Kaon portal to freeze-in dark matter

A bstract: We investigate freeze-in production of light dark matter through the quark flavor-changing operator $$ \left(\overline{s}{\gamma}_{\mu }d\right)\left(\overline{\chi}{\gamma}^{\mu}\chi \right) $$ s ¯ γ μ d χ ¯ γ μ χ in a low-reheating cosmology. For reheating temperatures below the QCD crossover, kaon decays and scatterings generate the dark matter abundance through $$ K\to \pi \chi \overline{\chi} $$ K → πχ χ ¯ and $$ K\pi \to \chi \overline{\chi} $$ Kπ → χ χ ¯ . The same interaction induces the rare kaon decays $$ {K}^{+}\to {\pi}^{+}\chi \overline{\chi} $$ K + → π + χ χ ¯ and $$ {K}_L\to {\pi}^0\chi \overline{\chi} $$ K L → π 0 χ χ ¯ . 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.