The Search for $K_L\to \ddot{I}{€}^0\ddot{I}{€}^0{\hat{I}}^3{\hat{I}}^3$ and $K_L\to \ddot{I}{€}^0\ddot{I}{€}^{0}X$ where $X\to 2{\hat{I}}^3$ at the KOTO Experiment

Abstract

We performed searches for $K_L\to \ddot{I}{€}^0\ddot{I}{€}^{0}X$ where $X$ may be an axion-like particle which promptly decays to two photons, and the first search for $K_L\to \ddot{I}{€}^0\ddot{I}{€}^0{\hat{I}}^3{\hat{I}}^3$ at the KOTO experiment using data taken in 2021. The search is performed for $X$ mass in the range of 160$\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($K_L\to \ddot{I}{€}^0\ddot{I}{€}^{0}X$) $< (1\unicode{x2013}20) \times 10^{-7}$ at the 95% confidence level (C.L.). No events were observed for the analysis of $K_L\to \ddot{I}{€}^0\ddot{I}{€}^0{\hat{I}}^3{\hat{I}}^3$, setting an upper limit on the branching ratio, BR($K_L\to \ddot{I}{€}^0\ddot{I}{€}^0{\hat{I}}^3{\hat{I}}^3$) $<1.69\times 10^{-6}$ at the 95% C.L.