Shell model analysis of competing contributions to the double-βdecay of48Ca

Abstract

Background: Neutrinoless double-$\ensuremath{\beta}$ decay, if observed, would reveal physics beyond the standard model of particle physics; namely, it would prove that neutrinos are Majorana fermions and that the lepton number is not conserved.Purpose: The analysis of the results of neutrinoless double-$\ensuremath{\beta}$ decay observations requires an accurate knowledge of several nuclear matrix elements (NME) for different mechanisms that may contribute to the decay. We provide a complete analysis of these NME for the decay of the ground state (g.s.) of ${}^{48}$Ca to the g.s. ${0}_{1}^{+}$ and first excited ${0}_{2}^{+}$ state of ${}^{48}$Ti.Method: For the analysis we used the nuclear shell model with effective two-body interactions that were fine-tuned to describe the low-energy spectroscopy of $pf$-shell nuclei. We checked our model by calculating the two-neutrino transition probability to the g.s. of ${}^{48}$Ti. We also make predictions for the transition to the first excited ${0}_{2}^{+}$ state of ${}^{48}$Ti.Results: We present results for all NME relevant for the neutrinoless transitions to the ${0}_{1}^{+}$ and ${0}_{2}^{+}$ states, and using the lower experimental limit for the g.s. to g.s. half-life, we extract upper limits for the neutrino physics parameters.Conclusions: We provide accurate NME for the two-neutrino and neutrinoless double-$\ensuremath{\beta}$ decay transitions in the $A=48$ system, which can be further used to analyze the experimental results of double-$\ensuremath{\beta}$ decay experiments when they become available.