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Cooper-Frye Negative Contributions in a Coarse-Grained Transport Approach

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 $E_{\rm lab} = 5-160A$ GeV, and collision centrality. The largest negative contributions we find are around 13% for the pion yield at midrapidity at $E_{\rm lab} = 20A$ GeV collisions.