with cross-sections for scattering on them. An example: density of nucleons is much more important for pion scattering rate than the density of pions, because the πN cross-section is bigger than the one for ππ scattering. The CERES collaboration argued that the universal pion meanfree path at freeze-out should be something of the order of 1 fm (maybe 2–3 fm) [1]. On the first sight this is rather surprising, because this length is much shorter than the size of the system. So far, however, we did not mention the expansion and the decrease of the density due to it. In rough terms, freezeUnderstanding of the freeze-out in ultra-relativistic heavy-ion collisions Boris Tomášik