Majorana neutrinos, neutrino mass spectrum, CP violation, and neutrinolessdouble beta decay: The three-neutrino mixing case - art. no. 053010

Assuming three-neutrino mixing and massive Majorana neutrinos, we study the implications of the neutrino oscillation solutions of the solar and atmosp heric neutrino problems and of the results of the CHOOZ experiment for the predictions of the effective Majorana mass in neutrinoless double-beta [(be ta beta)(0v)] decay, \ <m > \. The general case of CP nonconservation is in vestigated. The predicted values of \ <m > \, which determine the magnitude of the (beta beta)(0v)-decay rate, depend strongly on the type of neutrino mass spectrum and on the solution of the solar neutrino problem, as well a s on the values of the two Majorana CP-violating phases, present in the lep ton mixing matrix. We find that (i) \ <m > \ less than or similar to0.02 eV for a hierarchical neutrino mass spectrum, (ii) in \ <m > \ less than or s imilar to 0.09 eV if the spectrum is of the inverted hierarchy type, and (i ii) \ <m > \ less than or equal to m in the case of three quasidegenerate n eutrinos, m>0 being the common neutrino mass scale which is limited by the bounds from the H-3 beta -decay experiments, m<22.5 eV. The indicated maxim al values of <vertical bar><m > \ are reached in cases (i), (ii), and (iii) , respectively, for the large mixing angle (LMA) MSW solution, the small mi xing angle (SMA) MSW solution, and for all current solutions of the solar n eutrino problem. If CP invariance holds, \ <m > \ is very sensitive to the values of the relative CP parities of the massive Majorana neutrinos. The c ases of neutrino mass spectra which interpolate between the hierarchical or inverted hierarchy type and the quasidegenerate one are also studied. The observation of the (beta beta)(0v) decay with a rate corresponding to \ <m > \ greater than or similar to 0.02 can provide unique information on the n eutrino mass spectrum. Combined with information on the lightest neutrino m ass or the type of neutrino mass spectrum, it can give also information on the CP violation in the lepton sector and, if CP invariance holds, on the r elative CP parities of the massive Majorana neutrinos.