Search for Dark Particles in $K_L^0\to \gamma X$ at the KOTO Experiment

We report a search for an invisible particle $X$ in the decay $K_L^0\to \gamma X$ ($X\to \text{invisible}$), where $X$ can be interpreted as a massless or massive dark photon. No evidence for $X$ was found, based on 13 candidate events consistent with a predicted background of $12.66\pm {4.42}_{\text{stat.}}\pm {2.13}_{\text{syst.}}$ events. Upper limits on the branching ratio of $K_L^0\to \gamma X$ were set for the $X$ mass range $0\le m_X\le 425$ MeV/$c^2$. For massless $X$, the upper limit was $3.4\times {10}^{-7}$ at the $90\mathrm{\%}$ confidence level, while for massive $X$, the upper limits in the searched mass region ranged from $O({10}^{-7})$ to $O({10}^{-3})$.