In-medium properties of antikaons at finite temperature: the K^-/K^+ ratio at GSI

The $K^-/K^+$ ratio in heavy-ion collisions at GSI is studied including the properties of the participating hadrons in hot and dense matter, paying a particular attention to the in-medium properties of antikaons at finite temperature. The determination of the temperature and chemical potential at freeze-out conditions compatible with the ratio $K^-/K^+$ is very delicate, and depends on the approach adopted for the antikaon self-energy. Different approaches for the $K^-$ self-energy have been considered: non-interacting $K^-$, on-shell self-energy and single-particle spectral density. We observe that the use of an energy dependent $\bar{K}$ spectral density lowers considerably the freeze-out temperature with respect to the on-shell approach. We also conclude that the full off-shell approach gives rise to the "broad-band equilibration" advocated by Brown, Rho and Song.