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

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.

Evidence of massive neutrinos in the ${\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}{e}^{+}\ensuremath{\nu}$ decay spectrum was sought with the background ${\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}\ensuremath{\rightarrow}{e}^{+}$ decay chain highly suppressed. Upper limits (90% C.L.) on the neutrino mixing matrix element $|{U}_{ei}{|}^{2}$ in the neutrino mass region $60--129\text{ }\text{ }\mathrm{MeV}/{c}^{2}$ were set at the level of ${10}^{\ensuremath{-}8}$.

Experiment E949 at Brookhaven National Laboratory has observed three new events consistent with the decay K + → π + vv in the pion momentum region 140 < P π < 199 MeV/c in an exposure of 1.71 × 10 12 stopped kaons with an estimated total background of 0.93 ± 0.17(stat) +0.32 ―0.24 (syst) events. This brings the total number of observed K + → π + vv events to seven. Combining this observation with previous results, assuming the pion spectrum predicted by the standard model, results in a branching ratio of B(K + → π + vv) = (1.73 +1.15 ―1.05 ) × 10 ―10 . An interpretation of the results for alternative models of the decay K + → π + + nothing is also presented.

We have searched for the K+ -> pi(+)gamma gamma decay in the kinematic region with pi(+) momentum close to the end point. No events were observed, and the 90% confidence-level upper limit on the partial branching ratio was obtained, B (K+ -> pi(+)gamma gamma, P > 213 MeV/c) < 8.3 x 10(-9) under the assumption of chiral perturbation theory including next-to-leading order "unitarity" corrections. The same data were used to determine an upper limit on the K+ -> pi(+)gamma branching ratio of 2.3 x 10(-9) at the 90% confidence level. (c) 2005 Elsevier B.V. All rights reserved.