First observation of the rare decay mode $K^+ \to \mu^+ \nu_{\mu} \mu^+ \mu^-$ in the NA62 experiment at CERN SPS

The leptonic kaon decay $K^+ \to \mu^+ \nu_{\mu} \mu^+ \mu^-$ is among the clean modes to explore the flavour structure of the Standard Model. From the theoretical point of view, Chiral Perturbation Theory allows for an accurate calculation of the branching ratio and decay distributions. Experimentally, the decay mode has never been measured and only a limit on the branching ratio has been set so far. In this work, the selection of the $K^+ \to \mu^+ \nu_{\mu} \mu^+ \mu^-$ decays is presented, the abundant background from $K^+ \to \pi^+ \pi^+ \pi^-$ decays is evaluated and a preliminary measurement of the branching ratio is obtained from a subset of the available data sample recorded by the NA62 experiment at the CERN SPS in 2017.