Dilepton production and reaction dynamics in heavy-ion collisions at SIS energies from coarse-grained transport simulations

Dilepton invariant-mass spectra for heavy-ion collisions at SIS 18 and BEVALAC energies are calculated using a coarse-grained time evolution from the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model. The coarse-graining of the microscopic simulations enables to calculate thermal dilepton emission rates by application of in-medium spectral functions from equilibrium quantum-field theoretical calculations. The results show that extremely high baryon chemical potentials dominate the evolution of the created hot and dense fireball. Consequently, a significant modification of the $\rho$ spectral shape becomes visible in the dilepton invariant-mass spectrum, resulting in an enhancement in the low-mass region $M_{ee} = 200$ to 600 MeV/$c^{2}$. This enhancement, mainly caused by baryonic effects on the $\rho$ spectral shape, can fully describe the experimentally observed excess above the hadronic cocktail contributions in Ar+KCl ($E_{\mathrm{lab}}=1.76$ $A$GeV) reactions as measured by the HADES collaboration and also gives a good explanation of the older DLS Ca+Ca ($E_{\mathrm{lab}}=1.04$ $A$GeV) data. For the larger Au+Au ($E_{\mathrm{lab}}=1.23$ $A$GeV) system, we predict an even stronger excess from our calculations. A systematic comparison of the results for different system sizes from C+C to Au+Au shows that the thermal dilepton yield increases stronger ($\propto A^{4/3}$) than the hadronic background contributions, which scale with $A$, due to its sensitivity on the time evolution of the reaction. We stress that the findings of the present work are consistent with our previous coarse-graining results for the NA60 measurements at top SPS energy. We argue that it is possible to describe the dilepton results from SIS 18 up to SPS energies by considering the modifications of the $\rho$ spectral function inside a hot and dense medium within the same model.