Search and background studies for neutrinoless double-beta decay of Ge-76 and signals of new physics in data collected by the GERDA and LEGEND experiments

Neutrinos, one of the the most elusive particles in the Standard Model of particle physics, could either be Dirac or Majorana in nature, leading to distinct scenarios. The golden channel to explore their unknown nature is the neutrinoless double-beta decay (0νββ). This ultra-rare process, never observed to this date, would be possible only in the scenario of a Majorana neutrino where neutrinos coincide with their antiparticles. The LEGEND Project aims at answering at this question in a time frame of O(10) yr in two separate phases. The first phase, LEGEND-200, started operations at Laboratori Nazionali del Gran Sasso of INFN in 2023 with 142.38 kg of germanium detectors enriched in 76Ge and plans to install more in the coming months. The main focus of this dissertation consisted in the characterization of the first year of LEGEND-200 data taking, starting from the monitoring and quality assessment of acquired data, ending with an investigation of the residual background. A new estimation of the 76Ge 0νββ decay half-life was extracted, leading to a combined value of T^{0ν}_{1/2}>1.8×10^{26} yr when including data coming from GERDA Phase (I,II), MJD and LEGEND-200. The second part of this dissertation was devoted to an additional work carried on within the GERDA experiment. A search for full energy depositions from bosonic keV-scale dark matter candidates of masses between 65 keV and 1021 keV was performed. This analysis considered the absorption of dark matter candidates, including for the first time in a semiconductor experiment the dark Compton scattering interaction process. With a total exposure of 105.5 kg·yr, no evidence for a signal above the background was observed. The resulting exclusion limits deduced via a Bayesian study are among the most stringent direct constraints in the 140-1021 keV mass range. As an example, at a mass of 150 keV the dimensionless coupling of dark photons and axion-like particles to electrons was constrained to α′/α<8.7×10^{−24} and g_{ae}<3.3×10^{−12} at 90% CI, respectively. Additionally, a search for peak-like signals from beyond the Standard Model decays of nucleons and electrons was performed. We found for the inclusive decay of a single neutron in 76Ge a lower lifetime limit of τ_{n}>1.5×10^{24} yr and for a proton τ_{p}>1.3×10^{24} yr (90% CI). For the semi-invisible electron decay e^{-}→ν_{e}γ, a lower limit of τ_{e}>5.4×10^{25} yr at 90% CI was derived.