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Systematic Investigation of Negative Cooper-Frye Contributions in Heavy Ion Collisions Using Coarse-grained Molecular Dynamics

In most heavy ion collision simulations involving relativistic hydrodynamics, the Cooper-Frye formula is applied to transform the hydrodynamical fields to particles. In this article the so-called negative contributions in the Cooper-Frye formula are studied using a coarse-grained transport approach. The magnitude of negative contributions is investigated as a function of hadron mass, collision energy in the range of $E_{\rm lab} = 5$--$160A$ GeV, collision centrality and the energy density transition criterion defining the hypersurface. The microscopic results are compared to negative contributions expected from hydrodynamical treatment assuming local thermal equilibrium. The main conclusion is that the number of actual microscopic particles flying inward is smaller than the negative contribution one would expect in an equilibrated scenario. The largest impact of negative contributions is found to be on the pion rapidity distribution at midrapidity in central collisions. For this case negative contributions in equilibrium constitute 8--13\% of positive contributions depending on collision energy, but only 0.5--4\% in cascade calculation. The dependence on the collision energy itself is found to be non-monotonous with a maximum at 10-20$A$ GeV.