Observation of the $K^+\to\pi^+\nu\bar\nu$ decay and measurement of its branching ratio with the NA62 experiment

The ultra-rare $K^+\to\pi^+\nu\bar\nu$ decay is a golden mode to test the Standard Model: its branching ratio is predicted very precisely, and it is highly sensitive to indirect effects of physics beyond the Standard Model. The NA62 experiment at CERN has been designed to measure $\operatorname{BR}(K^+\to\pi^+\nu\bar\nu)$, and provided the most precise measurement of this branching ratio using data collected in 2016–2018. In this PhD thesis the analysis of data collected by NA62 in 2021–2022 is reported. This dataset was collected after upgrades to the experimental apparatus, and at a higher instantaneous beam intensity with respect to the previous 2016–2018 data taking. Combining NA62 data collected between 2016 and 2022, the first observation of the $K^+\to\pi^+\nu\bar\nu$ decay with a significance exceeding $5\sigma$ is reported, and a measurement of $\operatorname{BR}(K^+\to\pi^+\nu\bar\nu) = (13.0^{+3.3}_{-3.0}) \times 10^{-11}$ is obtained. To date, this is the smallest branching ratio ever measured with a signal significance above $5\sigma$.