Attenuation of the scintillation light in liquid argon and investigation of the double beta decay of ${}^{76}$Ge into excited states of ${}^{76}$Se in the GERDA experiment

The GERDA experiment searches for the neutrinoless double beta (0𝜈𝛽𝛽) decay of ${}^{76}$Ge. The observation of this decay would prove the Majorana character of the neutrino, i.e. that it is its own antiparticle. This would clarify the question which neutrino mass ordering is realized in nature and give a hint of the effective Majorana neutrino mass. Furthermore, the existence of the 0𝜈𝛽𝛽 decay would imply the violation of lepton number conservation which is a key feature in some theories explaining the asymmetry of matter and antimatter in the universe. The effective Majorana neutrino mass is connected with the half life of the 0𝜈𝛽𝛽 decay via a nuclear matrix element (NME), which is predicted by various theoretical models that are afflicted by large uncertainties. The accuracy of the different NMEs and their internal model assumptions can be increased by considering experimental investigations. While the NMEs for the 0𝜈𝛽𝛽 decay and the neutrino accompanied double beta (2𝜈𝛽𝛽) decay are numerically different, they rely on similar model assumptions. Thus, experimental constraints can be given by the 2𝜈𝛽𝛽 decay into the ground state, which has been already measured by GERDA with unprecedented precision for ${}^{76}$Ge, but also by the investigation of the 2𝜈𝛽𝛽 decay into excited states, which has not yet been observed for ${}^{76}$Ge. GERDA operates enriched germanium detectors in liquid argon (LAr) which serves as an additional background veto using the scintillation light that is created when energy is deposited in LAr. The signal signature of the decay into excited states can be enhanced with the application of the LAr veto, however, for that the efficiency of the LAr veto needs to be determined. One of the key parameters of the LAr efficiency is the attenuation of the scintillation light in LAr, which is dependent on the impurity composition and concentration in LAr. Therefore, the attenuation length of the scintillation light in LAr has been measured in GERDA with a dedicated setup in the course of this work. The analysis of the acquired data required intense computer simulations in order to describe the background for the measurement sufficiently. This also involved the measurement of the steel reflectivity in the visible and the UV region, where LAr scintillates. Therewith, the search for excited states has been performed in this work for the data accumulated in GERDA Phase I, Phase II and Phase II+ including the LAr veto for the latter two data sets. New limits have been set on the investigated excited states decay modes and some of the corresponding theoretical half life predictions could be disfavored, i.e. the underlying NMEs models can be constrained. The successor experiment LEGEND will continue searching for the 0𝜈𝛽𝛽 decay of ${}^{76}$Ge using more germanium detectors together with an improved LAr veto. The investigation of the decay of ${}^{76}$Ge into excited states will also be further pursued in LEGEND.