Evidence of a heavy neutrino, $ u_H$, in the $K^+tomu^+ u_H$ decays was sought using the E949 experimental data with an exposure of $1.70times 10^{12}$ stopped kaons. With the major background from the radiative $K^+tomu^+ u_mugamma$ decay understood
and suppressed, upper limits (90% C.L.) on the neutrino mixing matrix element between muon and heavy neutrino, $|U_{mu H}|^2$, were set at the level of $10^{-7}$ to $10^{-9}$ for the heavy neutrino mass region 175 to 300 MeV/$c^2$.
Experiment E949 at Brookhaven National Laboratory has observed three new events consistent with the decay K+ => pi+,nu,nubar in the pion momentum region 140 < P_pi < 199 MeV/c in an exposure of 1.71e12 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+ => pi+,nu,nubar events to seven. Combining this observation with previous results, assuming the pion spectrum predicted by the standard model, results in a branching ratio of (1.73+1.15-1.05)e-10. An interpretation of the results for alternative models of the decay K^ => pi+,nothing is also presented.
