Theory of neutrinoless double-beta decay - a brief review

Neutrinoless double-beta decay (0νββ-decay) is a unique probe for lepton number conservation and neutrino properties. This is a process with long and interesting history with important implications for particle physics and cosmology, but its observation is still elusive. The search for the 0νββ-decay represents the new frontiers of neutrino physics, allowing one to determine the Majorana nature of neutrinos and to fix the neutrino mass scale and possible CP-violation effects, which could explain the matter-antimatter asymmetry in the Universe. At present, a complete theory is missing and, thus, to motivate and guide the experiments, the mechanism mediated by light neutrinos is mostly considered. The subject of interest is an effective mass of Majorana neutrinos, which can be deduced from the measured half-life, once this process is definitely observed. The accuracy of the determination of this quantity is mainly determined by our knowledge of the nuclear matrix elements. There is a request to evaluate them with high precision, accuracy and reliability. Recently, there is an increased interest in the resonant neutrinoless double-electron capture, which may also establish the Majorana nature of neutrinos. This possibility is considered as alternative and complementary to searches for the 0νββ-decay