Search for the Rare Decays Π+→μ+νμνν¯ And

The rare pion decays ${\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ and ${\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}{e}^{+}{\ensuremath{\nu}}_{e}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ are allowed in the Standard Model but highly suppressed. These decays were searched for using data from the PIENU experiment. A first result for $\mathrm{\ensuremath{\Gamma}}({\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\nu}\overline{\ensuremath{\nu}})/\mathrm{\ensuremath{\Gamma}}({\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}})<8.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and an improved measurement $\mathrm{\ensuremath{\Gamma}}({\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}{e}^{+}{\ensuremath{\nu}}_{e}\ensuremath{\nu}\overline{\ensuremath{\nu}})/\mathrm{\ensuremath{\Gamma}}({\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}})<1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ were obtained.