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

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.