Rare decays of K and B mesons provide a powerful probe of dark sectors with light new particles. We show that the pair production of O(100 MeV) dark states can be probed with the decays of KL mesons, owing to the enhanced two-body kinematics, KL→X1X2 or X2X2. If either of these two particles is unstable, e.g., X2→X1π0, X2→X1γ or X1,2→γγ, such decays could easily mimic KL→π0νν¯ signatures, while not being ruled out by the decays of charged kaons. We construct explicit models that have enhanced KL decay signatures, and are constrained by the results of the KOTO experiment. We note that recently reported excess events can also be accommodated while satisfying all other constraints (B decays, colliders, beam dumps). These models are based on the extensions of the gauge and/or scalar sector of the theory. The lightest of X1,2 particles, if stable, could constitute the entirety of dark matter.
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The authors would like to thank A. Arvanitaki, D. Egana-Ugrinovic, K. Nakagiri, and T. Yamanaka for useful discussions and correspondence. M. P. expresses his gratitude to the organizers and participants of the HC2NP 2019 workshop (Tenerife) for the intellectually stimulating environment that led to some of the ideas explored in this paper. The work of K. K. is supported by the DOE Grant No. DE-SC0011842 at the University of Minnesota. The research at the Perimeter Institute is supported in part by the Government of Canada through NSERC and by the Province of Ontario through MEDT.