Search for the decays $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ and $K^{+}\to {\pi }^{+}{X}^0$ for $150<\mathrm{}{M}_{X^0}<250\mathrm{}$ MeV/${\mathit{c}}^2$

A search for the decays $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ and $K^{+}\to {\pi }^{+}{X}^0$, where $X^0$ is any weakly interacting neutral particle or system of neutral particles with $150<\mathrm{}{M}_{X^0}<250\mathrm{}$ MeV/${\mathit{c}}^2$, was performed in the pion kinematic region below the $K_{\pi 2}(K^{+}\to {\pi }^{+}{\pi }^0)$ peak. An upper limit on $B(K^{+}\to {\pi }^{+}\nu \overline{\nu })$ is set at 1.7 × ${10}^{-8\mathrm{}}$ (90% C.L.) and $B(K^{+}\to {\pi }^{+}{X}^0)$ is restricted to the ${10}^{-7\mathrm{}}$ level or lower. Limits are also set for the production of $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ through scalar or tensor interactions at 1.8 × ${10}^{-8\mathrm{}}$ and 1.0 × ${10}^{-8\mathrm{}}$ (90% C.L.), respectively.