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Rare leptonic kaon and pion decays $K^+(\pi^+) \to \mu^+\, \nu_{\mu}\, e^+e^-$ can be used to probe a dark photon of mass ${\cal O}(10)$~MeV, with thebackground coming from the mediation of a virtual photon. This is most relevantfor the 16.7-MeV dark photon proposed to explain a 6.8$\sigma$ anomaly recentlyobserved in $^8$Be transitions by the Atomki Collaboration. We evaluate thereach of future experiments for different scenarios of how the dark photoncouples with the standard model particles, and show that a great portion of thepreferred 16.7-MeV dark photon parameter space can be decisively probed. Wealso show the use of angular distributions to further distinguish the signalfrom the background.

Probing a dark photon using rare leptonic kaon and pion decays