Spectrometer and Kinematic Studies for New Physics Searches in Rare $K^+ \to \pi^+ \nu \bar\nu$ Decay at NA62 Experiment at CERN

The main focus of the presented thesis is twofold: First the STRAW spectrometer single track reconstruction efficiency evaluation carried out with $K^+ \to \pi^+ \pi^0$, $K^+ \to \pi^0 \mu^+ \nu$ and $K^+ \to \pi^0 e^+ \nu$ samples on the full 2016-2018 NA62 data set as well as on simulated decays is summarized. Secondly a new algorithm for matching kaon candidates with $\pi^+$ tracks based on likelihood hypothesis testing is proposed. Performance of the algorithm is studied with fully reconstructed $K^+ \to \pi^+ \pi^+ \pi^-$ event candidates and results of a part of the $K^+ \to \pi^+ \nu \overline{\nu}$ analysis with the new matching algorithm with the 2017 data sample are presented.