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Local energy-momentum conservation and initial conditions for quark-gluon plasma evolution in nucleus-nucleus collisions at SPS and RHIC BES energies

We investigate consequences of local energy-momentum conservation for initial eccentricity coefficients in heavy ion collisions at not too high energies relevant for CERN SPS and RHIC BES. Different models of energy density available for pion production are considered. We study dependence of eccentricity coefficients on space-time rapidity for different impact parameters. The naive formula how to define eccentricities breaks with our initial conditions and must be corrected. We predict considerable eccentricities for $ε_{1,2,3,4}$ and specific dependence on space-time rapidity as well as on impact parameter for lower energies. The effect becomes smaller at larger energies when restricting to narrow rapidity interval arround zero. Our predictions are in principle input for further hydrodynamical evolution but it is not clear whether they can be easily used. Our initial condition suggest a strong preequilibrium phase which is difficult for modelling.