Search for the rare decayK+→μ+νν¯ν

Evidence of the ${K}^{+}\\ensuremath{\\rightarrow}{\\ensuremath{\\mu}}^{+}\\ensuremath{\\nu}\\overline{\\ensuremath{\\nu}}\\ensuremath{\\nu}$ decay was searched for using E949 (Brookhaven National Laboratory, USA) experimental data with an exposure of $1.70\\ifmmode\\times\\else\\texttimes\\fi{}1{0}^{12}$ stopped kaons. The data sample is dominated by the background process ${K}^{+}\\ensuremath{\\rightarrow}{\\ensuremath{\\mu}}^{+}{\\ensuremath{\\nu}}_{\\ensuremath{\\mu}}\\ensuremath{\\gamma}$. An upper limit on the decay rate $\\mathrm{\\ensuremath{\\Gamma}}({K}^{+}\\ensuremath{\\rightarrow}{\\ensuremath{\\mu}}^{+}\\ensuremath{\\nu}\\overline{\\ensuremath{\\nu}}\\ensuremath{\\nu})l2.4\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}6}\\mathrm{\\ensuremath{\\Gamma}}({K}^{+}\\ensuremath{\\rightarrow}\\text{all})$ at 90% confidence level was set assuming the standard model muon spectrum. The data are presented in such a way as to allow calculation of rates for any assumed ${\\ensuremath{\\mu}}^{+}$ spectrum.