A search for the rare decay $K_L !to! pi^0 u overline{ u}$ 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 $K_L !to! pi^0 u overline{ u}$ 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 $135~{rm MeV}/c^2$.
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