Spectrometer and kinematic studies for new physics. Searches in rare K⁺ → π⁺ν(anti)ν decay at NA62 experiment at CERN

The LHC experiments have already reached their energy limitations and are starting high luminosity programs to continue direct searches for new physics signals. At the same time the importance of low energy experiments in the field of experimental particle physics is rising, as they offer a wide range of possibilities to challenge the Standard Model of particle physics and to look for indirect signs of new physics in quantum corrections and forbidden processes. The NA62 experiment at CERN is one of the most active particle experiments in the kaon physics today. It was designed specifically to study the ultra-rare 'golden decay' K⁺ → π⁺ν(anti)ν (K_{π^ν(anti)ν} ). A new result with the most precise measurement of the K branching fraction obtained from the full NA62 data set recorded in 2016-2018, has been recently presented at the ICHEP 2020 conference. The same data is used in multiple other analyses of rare kaon decays and searches for new particles from the hidden sector, also producing world leading results. NA62 is preparing for the new run expected to start in 2021. Analysis of the available data set showed that the NA62 has potential to reach the precision of the Standard Model K branching fraction prediction. Additionally, it revealed several drawbacks of the current experimental setup and indicated data analysis methods and algorithms that need improvement before the new run. This work details the author's contribution towards the K decay measurement at the NA62. The contribution is twofold, which is reflected in the organization of the presented thesis. First the analysis of the STRAW spectrometer reconstruction efficiency for single track events is presented. The efficiency is measured for π⁺, μ+ and e⁺ tracks from selected K⁺ → π⁺π⁰, K⁺ → π⁰μ⁺ and K⁺ → π⁰e⁺ν_e events, respectively. The track reconstruction efficiency for all three types of charged tracks is measured to be above 95% in 2016 and above 98% in 2017 and 2018 data sets when all reconstructed candidates are considered. The efficiency for tracks reconstructed using hits from all four STRAW chambers is above 92% in 2016 and above 94% in 2017 and 2018. The reconstruction efficiency measured on + tracks was used in the K analysis of 2017 and 2018 data sets. Secondly, one of the critical parts of the K analysis - the matching between the kaon and pion tracks - is studied. A new matching algorithm based on hypothesis testing using likelihood is proposed. Performance of the algorithm is studied with fully reconstructed K⁺ → π⁺π⁺π^- event candidates and decrease in mismatch rate of up to 80% is observed. Additionally, a part of the main K analysis was implemented independently in this work to study the effect of the proposed matching algorithm on the reconstruction tails of the two dominant kaon decay background sources, K⁺ → π⁺π⁰ and K⁺ → μ⁺ν, in the 2017 data. The new algorithm significantly improves the resolution tails of the kinematic variable m²_miss and thus reduces the K⁺ → π⁺π⁰ background by up to 30 %, leading to an increased signal-over-background ratio with a single event sensitivity comparable to the main analysis. After the planned upgrade of the NA62 detector system, the new matching algorithm is intended to be used in the main K analysis in the next run. (Author)