$K^{+}\rightarrow \mu^{+}\nu_{\mu} \nu \bar \nu$ and $K^{+}\rightarrow   e^{+}\nu_{e} \nu \bar \nu$ decays within the Chiral Perturbation Theory
  Decays $K^{+} \rightarrow \mu^{+}\nu_{\mu} \nu \bar \nu$ and $K^{+}\rightarrow e^{+}\nu_{e} \nu \bar \nu$ are examined to the leading order in momenta in the framework of Chiral Perturbation Theory. Predictions of the Standard Model for the muon and electron differential energy spectra and branching ratios of $K_{\mu 3 \nu}$ and $K_{e 3 \nu}$ are presented. 
D. Gorbunov and A. Mitrofanov
hep-ph hep-ex