We analyze dilepton emission from hot and dense matter using a hybrid approach based on the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport model with an intermediate hydrodynamic stage for the description of heavy-ion collisions at relativistic energies. During the hydrodynamic stage, the production of lepton pairs is described by radiation rates for a strongly interacting medium in thermal equilibrium. In the low mass region, hadronic thermal emission is evaluated assuming vector meson dominance including in-medium modifications of the rho meson spectral function through scattering from nucleons and pions in the heat bath. In the intermediate mass region, the hadronic rate is essentially determined by multi-pion annihilation processes. Emission from quark-antiquark annihilation in the quark gluon plasma is taken into account as well. When the system is sufficiently dilute, the hydrodynamic description breaks down and a transition to a final cascade stage is performed. In this stage dimuon emission is evaluated as commonly done in transport models. Focusing on the enhancement with respect to the contribution from long-lived hadron decays after freezout observed at the SPS in the low mass region of the dilepton spectra, the relative importance of the different thermal contributions and of the two dynamical stages is investigated. We find that three separated regions can be identified in the invariant mass spectra. Whereas the very low and the intermediate mass regions mostly receive contribution from the thermal dilepton emission, the region around the vector meson peak is dominated by the cascade emission. Above the rho-peak region the spectrum is driven by QGP radiation. Analysis of the dimuon transverse mass spectra reveals that the thermal hadronic emission shows an evident mass ordering not present in the emission from the QGP.
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