The invariant-mass spectrum of e e ÿ pairs produced in 12 C 12 C collisions at an incident energy of 2 GeV per nucleon has been measured for the first time. The measured pair production probabilities span over 5 orders of magnitude from the 0 -Dalitz to the =! invariant-mass region. Dalitz decays of 0 and account for all the yield up to 0:15 GeV=c 2 , but for only about 50% above this mass. A comparison with model calculations shows that the excess pair yield is likely due to baryon-resonance and vector-meson decays. Transport calculations based on vacuum spectral functions fail, however, to describe the entire mass region.The properties of hot and dense hadronic matter represent a key problem in heavy-ion physics, with far-reaching applications for other fields. They are governed by nonperturbative QCD and cannot be derived directly from the underlying Lagrangian. Models predict that hadron properties, such as mass and lifetime, depend on the temperature and density of the medium. While some hadronic many-body calculations give a broadening of the meson PRL 98, 052302 (2007)