Search for the Pair Production of Dark Particles $X$ with $K_L^0\to XX$, $X\to \gamma \gamma$

We present the first search for the pair production of dark particles $X$ via $K_L^0\to XX$ with $X$ decaying into two photons using the data collected by the KOTO experiment. No signal was observed in the mass range of 40 - 110 MeV/c${}^2$ and 210 - 240 MeV/c${}^2$. This sets upper limits on the branching fractions as $\mathcal{B}(K_L^0\to XX)$ $<$ (1-4) $\times$ 10${}^{-7}$ and $\mathcal{B}(K_L^0\to XX)$ $<$ (1-2) $\times$ 10${}^{-6}$ at the 90% confidence level for the two mass regions, respectively.