Effects of medium modification of pion production threshold in heavy ion collisions and the nuclear symmetry energy

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Using the relativistic Vlasov-Uehling-Uhlenbeck (RVUU) equation based on mean fields from the nonlinear relativistic models, we study the effect of medium modification of pion production threshold on the total pion yield and the π-/π+ ratio in Au+Au collisions. We find that the in-medium threshold effect enhances both the total pion yield and the π-/π+ ratio, compared to those without this effect. Furthermore, including the medium modification of the pion production threshold in asymmetric nuclear matter leads to a larger π-/π+ ratio for the NLρδ model with a stiffer symmetry energy than the NLρ model with a softer symmetry energy, opposite to that found without the in-medium threshold effect. Experimental data from the FOPI Collaboration are reproduced after including a density-dependent cross section for Δ baryon production from nucleon-nucleon collisions, which suppresses the total pion yield but hardly changes the π-/π+ ratio. The large errors in the experimentally measured π-/π+ ratio prevent, however, the distinction between the predictions from the NLρ and NLρδ models.