First observation of the rare decay $K^{+}\rightarrow\mu^{+}\nu_\mu\mu^{+}\mu^{-}$ at the NA62 experiment

The first observation of the rare decay $K^{+}\rightarrow\mu^{+}\nu_\mu\mu^{+}\mu^{-}$ using data collected by the NA62 Experiment in 2017 and 2018 is presented in this thesis. The $K^{+}\rightarrow\mu^{+}\nu_\mu\mu^{+}\mu^{-}$ branching ratio is measured using the $K^+\rightarrow\pi^+\mu^+\mu^-$ process as a normalisation channel. The number of observed data candidates is $1832$, with a background contamination of $168\pm9$. The analysis yields $\mathfrak{B}(K^{+}\rightarrow\mu^{+}\nu_\mu\mu^{+}\mu^{-}) = (1.307 \pm 0.034_{\mathrm{Stat}} \pm 0.025_{\mathrm{Syst}} \pm 0.012_{\mathrm{Ext}})\times 10^{-8}$, including a complete treatment of relevant systematic effects. The complete software package for the ANTI-0 detector, added to the NA62 setup in 2021, was developed by the author within the NA62 software framework and is described in detail. The software tools allowing for short and long-term verification of ANTI-0 data quality are presented, with their output used to summarise the commissioning and performance of the detector in the 2021, 2022 and 2023 NA62 data-taking campaigns.