K^-/K^+ ratio in heavy-ion collisions at GSI with an antikaon self-energy in hot and dense matter

The $K^-/K^+$ ratio produced in heavy-ion collisions at GSI energies is studied. The in-medium properties at finite temperature of the hadrons involved are included, paying a special attention to the in-medium properties of antikaons. Using a statistical approach, it is found that the determination of the temperature and chemical potential at freeze-out conditions compatible with the ratio $K^-/K^+$ is very delicate, and depends very strongly on the approximation adopted for the antikaon self-energy. The use of an energy dependent $\bar{K}$ spectral density, including both s and p-wave components of the $\bar{K}N$ interaction, lowers substantially the freeze-out temperature compared to the standard simplified mean-field treatment and gives rise to an overabundance of $K^-$ production in the dense and hot medium. Even a moderately attractive antikaon-nucleus potential obtained from our self-consistent many-body calculation does reproduce the ``broad-band equilibration'' advocated by Brown, Rho and Song due to the additional strength of the spectral function of the $K^-$ at low energies.