Analysis of the rare decay $K^+ \to \mu^+ \nu \mu^+ \mu^−$

The main goal of the NA62 experiment at CERN is a study of the ultra rare decay $K \to \pi \nu \bar{\nu}$. The collected statistics allows to analyse other rare decays, in particular, $K^+ \to \mu^+ \nu \mu^+ \mu^-$. Rare decays make it possible to experimentally investigate one of the aspects of the Standard Model, the chiral perturbative theory (ChPT). ChPT predicts decay probability of $K^+ \to \mu^+ \nu \mu^+ \mu^-: 1.35 \times 10^{-8}$. This decay channel is also of great interest due to the fact, that it was not experimentally observed, there is only an upper limit $< 4.1$ x $10^{-7}$ CL 90%. We present the research methodology, the first results of signal selection and the study of the background sources for the decay.