Abstract
The fundamental importance of searching for neutrinoless double-beta decay (0νββ-decay) is widely recognized. Observation of the decay would tell us that the total lepton number is not conserved and that, consequently, neutrinos are massive Majorana fermions. A brief history of the double-beta decay is presented. The 0νββ-decay is discussed in context of neutrino oscillation data. The perspectives of the experimental 0νββ-decay searches are analyzed. The importance of reliable determination of the 0νββ-decay nuclear matrix elements is pointed out. The problem of distinguishing of the light-neutrino exchange, heavy-neutrino exchange and the trilinear R-parity breaking supersymmetric (\(\not R_p \) SUSY) mechanisms of the 0νββ-decay is addressed. Further, the process of resonant neutrinoless double-electron capture (0νɛɛ) is revisited. Arguments are presented that an experimental search for the 0νɛɛ might be feasible.
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