Dark boson mediation of the $\pi^0\rightarrow \gamma e^+ e^-$ 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 $\pi^0$ decay width and then we extend the theory by adding dark sector vector particles which interact through $\gamma^\mu$, $\sigma^{\mu\nu}$ and $\sigma^{\mu\nu}\gamma^5$. We calculate the total decay width of $\pi^0\rightarrow \gamma e^+ e^-$ 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.