Measurement of the angular distributions of pions in the exclusive pion pair production with forward proton measured with ALFA detector in the ATLAS experiment

This thesis is devoted to the analysis of angular distributions of pion pairs produced in the process of central exclusive production, measured in the ATLAS experiment, with forward-scattered protons detected using the ALFA detector. The analysis was performed using data collected during special accelerator running periods in 2015 and 2018, at a center-of-mass energy of $\sqrt{s} = 13$~TeV. The analysed process belongs to the class of diffractive processes, which are characterized by the scattering of the interacting particles (protons) at small angles. When the particles produced in the interaction, referred to as the central state, are clearly separated from the beam particles by a so called rapidity gap, the process is referred to as central exclusive production. In proton-proton collisions at the LHC, this process proceeds predominantly via double exchange of a colorless trajectory known as the Pomeron. The central exclusive production is particularly useful due to the possibility of studying central states with well defined quantum numbers and a reduced background. The analysis of angular distributions of particles in the central state provides information on the spin structure of the central system. In this work, an event selection was performed and the datasets from 2015 and 2018 were harmonized. In particular, the effects of trigger prescaling as well as corrections related to the efficiencies of the ID and TRT detectors were taken into account. The main objective of the thesis was to analyze the angular distributions of pion pairs in the Gottfried-Jackson frame through a likelihood fit of spherical harmonics, whose moments were used for a~qualitative partial wave analysis of the pion pair production process. Contributions from S and D wave components were observed, together with angular structures associated with the presence of the $f_{0}(980)$ and $f_{2}(1270)$ resonances. The steps taken constitute an introduction to a quantitative partial wave analysis.