Probing a dark photon using rare leptonic kaon and pion decays
Rare leptonic kaon and pion decays $K^+(π^+) \to μ^+\, ν_μ\, e^+ e^-$ can be used to probe a dark photon of mass ${\cal O}(10)$~MeV, with the background coming from the mediation of a virtual photon. This is most relevant for the 16.7-MeV dark photon proposed to explain a 6.8$σ$ anomaly recently observed in $^8$Be transitions by the Atomki Collaboration. We evaluate the reach of future experiments for different scenarios of how the dark photon couples with the standard model particles, and show that a great portion of the preferred 16.7-MeV dark photon parameter space can be decisively probed. We also show the use of angular distributions to further distinguish the signal from the background.