The Search for $K_L\to {\pi }^0{\pi }^0\gamma \gamma$ and $K_L\to {\pi }^0{\pi }^{0}X$ where $X\to 2\gamma$ at the KOTO Experiment

We performed searches for $K_L\to {\pi }^0{\pi }^{0}X$ where $X$ may be an axion-like particle which promptly decays to two photons, and the first search for $K_L\to {\pi }^0{\pi }^0\gamma \gamma$ at the KOTO experiment using data taken in 2021. The search is performed for $X$ mass in the range of 160$\text{unicode}x2013$220 MeV/$c^2$. Three events were observed in the signal region, with two events near an $X$ mass of 177 MeV/$c^2$. This result led to a range of upper limits on the branching ratio, BR($K_L\to {\pi }^0{\pi }^{0}X$) $<(1\text{unicode}x201320)\times {10}^{-7}$ at the 95% confidence level (C.L.). No events were observed for the analysis of $K_L\to {\pi }^0{\pi }^0\gamma \gamma$, setting an upper limit on the branching ratio, BR($K_L\to {\pi }^0{\pi }^0\gamma \gamma$) $<1.69\times {10}^{-6}$ at the 95% C.L.