Novel multi-lepton signatures of dark sectors in light meson decays

We point out kaon decays to multiple charged leptons as a novel probe of light dark particles $X$. Previously neglected channels, such as $K^+\to \pi^+ \left(XX \to 2(e^+e^-)\right)$, $K_L\to \pi^0 \left( XX \to 2(e^+e^-)\right)$, and $K_S\to \left(XX \to 2(e^+e^-)\right)$ may have very large rates, exceeding not only the Standard Model expectations but also possible backgrounds, such as Dalitz decays of neutral pions. We apply this idea to dark sector models where the production of dark Higgses or heavy neutral leptons leads to final states with several visible dark photons. We also investigate a recently proposed model of an MeV-scale QCD axion, where the rates for kaon decays to multiple axion states are large due to the non-linear interactions of the axion with the light mesons. In addition, we point out new probes of this axion in pion decays, such as the single production of $a$ in $\pi^+ \to \nu \left((e^+)^* \to e^+ a\to e^+e^+e^-\right)$, double production in pion capture $\pi^-+(p \text{ or D})\to aa + (n\text{ or }nn) \to 2(e^+e^-) + (n\text{ or }nn)$, as well as $\pi^0 \to aaa\to 3(e^+e^-)$. The latter decay is fixed at $\mathcal{B}(\pi^0\to a a a) = 1.0 \times 10^{-3}$ for a $17$ MeV axion.