Particle Freeze-out within the Self-Consistent Hydrodynamics

Here I discuss some implicit assumptions of modern hydrodynamic models and argue that their accuracy cannot be better than 10-15 %. Then I formulate the correct conservation laws for the fluid emitting particles from an arbitrary freeze-out (FO) hypersurface (HS) and show that the derived momentum distribution function of emitted particles does not contain negative contributions which appear in the famous Cooper-Frye formula. Further I analyze the typical pitfalls of some hydro models trying to alternatively resolve the FO problem.