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An experiment to search for the $K^-pp$ bound state was performed via thein-flight $^3$He($K^-,n)$ reaction using 5.3 $\times$ $10^9$ kaons at 1 GeV/$c$at the J-PARC hadron experimental facility. In the semi-inclusive neutronmissing-mass spectrum at $\theta_{n}^{lab}=0^\circ$, no significant peak wasobserved in the region corresponding to $K^-pp$ binding energy larger than 80MeV, where a bump structure has been reported in the $\Lambda p$ final state indifferent reactions. Assuming the state to be isotropically decaying into$\Lambda p$, mass-dependent upper limits on the production cross section weredetermined to be 30--180, 70--250, and 100--270 $\mu$b/sr, for the naturalwidths of 20, 60, and 100 MeV, respectively, at 95\% confidence level.

Search for the deeply bound $K^-pp$ state from the semi-inclusive forward-neutron spectrum in the in-flight $K^-$ reaction on helium-3