We present a measurement of $e^+e^-$ pair production in central Pb-Au collisions at 158$A$ GeV/$c$. As reported earlier, a significant excess of the $e^+e^-$ pair yield over the expectation from hadron decays is observed. The improved mass resolution of the present data set, recorded with the upgraded CERES experiment at the CERN-SPS, allows for a comparison of the data with different theoretical approaches. The data clearly favor a substantial in-medium broadening of the $rho$ spectral function over a density-dependent shift of the $rho$ pole mass. The in-medium broadening model implies that baryon induced interactions are the key mechanism to in-medium modifications of the $rho$-meson in the hot fireball at SPS energy.
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