Medium effects on pion production in heavy ion collisions

Within the framework of the relativistic Vlasov-Uehling-Uhlenbeck transport model based on the relativistic nonlinear NL ρ interaction, we study pion in-medium effects on the π^-/π⁺ ratio in Au+Au collisions at the energy of E /A =400 MeV . These effects include the isospin-dependent pion s -wave and p -wave potentials, which are taken from calculations based on the chiral perturbation theory and the Δ -hole model, respectively. We find that the π^-/π⁺ ratio in this collision is suppressed by the pion s -wave potential but enhanced by the p -wave potential, with a net effect of a significantly suppressed π^-/π⁺ ratio. Including also the in-medium threshold effects on Δ resonance production and decay and using a nuclear symmetry energy with a slope parameter L =59 MeV by reducing the coupling of isovector-vector ρ meson to nucleon, our result is in good agreement with measured π^-/π⁺ ratio from the FOPI Collaboration. We further investigate the pion in-medium effects on the ratio of charged pions as a function of their kinetic energies.