Study of the extremely rare decay $K^+ \to \pi^+ \nu \bar\nu$ with the NA62 experiment at CERN

The decay $K^+ \to \pi^+ \nu \bar\nu$ has one of the most precisely predicted branching ratio at the level of $10^{−10}$. It is forbidden at the tree level, which makes it sensitive to the effects of new physics. The NA62 experiment at the CERN SPS aims to measure the branching ratio of the $K^+ \to \pi^+ \nu \bar\nu$ using a unique decay-in-flight technique. NA62 took data so far in 2016-2018. The statistics acquired in 2016 allowed to reach Standard Model sensitivity for $K^+ \to \pi^+ \nu \bar\nu$. Owing to the statistics collected in 2017, NA62 surpasses the present best sensitivity. In he scope of this thesis, the preliminary result obtained from 2017 data sample is reported.