Results on $\beta\beta$ decay with emission of two neutrinos or Majorons in $^{76}$Ge from GERDA Phase I

A search for neutrinoless \(\beta \beta \) decay processes accompanied with Majoron emission has been performed using data collected during Phase I of the GERmanium Detector Array (GERDA) experiment at the Laboratori Nazionali del Gran Sasso of INFN (Italy). Processes with spectral indices \(n = 1, 2, 3, 7\) were searched for. No signals were found and lower limits of the order of 10\(^{23}\) yr on their half-lives were derived, yielding substantially improved results compared to previous experiments with \(^{76}\)Ge. A new result for the half-life of the neutrino-accompanied \(\beta \beta \) decay of \(^{76}\)Ge with significantly reduced uncertainties is also given, resulting in \(T^{2\nu }_{1/2} = (1.926 \pm 0.094)\times 10^{21}\) yr.