Comprehensive Interpretation of Thermal Dileptons at the SPS

Employing thermal dilepton rates based on medium-modified electromagnetic correlation functions we show that recent dimuon spectra of the NA60 collaboration in central In-In collisions at the CERN-SPS can be understood in terms of radiation from a hot and dense hadronic medium. Earlier calculated \rho-meson spectral functions, as following from hadronic many-body theory, provide an accurate description of the data up to dimuon invariant masses of about M\simeq 0.9 GeV, with good sensitivity to details of the predicted \rho-meson line shape. This, in particular, identifies baryon-induced effects as the prevalent ones. We show that a reliable description of the \rho contribution opens the possibility to study further medium effects: at higher masses (M \simeq 0.9-1.5 GeV) 4-pion type annihilation is required to account for the experimentally observed excess indicating precursor effects of chiral symmetry restoration (``chiral mixing''), while remaining structures in the \omega and \phi region are suggestive for modifications in their line shapes as well.