Kaon Portal to Freeze-in Dark Matter

We investigate freeze-in production of light dark matter through the quark flavor-changing operator $(\bar{s}\gamma_\mu d)(\bar{\chi}\gamma^\mu\chi)$ in a low-reheating cosmology. For reheating temperatures below the QCD crossover, kaon decays and scatterings generate the dark matter abundance through $K\to\pi\chi\bar{\chi}$ and $K\pi\to\chi\bar{\chi}$. The same interaction induces the rare kaon decays $K^+\to\pi^+\chi\bar{\chi}$ and $K_L\to\pi^0\chi\bar{\chi}$. This links the freeze-in relic abundance to searches at NA62, KOTO, and KOTO II. We find that lower reheating temperatures require larger couplings to compensate for the Boltzmann-suppressed kaon abundance, making kaon-driven freeze-in dark matter testable at rare kaon decay experiments.