First measurement of the $K^{+} \rightarrow \pi^{+}\nu\overline{\nu}$ decay with the NA62 experiment at CERN

The decay $K^{+} \rightarrow \pi^{+}\nu\overline{\nu}$ with a very precisely predicted branching ratio of $8.4\times 10^{-10}$ 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 the branching ratio of the $K^{+} \rightarrow \pi^{+}\nu\overline{\nu}$ decay with a decay-in-flight technique, novel for this channel. The search for the $K^{+} \rightarrow \pi^{+}\nu\overline{\nu}$ decay is presented in this thesis, based on a sample of about $10^{11}$ $K^+$ decays collected in 2016 by the NA62 experiment. The Single Event Sensitivity is found to be $3\times 10^{-10}$ corresponding to about 0.26 $K^{+} \rightarrow \pi^{+}\nu\overline{\nu}$̄ and 0.15 background events expected. The analysis has revealed one candidate event compatible with the expectations. Interpreting the candidate as background leads to a 95$\%$ CL upper limit of $1.4\times10^{-9}$ on the $K^{+} \rightarrow \pi^{+}\nu\overline{\nu}$ branching ratio. Prospects for future developments are also reviewed.