Search for the $K_L \!\to\! \pi^0 \nu \overline{\nu}$ and $K_L \!\to\! \pi^0 X^0$ decays at the J-PARC KOTO experiment

A search for the rare decay $K_L \!\to\! \pi^0 \nu \overline{\nu}$ was performed. With the data collected in 2015, corresponding to $2.2 \times 10^{19}$ protons on target, a single event sensitivity of $( 1.30 \pm 0.01_{\rm stat.} \pm 0.14_{\rm syst.} ) \times 10^{-9}$ was achieved and no candidate events were observed. We set an upper limit of $3.0 \times 10^{-9}$ for the branching fraction of $K_L \!\to\! \pi^0 \nu \overline{\nu}$ at the 90% confidence level (C.L.), which improved the previous limit by almost an order of magnitude. An upper limit for $K_L \!\to\! \pi^0 X^0$ was also set as $2.4 \times 10^{-9}$ at the 90% C.L., where $X^0$ is an invisible boson with a mass of $135\ {\rm MeV/c^2}$.