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 $O(100\mathrm{MeV})$ dark states can be probed with the decays of $K_L$ mesons, owing to the enhanced two-body kinematics, $K_L\to X_1{X}_2$ or $X_2{X}_2$. If either of these two particles is unstable, e.g., $X_2\to X_1{\pi }^0$, $X_2\to X_1\gamma$ or $X_{1,2}\to \gamma \gamma$, such decays could easily mimic $K_L\to {\pi }^0\nu \overline{\nu }$ signatures, while not being ruled out by the decays of charged kaons. We construct explicit models that have enhanced $K_L$ 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 $X_{1,2}$ particles, if stable, could constitute the entirety of dark matter.

• Received 28 May 2020
• Accepted 19 August 2020

DOI:https://doi.org/10.1103/PhysRevD.102.055016

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society