Shell model calculations of double-beta decay lifetimes of $^{48}$Ca

Recent results from neutrino oscillation experiments have convincingly demonstrated that neutrinos have mass and they can mix. The neutrinoless double beta ($0\nu\beta\beta$) decay is the most sensitive process to determine the absolute scale of the neutrino masses, and the only one that can distinguish whether neutrino is a Dirac or a Majorana particle. A key ingredient for extracting the absolute neutrino masses from $0\nu\beta\beta$ decay experiments is a precise knowledge of the nuclear matrix elements (NME) for this process. We developed a new strategy for computing the NME for the two-neutrino ($2\nu\beta\beta$) decay mode of Ca48, using GXPF1 and GXPF1A interactions. We reproduce the experimental value of the half-life for the g.s. to g.s. transitions, and we predict the lifetime for the g.s. to the first $2^+$ excited state. We also developed a new shell model approach for computing the NME for the $0\nu\beta\beta$ mode and used it in the case of $^{48}$Ca. The dependence of the results on short range correlations, the neutrino energy, and on the effective interaction will be discussed.