Study of Lepton Number Conserving and Non-Conserving Processes Using GERDA Phase I Data

The GERmanium Detector Array (GERDA) experiment, located underground at the INFN Laboratori Nazionali del Gran Sasso (LNGS) in Italy, uses high-purity germanium detectors to search for neutrinoless double beta decay (0νββ) of Ge-76. The first phase of the experiment lasted from November 2011 to May 2013 and collected data with a total exposure of 21.6 kg · yr. In this thesis, a thorough analysis of these data was performed. A background model was developed to decompose the observed energy spectrum in its individual contributions. The region around the Q-value of 0νββ, Qββ , at 2039 keV was studied in great detail. As main contributions to the background in this region, alpha and beta decays of the U-238 chain, beta decays of the Th-232 chain, and beta decays of K-42 were identified. It was shown that the background around Qββ can be approximated with a flat distribution. Neutrino accompanied double beta decay (2νββ) is a lepton number conserving process allowed by the Standard Model. Due to the low background in the experiment, in the region dominated by 2νββ a signal-to-background ratio of 3 : 1 could be reached. This allowed to measure the half-life of the decay with a precision unprecedented by previous experiments, T1/2^2ν = (1.96 ± 0.13) · 10^21 yr. Several beyond-Standard Model theories predict neutrinoless double beta decay with majoron emission (0νββχ(χ)). Depending on the theory, this process can be lepton number violating or lepton number conserving. A search in the GERDA Phase I data gave no indication of contributions to the observed energy spectra for any of the majoron models. The lower limit on the half-life for the ordinary majoron model (spectral index n = 1) was determined to be T1/2^0νχ > 4.15 · 10^23 yr (90 % quantile). This limit and the limits derived for the other majoron modes constitute the most stringent limits on 0νββχ(χ) of Ge-76 measured to date. The primary scope of the GERDA experiment was the search for 0νββ of Ge-76. This lepton number violating decay is expected by extensions of the Standard Model. The observation of 0νββ would be the proof that the neutrino has a non-vanishing Majorona mass component. The analysis of the GERDA Phase I data did not reveal any hint for the presence of a signal from 0νββ. A lower limit on the half-life was derived, T1/2^0ν > 1.83 · 10^25 yr (90 % quantile).