Measurement of $Br(K^+ \to \pi^+ \nu \bar\nu)$ with the NA62 experiment at CERN

The ultra-rare decay $K^+ \to \pi^+ \nu \bar\nu$, with a very precisely predicted branching ratio of less than $10^{-10}$, is one of the best candidates to reveal indirect effects of new physics at the highest mass scales. The NA62 experiment at CERN SPS is designed to measure $Br(K^+ \to \pi^+ \nu \bar\nu)$ with a decay-in-flight technique, novel for this channel. NA62 took data in 2016, 2017 and 2018. Statistics collected in 2016 and 2017 allows NA62 to reach the Standard Model sensitivity for the $K^+ \to \pi^+ \nu \bar\nu$ search. The analysis of the 2018 data, topic of this PhD thesis, leads to the most precise preliminary measurement ever performed combining the full data set: $Br(K^+ \to \pi^+ \nu \bar\nu) = (1.10^{+0.40}_{-0.35 \; stat} \pm 0.03_{syst}) \cdot 10^{-10}$, with $3.5 \sigma$ significance for the process observation. The context of the measurement is presented, the details of the data analysis are described, with particular emphasis on the improvements achieved in the experimental sensitivity, and the prospects are illustrated.