Study of the rare and forbidden decays of η/η′ offers a sensitive probe to test fundamental symmetries of quantum chromodynamics and search for new physics beyond the Standard Model. To study the rare decays of η/η′ to π+π−e+e−, π+π−μ+μ− and e+e−μ+μ− at the BESIII detector, we developed several event generators based on the vector meson dominant model with finite-width corrections and the pseudoscalar mesons mixing theory. The various distributions from event generators are in good agreement with the theoretical predictions, which indicates that the event generators work very well after implemention in the BESIII Monte Carlo simulation package. In the BESIII physics analysis, the performance of the event generators will be improved in accordance with the distributions of different variables of η/η′ from data and the improvement on the theoretical calculations.
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