Pair production of dark particles in meson decays

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 $O(100\,{\rm MeV})$ dark states can be probed with the decays of $K_L$ mesons, owing to the enhanced two-body kinematics, $K_L\to X_1X_2$ or $X_2X_2$. If either or 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.