What does the rho-meson do? In-medium mass shift scenarios versus hadronic model calculations

The NA60 experiment has studied low-mass muon pair production in In-In collisions at $158 {\rm AGeV}$ with unprecedented precision. With these results there is hope that the in-medium modifications of the vector meson spectral function can be constrained more thoroughly than before. We investigate in particular what can be learned about collisional broadening by a hot and dense medium and what constrains the experimental results put on in-medium mass shift scenarios. The data show a clear indication of considerable in-medium broadening effects but disfavor mass shift scenarios where the $\rho$-meson mass scales with the square root of the chiral condensate. Scaling scenarios which predict at finite density a dropping of the $\rho$-meson mass that is stronger than that of the quark condensate are clearly ruled out since they are also accompanied by a sharpening of the spectral function.