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A search for the rare decay $K_L \!\to\! \pi^0 \nu \overline{\nu}$ wasperformed. With the data collected in 2015, corresponding to $2.2 \times10^{19}$ protons on target, a single event sensitivity of $( 1.30 \pm 0.01_{\rmstat} \pm 0.14_{\rm syst} ) \times 10^{-9}$ was achieved and no candidateevents were observed. We set an upper limit of $3.0 \times 10^{-9}$ for thebranching 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 orderof 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 massof $135~{\rm MeV}/c^2$.

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