Neutrinoless Double β\beta-Decay: Status and Future

A brief summary of the status of neutrino masses, mixing and oscillations is presented. Neutrinoless double $\beta$-decay is considered. Predictions for the effective Majorana mass are reviewed. A possible test of the calculations of nuclear matrix elements of the $0\nu\beta\beta$-decay is proposed.Comment: A report at the International conference ``Non-Accelerator New Physics'' NANP05 Dubna, Russia, June 20-25, 200

Neutrino Physics at the Turn of the Millenium

Recent solar & atmospheric nu-data strongly indicate need for physics beyond the Standard Model. I review the ways of reconciling them in terms of 3-nu oscillations. Though not implied by data, bi-maximal nu-mixing models emerge as a possibility. SUSY with broken R-parity provides an attractive way to incorporate it, opening the possibility of testing nu-anomalies at high- energy colliders such as the LHC or at the upcoming long-baseline or nu- factory experiments. Reconciling, in addition, the LSND hint requires a fourth, light sterile neutrino, nus. The simplest are the most symmetric scenarios, in which 2 of the 4 neutrinos are maximally-mixed and lie at the LSND scale, while the others are at the solar scale. The lightness of nus, the nearly maximal atmospheric mixing, and the solar/atmospheric splittings all follow naturally from the assumed lepton-number symmetry and its breaking. These basic schemes can be distinguished at neutral-current-sensitive solar & atmospheric neutrino experiments such as SNO. However underground experiments have not yet proven neutrino masses, as there are many alternatives. For example flavour changing interactions can play an important role in the explanation of solar and contained atmospheric data and could be tested e.g through \mu \to e + \gamma, \mu-e conversion in nuclei, unaccompanied by neutrino-less double beta decay. Conversely, a short-lived numu might play a role in the explanation of the atmospheric data. Finally, in the presence of a nus, a long-lived heavy nutau could delay the time at which the matter and radiation contributions to the energy density of the Universe become equal, reducing density fluctuations on smaller scales, thus saving the standard CDM scenario, while the light nue, numu and nus would explain the solar & atmospheric data.Comment: Invited talk at 2nd International Conference on Non-Accelerator New Physics (NANP-99), Dubna, June 28 - July 3, 199