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Dark boson mediation of the $π^0\rightarrow γe^+ e^-$ decay

The phenomenological implications to the decay of the neutral pion from the introduction of new dark particles are discussed. We calculate the contribution to the $π^0$ decay width and then we extend the theory by adding dark sector vector particles which interact through $γ^μ$, $σ^{μν}$ and $σ^{μν}γ^5$. We calculate the total decay width of $π^0\rightarrow γe^+ e^-$ where the electron-positron pair is produced through a decay of a dark meson. The implication of the presented model on the present and future searches for new dark particles is also discussed.