e+e--pair production in Pb-Au collisions at 158 GeV per nucleon

We present the combined results on electron-pair production in 158 GeV/n {Pb-Au} ($\sqrt{s}$= 17.2 GeV) collisions taken at the CERN SPS in 1995 and 1996, and give a detailed account of the data analysis. The enhancement over the reference of neutral meson decays amounts to a factor of 2.31$\pm0.19 (stat.)\pm0.55 (syst.)\pm0.69 (decays)$ for semi-central collisions (28% $\sigma/\sigma_{geo}$) when yields are integrated over $m>$ 200 MeV/$c^2$ in invariant mass. The measured yield, its stronger-than-linear scaling with $N_{ch}$, and the dominance of low pair $p_t$ strongly suggest an interpretation as {\it thermal radiation} from pion annihilation in the hadronic fireball. The shape of the excess centring at $m\approx$ 500 MeV/$c^2$, however, cannot be described without strong medium modifications of the $\rho$ meson. The results are put into perspective by comparison to predictions from Brown-Rho scaling governed by chiral symmetry restoration, and from the spectral-function many-body treatment in which the approach to the phase boundary is less explicit.