Investigating the QCD phase transitions with thermal dileptons: present status and new opportunities at the CERN SPS

Precision measurements of thermal dileptons produced in ultra-relativistic heavy ion collisions provide unique insight in the structure of the QCD phase diagram. In the first part of the talk I will review the results of the state-of-the-art measurements performed at the CERN SPS by the NA60 experiment. This experiment has quantitatively measured for the first time the spectral function of the rho meson in high energy nuclear collisions. Changes both in width and in mass were suggested since long time as a signature of the chiral transition. The experiment has also measured for the first time the production of thermal dilepton radiation from the quark-gluon plasma. In the second part, I will discuss the possibility to investigate quantitatively chiral symmetry restoration and the onset of deconfinement, in the region of moderate baryo-chemical potential, with a new campaign of precision measurements at the CERN SPS. In this region of the phase diagram, the quark-gluon plasma and hadronic phases should be separated by a first order transition region which is expected to end with a critical point. Novel high-precision dilepton measurements might address the measurement of rho-a_1 chiral-mixing. In addition the thermal dilepton spectrum provides the possibility to measure a caloric curve to investigate the first order phase transition.