  The dilepton emission in heavy-ion reactions at low beam energies is examined
within a hadronic transport approach. In this article the production of
electron-positron pairs from a new approach named SMASH (Simulating Many
Accelerated Strongly-interacting Hadrons) is introduced. The dilepton emission
is consistently taken into account below the hadronic threshold. The
calculations are systematically confronted with HADES data in the kinetic
energy range of $1 - 3.5A$ GeV for elementary, proton-nucleus and
nucleus-nucleus reactions. The present approach employing a resonance treatment
based on vacuum properties is validated by an excellent agreement with
experimental data up to system sizes of carbon-carbon collisions. After
establishing this well-understood baseline in elementary and small systems, the
significance of medium effects is investigated with a coarse-graining approach
based on the same hadronic evolution. The effect of explicit in-medium
modifications to the vector meson spectral functions is important for dilepton
invariant mass spectra in ArKCl and larger systems, even though the transport
approach with vacuum properties reveals similar features due the coupling to
baryonic resonance and the intrinsically included collisional broadening. This
article provides a comprehensive comparison of our calculations with published
dielectron results from the HADES collaboration. In addition, the emission of
dileptons is predicted in gold-gold and pion-beam experiments for which results
are expected soon.
