Search for RareK+Decays. I.K+→μ+νν¯ν

In a counter experiment at the LBL Bevatron, we have searched for the process $K^{+}\to {\mu }^{+}\nu \overline{\nu }\nu$ and have found no evidence for its existence. We have recorded ten events which could be examples of this decay mode, but could also be examples of $K^{+}\to {\mu }^{+}\nu \gamma$ in which the $\gamma$ was not detected. Treating these as unidentified events and assuming the ${\mu }^{+}$ spectrum proposed by Bardin, Bilenky, and Pontecorvo, we obtain a decay rate $\Gamma (K^{+}\to {\mu }^{+}\nu \overline{\nu }\nu )\le 6\times {10}^{-6\mathrm{}}\Gamma (K^{+}\to \mathrm{all})$ (90% confidence level). The data are presented in such a way as to allow calculation of rates for any assumed spectrum. The experiment provides a test for higher-order weak processes and sets constraints on certain first-order models.