Abstract
Many models of heavy ion collisions employ relativistic hydrodynamics to describe the system evolution at high densities. The Cooper-Frye formula is applied in most of these models to turn the hydrodynamical fields into particles. However, the number of particles obtained from the Cooper-Frye formula is not always positive-definite. Physically negative contributions of the Cooper-Frye formula are particles that stream backwards into the hydrodynamical region.We quantify the Cooper-Frye negative contributions in a coarse-grained transport approach, which allows to compare them to the actual number of underlying particles crossing the transition hypersurface. It is found that the number of underlying inward crossings is much smaller than the one the Cooper-Frye formula gives under the assumption of equilibrium distribution functions. The magnitude of Cooper-Frye negative contributions is also investigated as a function of hadron mass, collision energy in the range Elab = 5 — 160A GeV, and collision centrality. The largest negative contributions we find are around 13% for the pion yield at midrapidity at Elab = 20A GeV collisions.
Highlights
In the hot and dense system of strongly interacting matter created in heavy ion collisions the mean free path of the particles is much smaller than the size of the fireball
If the distribution of UrQMD particles is thermal on some closed hypersurface and the system is in chemical equilibrium, the Cooper-Frye formula should give results identical to explicit particle counting
It might be possible to explain this as a sign of chemical non-equilibrium in UrQMD, but when one looks at the positive and negative contributions to the pion distributions shown in Fig. 1, one sees that a difference in the pion density only is not sufficient to explain the differences in the contributions
Summary
In the hot and dense system of strongly interacting matter created in heavy ion collisions the mean free path of the particles is much smaller than the size of the fireball. This fact together with the assumption of fast thermal equilibration allows to apply relativistic hydrodynamics for the dynamical description of heavy ion collisions. State of the art simulations of heavy ion collisions couple hydrodynamics for the early stage of the evolution to hadron transport for the late stage. Such approaches are called hybrid approaches [1]
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