Theoretical investigation of the dependence of double beta decay tracks in a Ge detector on particle and nuclear physics parameters and separation from gamma ray events

Abstract

The sizes of tracks of events of neutrinoless double-beta decay in a Germanium detector depend on particle physics and nuclear physics parameters such as neutrino mass, right-handed current parameters, etc., and nuclear matrix elements. In this paper for the first time Monte Carlo simulations of neutrino-accompanied ($2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) and neutrinoless double-beta decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) events, and of various kinds of background processes such as multiple and other $\ensuremath{\gamma}$ interactions are reported for a Ge detector. The time history of the evolution of the individual events is followed and the sizes of the events (partial volumes in the detector inside which the energy of the event is released) are investigated. Effects of the angular correlations of the two electrons in $\ensuremath{\beta}\ensuremath{\beta}$ decay, which again depend on the above nuclear and (for $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay) on particle physics parameters, are taken into account and have been calculated for this purpose for the first time on basis of the experimental half-life of $^{76}\mathrm{G}\mathrm{e}$ and of realistic nuclear matrix elements. The sizes determine, together with the location of the events in the detector, the pulse shapes to be observed. It is shown for $\ensuremath{\beta}\ensuremath{\beta}$ decay of $^{76}\mathrm{G}\mathrm{e}$, that $\ensuremath{\beta}\ensuremath{\beta}$ events should be selectable with high efficiency by rejecting large size (high multiplicity) $\ensuremath{\gamma}$ events. Double-escape peaks of similar energy of $\ensuremath{\gamma}$ lines show concerning their sizes similar behavior as $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ events, and in that sense can be of some use for corresponding 'calibration' of pulse shapes of the detector. The possibility to distinguish $\ensuremath{\beta}\ensuremath{\beta}$ events from $\ensuremath{\gamma}$ events is found to be essentially independent of the particle physics parameters of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ process. A brief outlook is given on the potential of future experiments with respect to determination of the particle physics parameters $⟨{m}_{\ensuremath{\nu}}⟩,⟨\ensuremath{\lambda}⟩,⟨\ensuremath{\eta}⟩$.