A coarse-graining approach for dilepton production at SPS energies
  Coarse-grained output from transport calculations is used to determine thermal dilepton emission rates by applying medium-modified spectral functions from thermal quantum field theoretical models. By averaging over an ensemble of events generated with the UrQMD transport model, we extract the local thermodynamic properties at each time step of the calculation. With an equation of state the temperature $T$ and chemical potential $\mu_{\mathrm{B}}$ can be determined. The approach goes beyond simplified fireball models of the bulk-medium evolution by treating the full (3+1)-dimensional expansion of the system with realistic time and density profiles. For the calculation of thermal dilepton rates we use the in-medium spectral function of the $\rho$ meson developed by Rapp and Wambach and consider thermal QGP and multi-pion contributions as well. The approach is applied to the evaluation of dimuon production in In+In collisions at top SPS energy. Comparison to the experimental results of the NA60 experiment shows good agreement of this ansatz. We find that the experimentally observed low-mass dilepton excess in the mass region from 0.2 to 0.6 GeV can be explained by a broadening of the $\rho$ spectral function with a small mass shift. In contrast, the intermediate mass region ($M > 1.5$ GeV) is dominated by a contribution from the quark-gluon plasma. These findings agree with previous calculations with fireball parametrizations. This agreement in spite of differences in the reaction dynamics between both approaches indicates that the time-integrated dilepton spectra are not very sensitive to details of the space-time evolution of the collision. 
Stephan Endres, Hendrik van Hees, Janus Weil and Marcus Bleicher
nucl-th hep-ph